library(tidyverse)
library(ggplot2)
library(stats)
library(alr4)
library(smss)
knitr::opts_chunk$set(echo = TRUE)603Homework_Saisrinivas_Ambatipudi
Question 1:
United Nations (Data file: UN11in alr4) The data in the file UN11 contains several variables, including ppgdp, the gross national product per person in U.S. dollars, and fertility, the birth rate per 1000 females, both from the year 2009. The data are for 199 localities, mostly UN member countries, but also other areas such as Hong Kong that are not independent countries. The data were collected from the United Nations (2011). We will study the dependence of fertility on ppgdp. (a) Identify the predictor and the response. (b) Draw the scatterplot of fertility on the vertical axis versus ppgdp on the horizontal axis and summarize the information in this graph. Does a straight-line mean function seem to be plausible for a summary of this graph? (c) Draw the scatterplot of log(fertility) versus log(ppgdp) using natural logarithms. Does the simple linear regression model seem plausible for a summary of this graph? If you use a different base of logarithms, the shape of the graph won’t change, but the values on the axes will change.
Answer:
(a)
The dependence of fertility is examined in this study. Thus, the predictor (independent variable) is ppgdp (gross national product per person), and the response (dependent variable) is fertility (birth rate per 1000 females).
(b)
data(UN11)
UN11 region group fertility ppgdp
Afghanistan Asia other 5.968000 499.0
Albania Europe other 1.525000 3677.2
Algeria Africa africa 2.142000 4473.0
Angola Africa africa 5.135000 4321.9
Anguilla Caribbean other 2.000000 13750.1
Argentina Latin Amer other 2.172000 9162.1
Armenia Asia other 1.735000 3030.7
Aruba Caribbean other 1.671000 22851.5
Australia Oceania oecd 1.949000 57118.9
Austria Europe oecd 1.346000 45158.8
Azerbaijan Asia other 2.148000 5637.6
Bahamas Caribbean other 1.877000 22461.6
Bahrain Asia other 2.430000 18184.1
Bangladesh Asia other 2.157000 670.4
Barbados Caribbean other 1.575000 14497.3
Belarus Europe other 1.479000 5702.0
Belgium Europe oecd 1.835000 43814.8
Belize Latin Amer other 2.679000 4495.8
Benin Africa africa 5.078000 741.1
Bermuda Caribbean other 1.760000 92624.7
Bhutan Asia other 2.258000 2047.2
Bolivia Latin Amer other 3.229000 1977.9
Bosnia and Herzegovina Europe other 1.134000 4477.7
Botswana Africa africa 2.617000 7402.9
Brazil Latin Amer other 1.800000 10715.6
Brunei Darussalam Asia other 1.984000 32647.6
Bulgaria Europe other 1.546000 6365.1
Burkina Faso Africa africa 5.750000 519.7
Burundi Africa africa 4.051000 176.6
Cambodia Asia other 2.422000 797.2
Cameroon Africa africa 4.287000 1206.6
Canada North America oecd 1.691000 46360.9
Cape Verde Africa africa 2.279000 3244.0
Cayman Islands Caribbean other 1.600000 57047.9
Central African Republic Africa africa 4.423000 450.8
Chad Africa africa 5.737000 727.4
Chile Latin Amer oecd 1.832000 11887.7
China Asia other 1.559000 4354.0
Colombia Latin Amer other 2.293000 6222.8
Comoros Africa africa 4.742000 736.6
Congo Africa africa 4.442000 2665.1
Cook Islands Oceania other 2.530806 12212.1
Costa Rica Latin Amer other 1.812000 7703.8
Cote dIvoire Africa africa 4.224000 1154.1
Croatia Europe other 1.501000 13819.5
Cuba Caribbean other 1.451000 5704.4
Cyprus Asia other 1.458000 28364.3
Czech Republic Europe oecd 1.501000 18838.8
Democratic Republic of the Congo Africa africa 5.485000 200.6
Denmark Europe oecd 1.885000 55830.2
Djibouti Africa africa 3.589000 1282.6
Dominica Caribbean other 3.000000 7020.8
Dominican Republic Caribbean other 2.490000 5195.4
East Timor Asia other 5.918000 706.1
Ecuador Latin Amer other 2.393000 4072.6
Egypt Africa africa 2.636000 2653.7
El Salvador Latin Amer other 2.171000 3425.6
Equatorial Guinea Africa africa 4.980000 16852.4
Eritrea Africa africa 4.243000 429.1
Estonia Europe oecd 1.702000 14135.4
Ethiopia Africa africa 3.848000 324.6
Fiji Oceania other 2.602000 3545.7
Finland Europe oecd 1.875000 44501.7
France Europe oecd 1.987000 39545.9
French Polynesia Oceania other 2.033000 24669.0
Gabon Africa africa 3.195000 12468.8
Gambia Africa africa 4.689000 579.1
Georgia Asia other 1.528000 2680.3
Germany Europe oecd 1.457000 39857.1
Ghana Africa africa 3.988000 1333.2
Greece Europe oecd 1.540000 26503.8
Greenland NorthAtlantic other 2.217000 35292.7
Grenada Caribbean other 2.171000 7429.0
Guatemala Latin Amer other 3.840000 2882.3
Guinea Africa africa 5.032000 427.5
Guinea-Bissau Africa africa 4.877000 539.4
Guyana Latin Amer other 2.190000 2996.0
Haiti Caribbean other 3.159000 612.7
Honduras Latin Amer other 2.996000 2026.2
Hong Kong Asia other 1.137000 31823.7
Hungary Europe oecd 1.430000 12884.0
Iceland Europe other 2.098000 39278.0
India Asia other 2.538000 1406.4
Indonesia Asia other 2.055000 2949.3
Iran Asia other 1.587000 5227.1
Iraq Asia other 4.535000 888.5
Ireland Europe oecd 2.097000 46220.3
Israel Asia oecd 2.909000 29311.6
Italy Europe oecd 1.476000 33877.1
Jamaica Caribbean other 2.262000 4899.0
Japan Asia oecd 1.418000 43140.9
Jordan Asia other 2.889000 4445.3
Kazakhstan Asia other 2.481000 9166.7
Kenya Africa africa 4.623000 801.8
Kiribati Oceania other 3.500000 1468.2
Kuwait Asia other 2.251000 45430.4
Kyrgyzstan Asia other 2.621000 865.4
Laos Asia other 2.543000 1047.6
Latvia Europe other 1.506000 10663.0
Lebanon Asia other 1.764000 9283.7
Lesotho Africa africa 3.051000 980.7
Liberia Africa africa 5.038000 218.6
Libya Africa africa 2.410000 11320.8
Lithuania Europe other 1.495000 10975.5
Luxembourg Europe oecd 1.683000 105095.4
Macao Asia other 1.163000 49990.2
Madagascar Africa africa 4.493000 421.9
Malawi Africa africa 5.968000 357.4
Malaysia Asia other 2.572000 8372.8
Maldives Asia other 1.668000 4684.5
Mali Africa africa 6.117000 598.8
Malta Europe other 1.284000 19599.2
Marshall Islands Oceania other 4.384466 3069.4
Mauritania Africa africa 4.361000 1131.1
Mauritius Africa africa 1.590000 7488.3
Mexico Latin Amer oecd 2.227000 9100.7
Micronesia Oceania other 3.307000 2678.2
Moldova Europe other 1.450000 1625.8
Mongolia Asia other 2.446000 2246.7
Montenegro Europe other 1.630000 6509.8
Morocco Africa africa 2.183000 2865.0
Mozambique Africa africa 4.713000 407.5
Myanmar Asia other 1.939000 876.2
Namibia Africa africa 3.055000 5124.7
Nauru Oceania other 3.300000 6190.1
Nepal Asia other 2.587000 534.7
Neth Antilles Caribbean other 1.900000 20321.1
Netherlands Europe oecd 1.794000 46909.7
New Caledonia Oceania other 2.091000 35319.5
New Zealand Oceania oecd 2.135000 32372.1
Nicaragua Latin Amer other 2.500000 1131.9
Niger Africa africa 6.925000 357.7
Nigeria Africa africa 5.431000 1239.8
North Korea Asia other 1.988000 504.0
Norway Europe oecd 1.948000 84588.7
Oman Asia other 2.146000 20791.0
Pakistan Asia other 3.201000 1003.2
Palau Oceania other 2.000000 10821.8
Palestinian Territory Asia other 4.270000 1819.5
Panama Latin Amer other 2.409000 7614.0
Papua New Guinea Oceania other 3.799000 1428.4
Paraguay Latin Amer other 2.858000 2771.1
Peru Latin Amer other 2.410000 5410.7
Philippines Asia other 3.050000 2140.1
Poland Europe oecd 1.415000 12263.2
Portugal Europe oecd 1.312000 21437.6
Puerto Rico Caribbean other 1.757000 26461.0
Qatar Asia other 2.204000 72397.9
Republic of Korea Asia other 1.389000 21052.2
Romania Europe other 1.428000 7522.4
Russian Federation Europe other 1.529000 10351.4
Rwanda Africa africa 5.282000 532.3
Saint Lucia Caribbean other 1.907000 6677.1
Samoa Oceania other 3.763000 3343.3
Sao Tome and Principe Africa africa 3.488000 1283.3
Saudi Arabia Asia other 2.639000 15835.9
Senegal Africa africa 4.605000 1032.7
Serbia Europe other 1.562000 5123.2
Seychelles Africa africa 2.340000 11450.6
Sierra Leone Africa africa 4.728000 351.7
Singapore Asia other 1.367000 43783.1
Slovakia Europe oecd 1.372000 15976.0
Slovenia Europe oecd 1.477000 23109.8
Solomon Islands Oceania other 4.041000 1193.5
Somalia Africa africa 6.283000 114.8
South Africa Africa africa 2.383000 7254.8
Spain Europe other 1.504000 30542.8
Sri Lanka Asia other 2.235000 2375.3
St Vincent and Grenadines Caribbean other 1.995000 6171.7
Sudan Africa africa 4.225000 1824.9
Suriname Latin Amer other 2.266000 7018.0
Swaziland Africa africa 3.174000 3311.2
Sweden Europe oecd 1.925000 48906.2
Switzerland Europe oecd 1.536000 68880.2
Syria Asia other 2.772000 2931.5
Tajikistan Asia other 3.162000 816.0
Tanzania Africa africa 5.499000 516.0
TFYR Macedonia Europe other 1.397000 4434.5
Thailand Asia other 1.528000 4612.8
Togo Africa africa 3.864000 524.6
Tonga Oceania other 3.783000 3543.1
Trinidad and Tobago Caribbean other 1.632000 15205.1
Tunisia Africa africa 1.909000 4222.1
Turkey Asia oecd 2.022000 10095.1
Turkmenistan Asia other 2.316000 4587.5
Tuvalu Oceania other 3.700000 3187.2
Uganda Africa africa 5.901000 509.0
Ukraine Europe other 1.483000 3035.0
United Arab Emirates Asia other 1.707000 39624.7
United Kingdom Europe oecd 1.867000 36326.8
United States North America oecd 2.077000 46545.9
Uruguay Latin Amer other 2.043000 11952.4
Uzbekistan Asia other 2.264000 1427.3
Vanuatu Oceania other 3.750000 2963.5
Venezuela Latin Amer other 2.391000 13502.7
Viet Nam Asia other 1.750000 1182.7
Yemen Asia other 4.938000 1437.2
Zambia Africa africa 6.300000 1237.8
Zimbabwe Africa africa 3.109000 573.1
lifeExpF pctUrban
Afghanistan 49.49000 23
Albania 80.40000 53
Algeria 75.00000 67
Angola 53.17000 59
Anguilla 81.10000 100
Argentina 79.89000 93
Armenia 77.33000 64
Aruba 77.75000 47
Australia 84.27000 89
Austria 83.55000 68
Azerbaijan 73.66000 52
Bahamas 78.85000 84
Bahrain 76.06000 89
Bangladesh 70.23000 29
Barbados 80.26000 45
Belarus 76.37000 75
Belgium 82.81000 97
Belize 77.81000 53
Benin 58.66000 42
Bermuda 82.30000 100
Bhutan 69.84000 35
Bolivia 69.40000 67
Bosnia and Herzegovina 78.40000 49
Botswana 51.34000 62
Brazil 77.41000 87
Brunei Darussalam 80.64000 76
Bulgaria 77.12000 72
Burkina Faso 57.02000 27
Burundi 52.58000 11
Cambodia 65.10000 20
Cameroon 53.56000 59
Canada 83.49000 81
Cape Verde 77.70000 62
Cayman Islands 83.80000 100
Central African Republic 51.30000 39
Chad 51.61000 28
Chile 82.35000 89
China 75.61000 48
Colombia 77.69000 75
Comoros 63.18000 28
Congo 59.33000 63
Cook Islands 76.24547 76
Costa Rica 81.99000 65
Cote dIvoire 57.71000 51
Croatia 80.37000 58
Cuba 81.33000 75
Cyprus 82.14000 71
Czech Republic 81.00000 74
Democratic Republic of the Congo 50.56000 36
Denmark 81.37000 87
Djibouti 60.04000 76
Dominica 78.20000 67
Dominican Republic 76.57000 70
East Timor 64.20000 29
Ecuador 78.91000 68
Egypt 75.52000 44
El Salvador 77.09000 65
Equatorial Guinea 52.91000 40
Eritrea 64.41000 22
Estonia 79.95000 70
Ethiopia 61.59000 17
Fiji 72.27000 52
Finland 83.28000 85
France 84.90000 86
French Polynesia 78.07000 51
Gabon 64.32000 86
Gambia 60.30000 59
Georgia 77.31000 53
Germany 82.99000 74
Ghana 65.80000 52
Greece 82.58000 62
Greenland 71.60000 84
Grenada 77.72000 40
Guatemala 75.10000 50
Guinea 56.39000 36
Guinea-Bissau 50.40000 30
Guyana 73.45000 29
Haiti 63.87000 54
Honduras 75.92000 52
Hong Kong 86.35000 100
Hungary 78.47000 68
Iceland 83.77000 94
India 67.62000 30
Indonesia 71.80000 45
Iran 75.28000 71
Iraq 72.60000 66
Ireland 83.17000 62
Israel 84.19000 92
Italy 84.62000 69
Jamaica 75.98000 52
Japan 87.12000 67
Jordan 75.17000 79
Kazakhstan 72.84000 59
Kenya 59.16000 23
Kiribati 63.10000 44
Kuwait 75.89000 98
Kyrgyzstan 72.36000 35
Laos 69.42000 34
Latvia 78.51000 68
Lebanon 75.07000 87
Lesotho 48.11000 28
Liberia 58.59000 48
Libya 77.86000 78
Lithuania 78.28000 67
Luxembourg 82.67000 85
Macao 83.80000 100
Madagascar 68.61000 31
Malawi 55.17000 20
Malaysia 76.86000 73
Maldives 78.70000 41
Mali 53.14000 37
Malta 82.29000 95
Marshall Islands 70.60000 72
Mauritania 60.95000 42
Mauritius 76.89000 42
Mexico 79.64000 78
Micronesia 70.17000 23
Moldova 73.48000 48
Mongolia 72.83000 63
Montenegro 77.37000 61
Morocco 74.86000 59
Mozambique 51.81000 39
Myanmar 67.87000 34
Namibia 63.04000 39
Nauru 57.10000 100
Nepal 70.05000 19
Neth Antilles 79.86000 93
Netherlands 82.79000 83
New Caledonia 80.49000 57
New Zealand 82.77000 86
Nicaragua 77.45000 58
Niger 55.77000 17
Nigeria 53.38000 51
North Korea 72.12000 60
Norway 83.47000 80
Oman 76.44000 73
Pakistan 66.88000 36
Palau 72.10000 84
Palestinian Territory 74.81000 74
Panama 79.07000 75
Papua New Guinea 65.52000 13
Paraguay 74.91000 62
Peru 76.90000 77
Philippines 72.57000 49
Poland 80.56000 61
Portugal 82.76000 61
Puerto Rico 83.20000 99
Qatar 78.24000 96
Republic of Korea 83.95000 83
Romania 77.95000 58
Russian Federation 75.01000 73
Rwanda 57.13000 19
Saint Lucia 77.54000 28
Samoa 76.02000 20
Sao Tome and Principe 66.48000 63
Saudi Arabia 75.57000 82
Senegal 60.92000 43
Serbia 77.05000 56
Seychelles 78.00000 56
Sierra Leone 48.87000 39
Singapore 83.71000 100
Slovakia 79.53000 55
Slovenia 82.84000 49
Solomon Islands 70.00000 19
Somalia 53.38000 38
South Africa 54.09000 62
Spain 84.76000 78
Sri Lanka 78.40000 14
St Vincent and Grenadines 74.73000 50
Sudan 63.82000 41
Suriname 74.18000 70
Swaziland 48.54000 21
Sweden 83.65000 85
Switzerland 84.71000 74
Syria 77.72000 56
Tajikistan 71.23000 26
Tanzania 60.31000 27
TFYR Macedonia 77.14000 59
Thailand 77.76000 34
Togo 59.40000 44
Tonga 75.38000 24
Trinidad and Tobago 73.82000 14
Tunisia 77.05000 68
Turkey 76.61000 70
Turkmenistan 69.40000 50
Tuvalu 65.10000 51
Uganda 55.44000 13
Ukraine 74.58000 69
United Arab Emirates 78.02000 84
United Kingdom 82.42000 80
United States 81.31000 83
Uruguay 80.66000 93
Uzbekistan 71.90000 36
Vanuatu 73.58000 26
Venezuela 77.73000 94
Viet Nam 77.44000 31
Yemen 67.66000 32
Zambia 50.04000 36
Zimbabwe 52.72000 39plot(UN11$ppgdp, UN11$fertility,
main="Fertility vs PPGDP",
xlab="PPGDP (Gross National Product per Person)",
ylab="Fertility (Birth Rate per 1000 Females)")
model <- lm(fertility ~ ppgdp, data = UN11)
abline(model, col = "red", lwd = 2)
The graph first displays a severe negative association between a country’s gross national product per person and fertility rate, but after this point, there appears to be no change in fertility in relation to ppgdp. A straight-line mean function does not appear to be an adequate metric for this graph’s summary.
(c)
plot(log(UN11$ppgdp), log(UN11$fertility),
main="Log(Fertility) vs Log(PPGDP)",
xlab="Log(PPGDP)",
ylab="Log(Fertility)")
model <- lm(log(fertility) ~ log(ppgdp), data = UN11)
abline(model, col = "red", lwd = 2)
Throughout the graph, the connection between the variables appears to be negative. For a description of this graph, basic linear regression is feasible.
Question 2:
Annual income, in dollars, is an explanatory variable in a regression analysis. For a British version of the report on the analysis, all responses are converted to British pounds sterling (1 pound equals about 1.33 dollars, as of 2016).
- How, if at all, does the slope of the prediction equation change?
- How, if at all, does the correlation change?
Answer:
(a)
UN11$british <- 1.33 * UN11$ppgdp
summary(lm(fertility ~ british, UN11))
Call:
lm(formula = fertility ~ british, data = UN11)
Residuals:
Min 1Q Median 3Q Max
-1.9006 -0.8801 -0.3547 0.6749 3.7585
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.178e+00 1.048e-01 30.331 < 2e-16 ***
british -2.407e-05 3.500e-06 -6.877 7.9e-11 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.206 on 197 degrees of freedom
Multiple R-squared: 0.1936, Adjusted R-squared: 0.1895
F-statistic: 47.29 on 1 and 197 DF, p-value: 7.903e-11summary(lm(fertility ~ ppgdp, UN11))
Call:
lm(formula = fertility ~ ppgdp, data = UN11)
Residuals:
Min 1Q Median 3Q Max
-1.9006 -0.8801 -0.3547 0.6749 3.7585
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.178e+00 1.048e-01 30.331 < 2e-16 ***
ppgdp -3.201e-05 4.655e-06 -6.877 7.9e-11 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.206 on 197 degrees of freedom
Multiple R-squared: 0.1936, Adjusted R-squared: 0.1895
F-statistic: 47.29 on 1 and 197 DF, p-value: 7.903e-11The slope of the prediction equation will change when income is converted from dollars to pounds sterling. Since 1 pound equals about 133. dollars (as of 2016), to convert the annual income to pounds, you will need to divide the annual income in dollars by 133. The slope of the equation in pounds will be the same as the original slope in dollars. The magnitude of the slope changes due to the change in units, but the relationship between the variables remains the same.
(b)
cor(UN11$ppgdp, UN11$fertility)[1] -0.4399891cor(UN11$british, UN11$fertility)[1] -0.4399891When converting from dollars to pounds sterling, the correlation between variables will not change. The correlation coefficients are only a measure of the relative relationship between the two variables, not the units they are measured in. The correlation coefficients of the variables remain the same since the conversion from dollars to pounds only involves a linear transformation.
Question 3:
Water runoff in the Sierras (Data file: water in alr4) Can Southern California’s water supply in future years be predicted from past data? One factor affecting water availability is stream runoff. If runoff could be predicted, engineers, planners, and policy makers could do their jobs more efficiently. The data file contains 43 years’ worth of precipitation measurements taken at six sites in the Sierra Nevada mountains (labeled APMAM, APSAB, APSLAKE, OPBPC, OPRC, and OPSLAKE) and stream runoff volume at a site near Bishop, California, labeled BSAAM. Draw the scatterplot matrix for these data and summarize the information available from these plots. (Hint: Use the pairs() function.)
Answer:
data(water)
water Year APMAM APSAB APSLAKE OPBPC OPRC OPSLAKE BSAAM
1 1948 9.13 3.58 3.91 4.10 7.43 6.47 54235
2 1949 5.28 4.82 5.20 7.55 11.11 10.26 67567
3 1950 4.20 3.77 3.67 9.52 12.20 11.35 66161
4 1951 4.60 4.46 3.93 11.14 15.15 11.13 68094
5 1952 7.15 4.99 4.88 16.34 20.05 22.81 107080
6 1953 9.70 5.65 4.91 8.88 8.15 7.41 67594
7 1954 5.02 1.45 1.77 13.57 12.45 13.32 65356
8 1955 6.70 7.44 6.51 9.28 9.65 9.80 67909
9 1956 10.50 5.85 3.38 21.20 18.55 17.42 92715
10 1957 9.10 6.13 4.08 9.55 9.20 8.25 70024
11 1958 8.75 5.23 5.90 15.25 14.80 17.48 99216
12 1959 8.10 3.77 4.56 9.05 6.85 9.56 55786
13 1960 3.75 1.47 1.78 4.57 6.10 7.65 46153
14 1961 10.15 5.09 4.86 8.90 7.15 9.00 47947
15 1962 6.15 3.52 3.30 16.90 14.75 17.68 76877
16 1963 12.75 8.17 10.16 16.75 11.55 15.53 88443
17 1964 7.35 4.33 4.85 5.25 7.45 8.20 54634
18 1965 11.25 6.56 7.60 8.40 13.20 13.29 78806
19 1966 4.05 1.90 2.00 10.85 8.25 12.56 56542
20 1967 12.65 6.62 7.14 23.25 17.00 23.66 116244
21 1968 4.65 3.84 3.34 7.10 6.80 8.28 60857
22 1969 5.35 3.62 4.62 43.37 24.85 33.07 146345
23 1970 4.05 1.98 2.94 8.95 11.25 11.00 73726
24 1971 5.90 5.72 5.42 8.45 10.90 10.82 65530
25 1972 9.45 4.82 6.79 7.90 7.60 8.06 60772
26 1973 3.45 2.63 2.88 14.80 14.70 15.86 91696
27 1974 4.25 2.54 2.36 18.05 16.90 16.42 87377
28 1975 7.90 4.42 6.78 11.50 9.55 12.56 77306
29 1976 9.38 8.30 9.70 6.80 5.25 4.73 44756
30 1977 7.08 4.40 3.90 4.05 4.35 4.60 41785
31 1978 11.92 5.78 6.70 25.30 20.55 21.94 112653
32 1979 3.88 2.26 3.10 15.97 11.83 13.88 79975
33 1980 5.80 3.10 3.34 24.40 19.15 23.78 106821
34 1981 2.70 2.22 2.48 8.99 9.45 12.14 69177
35 1982 18.08 11.96 13.02 18.55 18.40 19.45 120463
36 1983 8.20 4.98 5.76 19.25 22.90 23.86 135043
37 1984 7.65 5.30 5.74 14.45 13.15 14.42 102001
38 1985 5.22 4.42 4.04 11.45 10.16 13.06 77790
39 1986 4.93 3.26 4.58 26.47 15.33 26.46 118144
40 1987 5.99 2.76 3.98 4.80 6.85 6.36 61229
41 1988 6.83 6.82 5.18 7.20 9.01 9.88 58942
42 1989 8.80 5.06 4.92 8.05 9.60 9.58 53965
43 1990 7.10 5.06 6.05 5.80 6.50 8.41 49774pairs(water)
According to the above figure, the stream run-off variable has a link with the ‘O’ named lakes but no significant association with the ’A named lakes.
Question 4:
Professor ratings (Data file: Rateprof in alr4) In the website and online forum RateMyProfessors.com, students rate and comment on their instructors. Launched in 1999, the site includes millions of ratings on thousands of instructors. The data file includes the summaries of the ratings of 364 instructors at a large campus in the Midwest (Bleske-Rechek and Fritsch, 2011). Each instructor included in the data had at least 10 ratings over a several year period. Students provided ratings of 1–5 on quality, helpfulness, clarity, easiness of instructor’s courses, and raterInterest in the subject matter covered in the instructor’s courses. The data file provides the averages of these five ratings. Create a scatterplot matrix of these five variables. Provide a brief description of the relationships between the five ratings.
Answer:
data(Rateprof)
Rateprof gender numYears numRaters numCourses pepper discipline
1 male 7 11 5 no Hum
2 male 6 11 5 no Hum
3 male 10 43 2 no Hum
4 male 11 24 5 no Hum
5 male 11 19 7 no Hum
6 male 10 15 9 no Hum
7 male 7 17 3 no Hum
8 male 11 16 3 no Hum
9 male 11 12 4 no Hum
10 male 7 18 4 no Hum
11 male 11 11 4 no Hum
12 male 6 33 4 yes Hum
13 male 4 23 5 no Hum
14 male 10 34 2 yes Hum
15 male 11 23 8 yes Hum
16 male 3 27 5 yes Hum
17 male 1 14 2 yes Hum
18 male 11 19 7 no Hum
19 male 6 11 5 no Hum
20 male 11 14 5 no Hum
21 male 7 59 9 no Hum
22 male 10 28 5 no Hum
23 male 1 13 3 no Hum
24 male 10 15 5 no Hum
25 male 7 16 2 no Hum
26 male 11 35 6 no Hum
27 male 7 11 2 no Hum
28 male 11 23 10 no Hum
29 male 11 27 6 no Hum
30 male 11 42 5 yes Hum
31 male 11 38 4 no Hum
32 male 11 20 8 no Hum
33 male 11 44 6 no Hum
34 male 11 57 3 yes Hum
35 male 10 15 3 no Hum
36 male 9 46 5 no Hum
37 male 11 10 4 no Hum
38 male 3 18 2 no Hum
39 male 11 79 7 no Hum
40 male 11 18 2 no Hum
41 male 3 26 5 no Hum
42 male 11 52 2 no Hum
43 male 11 10 2 no Hum
44 male 7 26 5 no Hum
45 male 10 15 3 no Hum
46 male 11 45 8 no Hum
47 male 3 12 3 yes Hum
48 male 7 12 2 no Hum
49 male 11 16 3 no Hum
50 male 9 36 8 no Hum
51 male 11 24 5 no Hum
52 male 3 29 4 no Hum
53 male 11 65 4 no Hum
54 male 11 11 4 no Hum
55 male 2 14 4 yes Hum
56 male 11 14 7 no Hum
57 male 11 29 6 no Hum
58 male 11 54 6 yes Hum
59 male 4 12 3 no Hum
60 male 11 57 5 no Hum
61 male 9 13 6 no Hum
62 male 5 33 3 no Hum
63 male 8 46 7 no Hum
64 male 11 19 4 no Hum
65 female 11 18 6 yes Hum
66 female 9 28 3 no Hum
67 female 11 21 7 no Hum
68 female 8 26 8 yes Hum
69 female 11 10 2 no Hum
70 female 2 14 4 no Hum
71 female 7 27 6 no Hum
72 female 10 22 3 no Hum
73 female 4 36 6 no Hum
74 female 2 14 4 yes Hum
75 female 11 19 6 no Hum
76 female 11 86 8 no Hum
77 female 8 25 8 no Hum
78 female 8 26 7 yes Hum
79 female 10 16 2 no Hum
80 female 9 20 3 no Hum
81 female 11 30 4 no Hum
82 female 7 12 3 no Hum
83 female 10 21 3 no Hum
84 female 1 19 4 yes Hum
85 female 11 12 3 yes Hum
86 female 4 31 3 yes Hum
87 female 4 22 2 yes Hum
88 female 4 13 5 no Hum
89 female 11 22 5 no Hum
90 female 11 26 8 no Hum
91 female 11 15 3 no Hum
92 female 2 20 5 no Hum
93 female 11 24 7 no Hum
94 female 11 69 3 no Hum
95 female 10 37 6 no Hum
96 female 9 36 7 no Hum
97 female 7 32 3 no Hum
98 female 2 11 3 no Hum
99 female 11 41 2 no Hum
100 female 7 34 7 no Hum
101 female 5 15 4 no Hum
102 female 11 38 3 no Hum
103 female 2 10 4 yes Hum
104 female 11 29 5 no Hum
105 female 1 10 4 yes Hum
106 female 11 27 5 no Hum
107 female 11 36 4 no Hum
108 female 9 19 3 no Hum
109 female 11 14 2 no Hum
110 female 8 17 5 no Hum
111 female 10 54 3 no Hum
112 female 11 21 5 no Hum
113 female 5 33 6 no Hum
114 female 11 47 8 no Hum
115 female 11 58 5 no Hum
116 female 7 14 4 yes Hum
117 female 11 10 5 no Hum
118 female 9 36 6 no Hum
119 female 7 14 5 yes Hum
120 female 11 26 5 no Hum
121 female 8 39 5 no Hum
122 female 11 16 6 no Hum
123 female 5 67 3 no Hum
124 female 9 29 4 no Hum
125 female 11 26 6 no Hum
126 female 6 24 7 no Hum
127 female 7 16 5 yes Hum
128 female 5 20 2 no Hum
129 female 10 35 6 no Hum
130 female 5 36 9 no Hum
131 female 4 28 3 no Hum
132 female 11 10 4 no Hum
133 female 9 53 7 no Hum
134 female 2 13 2 no Hum
135 male 7 10 2 no SocSci
136 male 7 21 2 no SocSci
137 male 2 33 2 no SocSci
138 male 7 11 2 no SocSci
139 male 6 18 3 no SocSci
140 male 11 30 2 no SocSci
141 male 7 14 2 no SocSci
142 male 4 15 5 yes SocSci
143 male 11 50 4 no SocSci
144 male 3 10 3 no SocSci
145 male 11 30 5 no SocSci
146 male 11 53 3 no SocSci
147 male 11 46 4 yes SocSci
148 male 11 30 5 no SocSci
149 male 11 42 7 no SocSci
150 male 11 74 8 no SocSci
151 male 10 51 4 no SocSci
152 male 11 31 4 no SocSci
153 male 11 19 2 no SocSci
154 male 11 56 4 no SocSci
155 male 11 72 7 no SocSci
156 male 8 67 4 no SocSci
157 male 11 85 7 no SocSci
158 male 9 14 1 no SocSci
159 male 9 47 7 no SocSci
160 male 10 69 2 no SocSci
161 male 2 11 2 no SocSci
162 male 11 56 6 no SocSci
163 male 10 14 5 no SocSci
164 male 7 23 7 no SocSci
165 male 6 36 5 no SocSci
166 male 11 44 8 no SocSci
167 female 6 19 4 no SocSci
168 female 4 11 5 no SocSci
169 female 11 10 1 yes SocSci
170 female 10 56 2 no SocSci
171 female 11 85 3 no SocSci
172 female 2 16 1 yes SocSci
173 female 7 39 5 yes SocSci
174 female 11 31 4 no SocSci
175 female 8 24 3 no SocSci
176 female 11 67 3 no SocSci
177 female 2 15 3 no SocSci
178 female 6 46 3 no SocSci
179 female 9 13 6 no SocSci
180 female 4 27 3 no SocSci
181 female 11 35 3 no SocSci
182 female 1 32 4 no SocSci
183 female 3 22 2 yes SocSci
184 female 11 51 3 no SocSci
185 female 8 11 2 no SocSci
186 female 10 52 3 no SocSci
187 female 10 62 5 no SocSci
188 female 3 13 1 no SocSci
189 female 2 20 2 no SocSci
190 female 11 32 4 no SocSci
191 female 5 23 3 no SocSci
192 female 11 62 1 no SocSci
193 female 5 42 6 yes SocSci
194 female 11 24 2 no SocSci
195 female 5 26 6 no SocSci
196 female 3 12 4 yes SocSci
197 female 11 32 4 no SocSci
198 female 9 50 5 no SocSci
199 female 11 57 4 no SocSci
200 female 11 15 4 no SocSci
201 male 8 32 4 yes STEM
202 male 11 17 9 no STEM
203 male 11 23 5 no STEM
204 male 11 13 4 no STEM
205 male 1 13 2 no STEM
206 male 6 18 7 no STEM
207 male 1 11 3 yes STEM
208 male 10 26 4 no STEM
209 male 6 15 4 no STEM
210 male 11 25 2 no STEM
211 male 11 21 3 no STEM
212 male 11 43 3 no STEM
213 male 11 51 6 no STEM
214 male 11 11 2 no STEM
215 male 11 27 2 no STEM
216 male 11 37 5 no STEM
217 male 11 35 3 no STEM
218 male 11 29 2 no STEM
219 male 4 30 2 no STEM
220 male 11 28 6 yes STEM
221 male 11 33 3 no STEM
222 male 11 28 6 no STEM
223 male 11 62 5 no STEM
224 male 5 38 7 no STEM
225 male 11 14 1 no STEM
226 male 5 25 3 no STEM
227 male 11 53 8 no STEM
228 male 7 20 3 no STEM
229 male 11 21 10 no STEM
230 male 6 40 6 no STEM
231 male 11 13 3 no STEM
232 male 11 67 4 no STEM
233 male 11 19 5 no STEM
234 male 10 17 2 no STEM
235 male 11 22 7 no STEM
236 male 11 16 3 no STEM
237 male 6 35 6 no STEM
238 male 8 38 5 no STEM
239 male 11 67 6 no STEM
240 male 11 35 4 no STEM
241 male 11 32 5 no STEM
242 male 11 58 4 no STEM
243 male 11 21 3 no STEM
244 male 10 12 4 no STEM
245 male 11 45 7 no STEM
246 male 3 14 2 no STEM
247 male 9 41 5 no STEM
248 male 1 10 3 no STEM
249 male 11 30 3 no STEM
250 male 11 25 12 no STEM
251 male 11 37 7 no STEM
252 male 11 23 4 no STEM
253 male 11 65 3 no STEM
254 male 11 54 7 no STEM
255 male 8 41 5 no STEM
256 male 9 13 6 no STEM
257 male 11 52 6 no STEM
258 male 4 33 8 yes STEM
259 male 8 20 6 no STEM
260 male 2 13 2 no STEM
261 male 11 52 5 no STEM
262 male 6 20 3 no STEM
263 male 5 39 3 no STEM
264 male 11 53 8 no STEM
265 male 11 49 7 no STEM
266 male 11 49 6 no STEM
267 male 11 57 7 no STEM
268 male 11 17 5 no STEM
269 male 11 30 10 no STEM
270 male 11 13 3 no STEM
271 male 11 29 6 no STEM
272 male 11 29 3 no STEM
273 male 11 11 6 no STEM
274 male 10 12 2 no STEM
275 male 11 18 5 no STEM
276 male 3 15 3 no STEM
277 female 11 25 3 no STEM
278 female 8 10 4 no STEM
279 female 11 13 3 yes STEM
280 female 11 47 8 no STEM
281 female 5 11 6 no STEM
282 female 11 18 5 no STEM
283 female 4 21 1 no STEM
284 female 7 42 2 no STEM
285 female 9 33 1 no STEM
286 female 3 27 3 no STEM
287 female 11 12 3 no STEM
288 female 11 45 4 no STEM
289 female 11 49 3 no STEM
290 female 11 36 3 yes STEM
291 female 11 54 4 no STEM
292 female 10 31 6 no STEM
293 female 6 17 4 no STEM
294 female 7 30 4 no STEM
295 female 4 11 3 no STEM
296 female 2 17 5 no STEM
297 female 8 80 8 no STEM
298 female 11 39 4 no STEM
299 female 11 26 4 no STEM
300 female 11 29 4 no STEM
301 female 11 60 7 no STEM
302 female 1 16 3 no STEM
303 female 3 10 5 no STEM
304 male 3 14 2 no Pre-prof
305 male 6 14 7 no Pre-prof
306 male 7 12 4 no Pre-prof
307 male 11 13 3 no Pre-prof
308 male 11 11 5 no Pre-prof
309 male 8 39 2 no Pre-prof
310 male 8 32 3 yes Pre-prof
311 male 2 10 2 no Pre-prof
312 male 10 21 5 yes Pre-prof
313 male 11 10 3 no Pre-prof
314 male 7 12 3 no Pre-prof
315 male 5 15 3 yes Pre-prof
316 male 11 53 6 no Pre-prof
317 male 8 68 3 no Pre-prof
318 male 7 48 4 no Pre-prof
319 male 2 10 1 no Pre-prof
320 male 11 36 3 no Pre-prof
321 male 8 15 2 yes Pre-prof
322 male 3 32 3 yes Pre-prof
323 male 9 23 5 no Pre-prof
324 male 4 14 4 no Pre-prof
325 male 8 12 4 no Pre-prof
326 male 11 31 2 no Pre-prof
327 male 11 24 3 yes Pre-prof
328 male 8 33 4 no Pre-prof
329 male 6 50 2 yes Pre-prof
330 male 8 11 6 no Pre-prof
331 male 11 19 3 no Pre-prof
332 male 6 19 1 no Pre-prof
333 male 11 57 5 no Pre-prof
334 male 11 34 3 no Pre-prof
335 male 6 16 2 no Pre-prof
336 male 8 29 3 no Pre-prof
337 male 11 45 6 no Pre-prof
338 male 11 21 4 no Pre-prof
339 female 9 10 1 no Pre-prof
340 female 7 10 4 no Pre-prof
341 female 11 24 3 no Pre-prof
342 female 5 10 2 no Pre-prof
343 female 7 10 2 no Pre-prof
344 female 11 16 4 no Pre-prof
345 female 11 16 2 no Pre-prof
346 female 11 10 5 no Pre-prof
347 female 2 15 1 no Pre-prof
348 female 2 29 2 yes Pre-prof
349 female 3 24 2 no Pre-prof
350 female 2 11 4 no Pre-prof
351 female 11 22 9 yes Pre-prof
352 female 11 62 3 no Pre-prof
353 female 11 21 3 no Pre-prof
354 female 9 53 4 no Pre-prof
355 female 5 12 2 no Pre-prof
356 female 11 11 2 no Pre-prof
357 female 11 38 2 no Pre-prof
358 female 11 46 4 no Pre-prof
359 female 11 10 3 no Pre-prof
360 female 3 24 4 no Pre-prof
361 female 11 27 4 no Pre-prof
362 female 5 21 3 no Pre-prof
363 female 4 15 2 no Pre-prof
364 female 2 10 3 no Pre-prof
365 female 9 11 5 no Pre-prof
366 female 2 11 4 no Pre-prof
dept quality helpfulness clarity easiness
1 English 4.636364 4.636364 4.636364 4.818182
2 Religious Studies 4.318182 4.545455 4.090909 4.363636
3 Art 4.790698 4.720930 4.860465 4.604651
4 English 4.250000 4.458333 4.041667 2.791667
5 Spanish 4.684211 4.684211 4.684211 4.473684
6 Spanish 4.233333 4.266667 4.200000 4.533333
7 Spanish 4.382353 4.352941 4.411765 4.117647
8 English 2.062500 2.062500 2.062500 1.437500
9 Music 2.041667 2.166667 2.000000 1.750000
10 English 4.111111 4.222222 4.000000 3.666667
11 Philosophy 4.727273 4.909091 4.545455 4.000000
12 Philosophy 3.724242 3.848485 3.606060 4.242424
13 Music 2.804348 2.695652 2.913043 2.217391
14 Music 4.838235 4.823529 4.852941 4.676471
15 Spanish 4.565217 4.565217 4.565217 2.826087
16 Religious Studies 4.944444 4.962963 4.925926 3.703704
17 English 4.464286 4.714286 4.214286 3.214286
18 History 4.184211 4.368421 4.000000 3.631579
19 Art 3.909091 4.090909 3.727273 2.272727
20 Art 3.500000 3.285714 3.714286 3.285714
21 Philosophy 3.474576 3.542373 3.406780 2.355932
22 English 3.696429 3.714286 3.678571 3.642857
23 English 3.576923 3.461538 3.692308 4.615385
24 Philosophy 1.633333 1.600000 1.666667 2.266667
25 History 3.531250 3.312500 3.750000 2.562500
26 History 3.114286 3.057143 3.171429 3.857143
27 Music 4.909091 5.000000 4.818182 4.181818
28 English 4.239130 4.434783 4.043478 2.826087
29 Spanish 3.981481 4.037037 3.925926 3.148148
30 English 4.392857 4.500000 4.285714 3.166667
31 History 4.526316 4.473684 4.578947 3.131579
32 German 4.075000 4.150000 4.000000 3.250000
33 Philosophy 2.829546 3.022727 2.636364 2.045454
34 Religious Studies 4.552632 4.561404 4.543860 3.614035
35 Music 3.700000 3.600000 3.800000 3.133333
36 English 1.891304 2.239130 1.543478 3.869565
37 French 4.277778 4.222222 4.333333 3.888889
38 English 4.416667 4.611111 4.222222 3.111111
39 History 2.569620 2.696203 2.443038 2.658228
40 Theater 3.472222 3.111111 3.833333 3.388889
41 English 2.442308 2.692308 2.192308 2.230769
42 Religious Studies 3.067308 3.403846 2.692308 3.076923
43 Religious Studies 3.600000 3.600000 3.600000 3.200000
44 Spanish 4.115385 4.230769 4.000000 2.884615
45 English 2.900000 3.200000 2.600000 3.800000
46 English 3.388889 3.711111 3.111111 2.844444
47 Philosophy 4.708334 4.750000 4.666666 3.666667
48 FLTR 3.291667 3.333333 3.250000 3.333333
49 History 2.250000 2.062500 2.437500 2.812500
50 English 3.555556 3.722222 3.388889 2.777778
51 French 3.854167 3.875000 3.833333 3.000000
52 History 3.913793 3.965517 3.862069 2.965517
53 History 3.469231 3.353846 3.584615 3.061538
54 Art 3.045455 3.090909 3.000000 3.363636
55 Spanish 3.464286 3.285714 3.642857 3.357143
56 German 4.000000 4.000000 4.000000 2.500000
57 Music 3.982759 3.862069 4.103448 3.310345
58 History 4.518519 4.518519 4.518519 4.074074
59 Theater 2.958333 2.833333 3.083333 2.500000
60 History 2.085965 2.280702 1.894737 2.631579
61 Theater 3.538462 3.461538 3.615385 3.230769
62 English 2.924242 2.696970 3.151515 3.454545
63 English 2.293478 2.282609 2.304348 2.456522
64 English 3.684211 3.684211 3.684211 3.157895
65 German 4.666666 4.888889 4.444445 3.055556
66 Womens Studies 4.732143 4.857143 4.607143 4.500000
67 Womens Studies 4.880952 4.952381 4.809524 4.809524
68 English 4.653846 4.615385 4.692308 4.076923
69 History 3.100000 3.500000 2.700000 3.000000
70 Spanish 2.107143 1.928571 2.285714 2.000000
71 Spanish 4.180000 4.320000 4.040000 3.720000
72 English 3.500000 3.500000 3.500000 2.272727
73 English 4.625000 4.666667 4.583333 4.527778
74 Spanish 4.428571 4.642857 4.214286 4.000000
75 English 2.394737 2.263158 2.526316 1.736842
76 English 1.674419 1.686047 3.360465 1.558140
77 English 3.760000 3.840000 3.680000 2.920000
78 English 4.538462 4.769231 4.307692 3.500000
79 Religious Studies 1.875000 2.187500 1.562500 2.687500
80 Religious Studies 4.025000 3.950000 4.100000 2.650000
81 Spanish 3.550000 3.666667 3.433333 1.966667
82 Spanish 3.166667 3.333333 3.000000 3.916667
83 English 2.523810 2.428571 2.619048 1.857143
84 Spanish 3.710526 3.894737 3.526316 2.789474
85 Art 4.458333 4.500000 4.416667 4.166667
86 Spanish 4.709677 4.806452 4.612903 3.645161
87 English 4.500000 4.545455 4.454545 3.636364
88 French 3.461538 3.307692 3.615385 2.923077
89 French 4.545455 4.545455 4.545455 3.500000
90 English 3.500000 3.807692 3.192308 3.692308
91 English 2.200000 2.000000 2.400000 2.400000
92 English 3.925000 4.000000 3.500000 3.850000
93 History 3.958333 3.916667 4.000000 2.750000
94 Religious Studies 2.782609 3.000000 2.565218 3.768116
95 English 1.756757 1.810811 1.702703 1.783784
96 English 4.851351 4.945946 4.756757 3.729730
97 English 3.218750 3.343750 3.093750 2.156250
98 Spanish 3.312500 3.416667 3.208333 2.458333
99 Womens Studies 3.695122 3.731707 3.658537 3.390244
100 Art History 3.794118 3.794118 3.794118 4.088235
101 Spanish 3.233333 3.266667 3.200000 3.400000
102 Spanish 3.236842 3.631579 2.842105 3.421053
103 English 4.700000 4.700000 4.700000 3.700000
104 English 1.482759 1.517241 1.448276 2.068966
105 Spanish 3.950000 3.900000 4.000000 3.400000
106 English 3.537037 3.629630 3.444444 2.814815
107 English 3.208333 3.222222 3.194444 2.083333
108 English 2.394737 2.684211 2.105263 1.789474
109 Dance 3.500000 3.714286 3.285714 3.500000
110 English 3.470588 3.529412 3.411765 3.294118
111 English 4.305556 4.259259 4.351852 3.203704
112 English 3.095238 3.142857 3.047619 3.857143
113 Philosophy 2.469697 2.454545 2.484848 2.666667
114 English 2.904255 3.021277 2.787234 3.361702
115 History 3.189655 3.206897 3.172414 3.672414
116 Spanish 4.678571 4.714286 4.642857 4.071429
117 Art and design 3.200000 2.800000 3.600000 2.000000
118 History 3.833333 3.805556 3.861111 2.638889
119 Music 3.785714 3.500000 4.071429 3.285714
120 Music 3.442308 3.346154 3.500000 4.038462
121 History 2.589744 2.641026 2.538462 3.923077
122 History 2.437500 2.375000 2.500000 3.187500
123 English 2.977612 2.955224 3.000000 2.373134
124 English 3.224138 3.172414 3.275862 2.965517
125 German 2.750000 2.961539 2.538461 3.038461
126 English 3.729167 4.041666 3.416667 3.166667
127 Japanese 4.625000 4.812500 4.437500 3.062500
128 English 3.825000 4.000000 3.650000 2.550000
129 History 3.200000 3.171429 3.228571 3.028571
130 English 3.347222 3.333333 3.361111 3.500000
131 English 3.000000 3.074074 2.851852 3.592593
132 Music 4.100000 4.100000 4.100000 2.600000
133 English 2.792453 2.698113 2.886792 2.735849
134 Spanish 3.076923 3.076923 3.076923 3.461538
135 Psychology 4.800000 4.900000 4.700000 4.400000
136 Communication 4.571429 4.571429 4.571429 4.238095
137 Psychology 4.757576 4.818182 4.696970 3.969697
138 Communication 3.636364 3.545455 3.727273 3.727273
139 Communication 3.583333 3.222222 3.944444 3.833333
140 Psychology 4.400000 4.366667 4.433333 4.133333
141 Communication 4.071429 4.071429 4.142857 3.142857
142 Psychology 4.333333 4.333333 4.333333 2.933333
143 Sociology 4.250000 4.220000 4.280000 2.480000
144 Geography 4.150000 4.100000 4.200000 2.800000
145 Political Science 3.366667 3.566667 3.166667 2.366667
146 Anthropology 4.490566 4.283019 4.698113 3.603774
147 Political Science 4.130435 3.934783 4.326087 3.217391
148 Psychology 2.700000 2.866667 2.533333 1.633333
149 Political Science 3.142857 3.119048 3.166667 2.547619
150 Geography 2.621622 2.662162 2.581081 2.175676
151 Psychology 4.372549 4.176471 4.568627 3.588235
152 Psychology 1.467742 1.483871 1.451613 2.483871
153 Psychology 3.421053 3.578947 3.263158 4.368421
154 Anthropology 2.419643 2.375000 2.464286 2.142857
155 Political Science 3.833333 3.805556 3.861111 2.611111
156 Political Science 4.216418 4.104477 4.328358 2.537314
157 Political Science 2.494118 2.764706 2.223529 2.082353
158 Psychology 4.178571 4.142857 4.214286 2.428571
159 Sociology 2.872340 3.340426 2.404255 3.808511
160 Sociology 3.086957 3.420290 2.753623 3.579710
161 Anthropology 3.409091 3.454545 3.363636 3.818182
162 Political Science 2.535714 2.446429 2.625000 2.500000
163 Communication 1.604167 1.500000 1.708333 2.083333
164 Communication 2.630435 3.173913 2.086957 3.173913
165 Communication 2.916667 3.138889 2.694444 3.500000
166 Sociology 2.733333 2.622222 2.844444 3.177778
167 Communication Disorders 4.684211 4.894737 4.473684 4.210526
168 Communication 4.000000 4.272727 3.727273 3.636364
169 Communication 4.600000 4.700000 4.500000 4.500000
170 Sociology 4.544643 4.517857 4.571429 4.303571
171 Psychology 4.311765 4.305882 4.317647 4.435294
172 Psychology 4.937500 4.937500 4.937500 4.000000
173 Psychology 4.115385 4.179487 4.051282 2.410256
174 Communication 2.435484 2.451613 2.419355 1.870968
175 Psychology 4.574074 4.703704 4.444444 2.888889
176 Sociology 3.880597 3.746269 4.029851 3.910448
177 Sociology 3.666667 3.866667 3.466667 3.533333
178 Sociology 4.195652 4.413043 3.978261 3.869565
179 Anthropology 4.153846 4.384615 3.923077 4.076923
180 Communication 2.000000 1.962963 2.037037 3.185185
181 Communication 3.742857 3.714286 3.771429 2.885714
182 Sociology 2.171875 2.437500 1.906250 4.093750
183 Psychology 4.295455 4.318182 4.272727 3.954545
184 Psychology 3.686275 3.686275 3.686275 2.764706
185 Communication 3.636364 4.090909 3.181818 3.363636
186 Psychology 4.076923 4.076923 4.076923 3.423077
187 Anthropology 3.435484 3.274194 3.596774 2.322581
188 Communication 2.730769 2.230769 3.230769 3.461538
189 Psychology 3.625000 3.550000 3.700000 3.500000
190 Psychology 4.562500 4.468750 4.656250 3.875000
191 Sociology 3.173913 3.130435 3.217391 3.173913
192 Communication 3.741935 3.612903 3.870968 3.483871
193 Psychology 4.535714 4.547619 4.523810 2.500000
194 Communication 4.083333 3.958333 4.208333 3.333333
195 Communication Disorders 2.807692 2.730769 2.884615 3.576923
196 Geography 3.791667 3.500000 4.083334 3.000000
197 Communication 3.343750 3.218750 3.468750 2.718750
198 Psychology 2.580000 2.600000 2.560000 2.860000
199 Political Science 2.728070 2.526316 2.929825 2.684210
200 Communication 3.966667 3.800000 4.133333 3.400000
201 Math 4.921875 5.000000 4.843750 3.812500
202 Math 2.529412 2.411765 2.647059 2.235294
203 Chemistry 2.565218 2.565218 2.565218 1.391304
204 Chemistry 4.269231 4.461538 4.076923 2.615385
205 Math 3.730769 3.692308 3.769231 3.846154
206 Math 2.638889 2.833333 2.444444 2.055556
207 Geology 4.954545 4.909091 5.000000 4.363636
208 Chemistry 4.480769 4.384615 4.576923 3.038462
209 Biology 2.646667 2.800000 2.533333 2.000000
210 Physics 4.720000 4.760000 4.680000 2.560000
211 Chemistry 2.619048 2.904762 2.333333 1.571429
212 Astronomy/Physics 4.918605 5.000000 4.837209 3.279070
213 Math 4.549020 4.627451 4.470588 4.039216
214 Biology 4.045455 4.090909 4.000000 3.000000
215 Chemistry 4.796296 4.925926 4.666667 3.148148
216 Chemistry 3.067568 3.108108 3.027027 2.189189
217 Biology 3.385714 3.028571 3.742857 1.628571
218 Chemistry 4.000000 3.655172 4.344828 2.137931
219 Chemistry 1.750000 2.166667 1.333333 2.666667
220 Computer Science 4.321429 4.392857 4.250000 2.714286
221 Physics 4.666667 4.757576 4.575758 3.212121
222 Math 2.714286 2.892857 2.535714 2.750000
223 Math 3.338710 3.645161 3.048387 3.193548
224 Math 3.986842 4.026316 3.947368 3.842105
225 Physics and Astronomy 3.821429 4.071429 3.571429 3.214286
226 Geology 3.482759 3.482759 3.482759 3.206897
227 Chemistry 3.490566 3.924528 3.056604 3.000000
228 Geology 4.625000 4.600000 4.650000 3.700000
229 Physics & Astronomy 3.452381 3.523810 3.380952 2.238095
230 Biology 2.287500 2.450000 2.125000 1.900000
231 Biology 3.038462 3.384615 2.692308 2.230769
232 Biology 4.365672 4.447761 4.283582 1.820896
233 Physics 3.684211 3.947368 3.421053 2.157895
234 Geology 3.500000 3.294118 3.705882 2.823529
235 Physics 4.159091 4.363636 3.954545 3.090909
236 Math 3.562500 3.437500 3.687500 3.375000
237 Chemistry 3.562500 3.437500 3.687500 3.375000
238 Geology 3.960526 4.000000 3.921053 2.578947
239 Math 4.231343 4.164179 4.298507 4.164179
240 Biology 2.671429 2.885714 2.457143 1.971429
241 Math 4.015625 3.937500 4.093750 4.406250
242 Biology 3.103448 3.275862 2.931034 2.224138
243 Physics and Astronomy 4.166667 4.428571 3.904762 3.095238
244 Biology 2.791667 2.750000 2.833333 1.750000
245 Math 3.966667 4.088889 3.844444 2.533333
246 Geology 4.107143 4.142857 4.142857 3.071429
247 Chemistry 3.329268 3.512195 3.146341 3.000000
248 Geology 2.800000 2.900000 2.700000 2.400000
249 Biology 4.066667 3.900000 4.233333 2.933333
250 Computer Science 4.620000 4.720000 4.520000 2.480000
251 Math 3.000000 3.081081 2.918919 3.054054
252 Chemistry 2.586957 2.608696 2.565217 2.695652
253 Math 1.915385 2.076923 1.723077 2.107692
254 Geology 4.527778 4.537037 4.518519 2.888889
255 Chemistry 3.890244 4.073171 3.707317 2.634146
256 Math 4.384615 4.461538 4.307692 3.846154
257 Math 3.451923 3.596154 3.269231 3.692308
258 Math 3.878788 4.030303 3.727273 3.515152
259 Physics 3.950000 3.900000 4.000000 3.200000
260 Chemistry 4.846154 4.923077 4.769231 3.769231
261 Math 2.865385 2.826923 2.903846 2.250000
262 Chemistry 3.000000 3.400000 2.600000 2.300000
263 Biology 3.166667 3.333333 3.000000 2.153846
264 Math 3.264151 3.339623 3.188679 3.528302
265 Math 2.928571 3.081633 2.775510 3.591837
266 Physics & Astronomy 4.265306 4.265306 4.265306 3.204082
267 Math 2.508772 2.561404 2.473684 3.017544
268 Chemistry 4.235294 4.235294 4.235294 2.705882
269 Computer Science 2.850000 2.933333 2.766667 2.200000
270 Geology 3.307692 3.461539 3.153846 2.769231
271 Math 2.620690 2.758621 2.482759 3.034483
272 Chemistry 3.103448 3.172414 3.034483 2.758621
273 Computer Science 3.727273 4.000000 3.454545 3.272727
274 Geology 2.375000 2.416667 2.333333 2.750000
275 Math 3.722222 3.944444 3.500000 3.500000
276 Chemistry 2.500000 2.733333 2.266667 2.733333
277 Math 4.940000 5.000000 4.880000 4.800000
278 Biology 2.900000 3.100000 2.700000 1.500000
279 Biology 4.692308 4.769231 4.615385 4.230769
280 Math 3.436170 3.531915 3.340425 4.744681
281 Math 3.772727 3.818182 3.727273 3.727273
282 Chemistry 2.750000 2.777778 2.722222 2.444444
283 Chemistry 2.619048 3.190476 2.047619 2.523810
284 Geology 4.285714 4.452381 4.119048 3.619048
285 Biology 4.015152 4.181818 3.848485 1.878788
286 Math 4.981481 5.000000 4.962963 3.962963
287 Math 4.583333 4.500000 4.666667 3.666667
288 Biology 2.422222 2.533333 2.311111 2.022222
289 Math 2.336735 2.591837 2.081633 2.183673
290 Biology 4.500000 4.555556 4.444444 3.305556
291 Geology 3.555556 3.555556 3.555556 2.500000
292 Math 4.064516 4.096774 4.032258 3.258065
293 Biology 3.529412 3.470588 3.588235 2.117647
294 Biology 4.233333 4.366667 4.100000 2.933333
295 Biology 3.454545 3.363636 3.545455 2.636364
296 Math 2.352941 2.411765 2.294118 2.000000
297 Math 2.087500 2.375000 1.800000 2.387500
298 Physics 3.653846 4.076923 3.230769 2.794872
299 Biology 2.153846 2.346154 1.961538 2.115385
300 Computer Science 2.655172 2.689655 2.620690 2.655172
301 Math 2.608333 2.716667 2.466667 3.483333
302 Physics and Astronomy 2.406250 2.375000 2.437500 1.937500
303 Math 2.900000 3.200000 2.600000 3.100000
304 Kins 2.392857 2.142857 2.642857 1.428572
305 Kins 4.892857 4.928571 4.857143 4.857143
306 Kins 2.958333 3.000000 2.916667 3.833333
307 Kins 2.000000 2.000000 2.000000 2.846154
308 Business 3.954545 4.363636 3.545455 3.636364
309 Economics 4.294872 4.384615 4.205128 3.769231
310 Kins 4.453125 4.343750 4.562500 4.625000
311 Accounting 4.200000 4.600000 4.200000 2.400000
312 Kins 4.904762 4.857143 4.952381 4.809524
313 Finance 3.100000 3.500000 2.700000 1.900000
314 Environmental Public Health 3.166667 3.166667 3.250000 3.583333
315 Information Systems 3.433333 3.533333 3.333333 3.600000
316 Economics 4.811321 4.849057 4.773585 4.132075
317 Economics 3.919118 4.250000 3.588235 2.911765
318 Accounting 4.062500 4.229167 3.895833 1.750000
319 Business 2.600000 3.100000 2.200000 4.300000
320 Business 2.791667 2.750000 2.777778 2.194444
321 Finance 4.166667 4.266667 4.066667 3.000000
322 Information Systems 4.250000 4.218750 4.281250 4.125000
323 Economics 4.260870 4.478261 4.043478 4.130435
324 Business 4.178571 4.071429 4.285714 3.142857
325 Managerial Science 2.916667 3.000000 2.833333 2.333333
326 Accounting 2.919355 2.645161 3.193548 2.322581
327 Marketing 4.562500 4.791667 4.333333 3.666667
328 Economics 4.393939 4.424242 4.363636 3.454545
329 Criminal Justice 4.640000 4.560000 4.720000 3.940000
330 Curriculum and Instruction 2.590909 2.636364 2.545454 2.272727
331 Library Science 4.394737 4.473684 4.315789 3.368421
332 Finance 3.447368 3.105263 3.789474 2.473684
333 Economics 3.719298 3.912281 3.526316 2.561404
334 Business 2.720588 2.764706 2.676471 2.647059
335 Business 3.687500 3.812500 3.562500 3.437500
336 Special Education 3.136364 3.000000 3.272727 2.090909
337 Economics 4.288889 4.466667 4.111111 3.155556
338 Social Work 3.095238 2.809524 3.380952 2.666667
339 Business 4.050000 3.900000 4.200000 4.900000
340 Special Education 4.850000 4.900000 4.800000 4.900000
341 Accounting 4.861111 4.833333 4.888889 4.722222
342 Kins 4.850000 4.800000 4.900000 4.000000
343 Management 3.350000 3.600000 3.100000 3.700000
344 Marketing 3.562500 3.687500 3.437500 4.125000
345 Business 4.687500 4.625000 4.750000 3.500000
346 Marketing 3.600000 3.600000 3.600000 2.700000
347 Managerial Science 3.433333 3.666667 3.200000 3.200000
348 Economics 4.120690 4.344828 3.896552 4.034483
349 Economics 4.083330 4.583330 3.583330 4.166670
350 Social Work 3.181818 3.272727 3.090909 3.545455
351 Kins 4.340909 4.545455 4.090909 4.454545
352 Accounting 3.491935 3.612903 3.370968 2.467742
353 Management 4.500000 4.428571 4.571429 3.619048
354 Economics 3.584906 3.415094 3.754717 3.037736
355 Kins 3.708333 3.583333 3.833333 4.250000
356 Accounting 3.318182 3.090909 3.545455 2.181818
357 Economics 3.513158 3.657895 3.368421 3.868421
358 Economics 4.228261 4.304348 4.152174 3.369565
359 Kins 1.900000 1.900000 1.900000 3.800000
360 Economics 1.937500 2.250000 1.625000 2.333333
361 Business 3.462963 3.333333 3.592593 3.111111
362 Social Work 2.619048 2.714286 2.523810 3.619048
363 Accounting 2.966667 3.066667 2.866667 2.666667
364 Accounting 3.250000 3.200000 3.300000 3.000000
365 Nursing 1.909091 1.909091 1.909091 2.272727
366 Marketing 1.409091 1.363636 1.454545 2.636364
raterInterest sdQuality sdHelpfulness sdClarity sdEasiness sdRaterInterest
1 3.545455 0.55185640 0.6741999 0.5045250 0.4045199 1.1281521
2 4.000000 0.90201795 0.9341987 0.9438798 0.5045250 1.0744356
3 3.432432 0.45293432 0.6663898 0.4129681 0.5407021 1.2369438
4 3.181818 0.93250483 0.9315329 0.9990938 0.5882300 1.3322506
5 4.214286 0.65001124 0.8200699 0.5823927 0.6117753 0.9749613
6 3.916667 0.86327170 1.0327956 0.7745967 0.6399405 0.6685579
7 3.812500 0.94421613 0.9963167 0.9393364 0.6966305 1.2230427
8 2.937500 1.19547760 1.3400871 1.1236103 0.7274384 1.6111590
9 3.750000 1.07573090 1.3371159 1.0444659 0.7537783 1.2880570
10 4.176471 0.90025413 1.0032627 0.9074852 0.7669650 1.5381123
11 2.900000 0.34377584 0.3015113 0.5222330 0.7745967 1.1972190
12 3.333333 1.23870660 1.3257359 1.2975793 0.7917663 1.2909944
13 3.217391 0.98556780 1.0632191 1.1246431 0.7952428 1.1660548
14 4.718750 0.51816386 0.6262243 0.4357058 0.8060600 0.5811210
15 3.952381 0.99206334 1.0368697 0.9920634 0.8340577 1.0712698
16 3.592593 0.16012815 0.1924501 0.2668803 0.8688992 1.1522306
17 2.357143 0.60333323 0.4688072 0.8925824 0.8925824 1.1507284
18 3.526316 0.69142620 0.6839856 0.8164966 0.8950808 1.1239030
19 4.000000 1.26131250 1.4459976 1.1908744 0.9045340 1.0000000
20 3.230769 1.25575600 1.3827827 1.2666473 0.9138736 1.2351685
21 3.537037 1.59585600 1.6433989 1.5878705 0.9240599 1.3418231
22 3.250000 1.23482860 1.2724180 1.3348206 0.9511898 1.3228756
23 2.923077 1.57911040 1.6641006 1.6012815 0.9607689 1.4978617
24 3.400000 0.71879530 0.9102590 1.0465362 0.9611501 1.2983506
25 3.800000 0.93930380 1.1383468 0.9309493 0.9639329 0.9411239
26 3.000000 1.27236300 1.3271566 1.3823619 0.9744639 1.5811388
27 4.909091 0.20225996 0.0000000 0.4045199 0.9816498 0.3015113
28 3.333333 1.12683750 1.1609591 1.2605288 0.9840627 1.3284223
29 4.153846 1.08735290 1.1596247 1.1410496 0.9885383 0.8338972
30 3.516129 1.00932060 1.1529390 0.9947598 1.0101115 1.3384311
31 4.029412 0.62544435 0.6872130 0.7580765 1.0179750 1.0294245
32 3.631579 1.38862860 1.3484884 1.4867839 1.0195458 1.1160708
33 3.475000 1.35519330 1.5017607 1.3655378 1.0332731 1.3772417
34 3.901961 0.72999640 0.8867586 0.8252743 1.0480319 1.1533413
35 3.933333 1.26491100 1.2983506 1.3201731 1.0600988 0.7988086
36 2.347826 1.03769530 1.4634022 0.8084697 1.0668478 1.1588767
37 3.882353 0.84404874 1.0602750 0.7669650 1.0786096 0.9926198
38 3.500000 0.57522374 0.9785276 0.7320845 1.0786096 0.9851844
39 2.956522 1.17597260 1.3141676 1.2273260 1.0846963 1.3109806
40 4.000000 1.18162680 1.4095844 1.0981267 1.0921586 1.0954451
41 2.692308 1.37351320 1.5942203 1.2967415 1.1066234 1.2890068
42 3.442308 1.14630200 1.2408033 1.2452020 1.1175280 1.1784580
43 4.300000 1.50554530 1.5055453 1.5776213 1.1352924 0.4830459
44 4.320000 0.86380196 0.8629110 1.0954451 1.1428709 0.9882645
45 2.733333 1.28452320 1.3732131 1.3522468 1.1464230 1.3870146
46 3.185185 1.42577290 1.4866408 1.5109031 1.1472409 1.3877773
47 3.416667 0.54181236 0.4522670 0.6513389 1.1547005 1.4433757
48 3.416667 1.33923880 1.3026779 1.5447860 1.1547005 1.4433757
49 3.200000 0.96609180 1.1236103 1.0935416 1.1672617 1.2649110
50 3.290322 1.40802690 1.4660171 1.4595063 1.1737878 1.2556325
51 4.227273 1.27244340 1.2958965 1.3405601 1.1795356 0.9725675
52 4.320000 1.40196910 1.4010904 1.4814119 1.1796718 0.9451631
53 3.280702 1.28049350 1.3855366 1.3450407 1.1842313 1.3059532
54 3.636364 1.42222620 1.6403991 1.2649111 1.2060454 0.9244163
55 2.785714 1.51231200 1.7288756 1.3926810 1.2157393 1.4238934
56 3.875000 1.19292780 1.4142136 1.0377490 1.2247449 0.6408699
57 4.333333 1.24987690 1.4814119 1.2633523 1.2846191 1.2038585
58 4.340909 0.70015470 0.7458246 0.8182065 1.2863852 1.0330173
59 3.500000 1.23322070 1.4034589 1.3113722 1.3142575 1.0000000
60 3.166667 1.15177480 1.2642670 1.2054076 1.3447196 1.4241846
61 3.800000 1.16299780 1.5607362 0.8697185 1.3634421 1.6193277
62 2.696970 1.28160800 1.3803271 1.3257359 1.3713795 1.2370542
63 3.806452 1.33988430 1.4089089 1.3311576 1.3777038 1.3271361
64 2.933333 1.18098970 1.2495613 1.2495613 1.3849652 1.1629192
65 3.937500 0.42008403 0.3233808 0.7047922 1.0556415 0.7719024
66 3.333333 0.44058344 0.4483951 0.5669467 0.5091751 1.2089410
67 3.428571 0.21821790 0.2182179 0.4023739 0.5117663 1.2478553
68 3.550000 0.62879616 0.6972473 0.6793662 0.6275716 1.0505954
69 2.800000 1.12546290 1.3540064 1.0593499 0.6666667 1.2292726
70 3.166667 1.04105290 1.2066665 1.1387288 0.6793662 1.4034589
71 3.840000 0.77567180 0.8524475 0.8888194 0.7371115 0.9865766
72 3.000000 1.38873020 1.5039630 1.4392458 0.7672969 1.4832397
73 3.722222 0.59009683 0.6324555 0.7319251 0.7740842 1.0852547
74 3.214286 0.26726124 0.4972452 0.5789342 0.7844645 1.1217138
75 3.066667 1.51454940 1.6276126 1.6113632 0.8056816 1.4375906
76 2.814815 1.07585110 1.1808435 1.0584168 0.8059288 1.2258784
77 3.631579 1.20864940 1.2330483 1.2489996 0.8124038 1.2115429
78 3.730769 0.54631630 0.4296689 0.7358930 0.8602325 1.1156233
79 2.666667 0.82663980 1.1086779 0.8139410 0.8732125 1.2909944
80 3.812500 1.15251450 1.2343760 1.1652874 0.8750940 1.1672618
81 4.000000 1.15482500 1.0933445 1.2507469 0.8899180 1.1126973
82 3.777778 1.05169420 1.0730867 1.2060454 0.9003366 1.7159384
83 2.450000 1.25972410 1.4342743 1.3219754 0.9102590 1.3562720
84 4.157895 1.26178660 1.2864567 1.3485968 0.9176629 1.2588865
85 3.750000 0.68947720 0.9045340 0.6685579 0.9374369 1.1381804
86 3.870968 0.49622230 0.4774484 0.6672041 0.9503819 1.4081178
87 3.545455 0.80178374 0.8578641 0.9116846 0.9534626 1.0107646
88 3.153846 0.98871840 1.1094004 1.1929279 0.9540736 1.2142318
89 3.818182 0.87163080 1.0568269 0.8004328 0.9636241 1.2960145
90 3.153846 1.20830460 1.3272296 1.2006409 0.9703290 1.3473621
91 2.769231 1.34695420 1.3093073 1.4540584 0.9856108 1.4232502
92 3.250000 1.05475120 1.1697953 1.0894228 0.9880869 1.2926920
93 3.666667 1.13172300 1.4116492 0.9780193 0.9890707 1.3904436
94 2.903226 1.24699130 1.3612279 1.2541491 1.0021291 1.3755437
95 2.545455 1.06472230 1.1263964 1.1514451 1.0037467 1.5429458
96 3.750000 0.30878040 0.2292434 0.4947168 1.0178586 1.2181424
97 2.937500 1.24393690 1.3102419 1.4223872 1.0194678 1.1341474
98 3.125000 1.46563900 1.5012072 1.5316705 1.0206207 1.2618999
99 3.358974 1.24939010 1.3968606 1.2571745 1.0217154 1.1582014
100 2.794118 1.14228400 1.2499554 1.2739681 1.0259555 1.2739681
101 3.400000 1.34783780 1.4864467 1.3732131 1.0555973 1.3522468
102 3.457143 1.42722960 1.4597492 1.5338754 1.0560400 1.2912114
103 3.400000 0.78881060 0.9486833 0.6749486 1.0593499 1.0749677
104 2.400000 0.66120505 0.7847060 0.6316762 1.0667385 1.3844373
105 3.900000 0.89597870 1.4491377 0.6666667 1.0749677 0.8755950
106 3.166667 1.31504550 1.3414650 1.3681355 1.0754976 1.4345630
107 2.647059 1.15495820 1.3117297 1.0907257 1.0790207 1.2524486
108 2.842105 1.03519920 1.2495613 1.1002392 1.0841765 1.3849652
109 3.846154 1.17669680 1.2666474 1.2043876 1.0919284 1.7246330
110 2.875000 1.15204420 1.3284223 1.1757351 1.1048024 1.6683325
111 2.920000 1.01133510 1.1190492 0.9935150 1.1053836 1.2590894
112 2.850000 1.51343190 1.6212870 1.5961263 1.1084094 1.0021622
113 3.363636 1.36324180 1.4809395 1.4603341 1.1086779 1.0552897
114 3.380952 1.35389260 1.5671819 1.3011061 1.1117071 1.1032630
115 3.333333 1.21694030 1.3861295 1.2860647 1.1299423 0.9712859
116 4.071429 0.63872296 0.6112498 0.8418974 1.1411388 1.1411388
117 3.000000 1.41813650 1.6193277 1.3498971 1.1547005 1.2472191
118 3.166667 1.06904500 1.2608261 1.0994226 1.1748016 1.2761549
119 3.714286 0.87077080 1.0919285 0.7300459 1.2043875 1.2043875
120 1.098039 1.57052170 1.7191232 1.7191232 1.2159200 1.1972190
121 3.105263 1.33215200 1.4232502 1.3542556 1.2222631 1.4292216
122 3.062500 1.22304260 1.5438048 1.0954451 1.2230427 1.4361407
123 2.552239 1.47307360 1.6554120 1.4142136 1.2288923 1.1452614
124 2.827586 1.36660560 1.5369024 1.3600565 1.2387424 1.4159541
125 3.277778 1.19373370 1.3705698 1.1740791 1.2483835 1.2307339
126 3.333333 1.33025940 1.3376712 1.5012072 1.2740442 1.1671841
127 4.533333 0.64549720 0.5439056 0.8920949 1.2893797 0.6399405
128 3.235294 1.29039980 1.3764944 1.3869694 1.3168943 1.1472473
129 3.657143 1.31842150 1.3823619 1.3303187 1.3169866 1.1867617
130 3.500000 1.53910660 1.5856499 1.6062873 1.3416408 1.3471506
131 3.148148 1.27097790 1.3846945 1.3503192 1.3660516 1.0635103
132 3.300000 1.24275680 1.3703203 1.1972190 1.4298407 1.6363917
133 2.913043 1.35317990 1.3948381 1.4366143 1.4431662 1.2441166
134 2.615385 1.32045050 1.4978617 1.3204506 1.4500221 1.0439078
135 4.500000 0.25819890 0.3162278 0.4830459 0.5163978 0.5477226
136 4.095238 0.63807750 0.6761234 0.6761234 0.7003401 0.9952267
137 4.000000 0.28287620 0.3916747 0.4666937 0.7699370 0.7905694
138 3.333333 1.22659910 1.3684763 1.1908744 0.7862454 1.3228757
139 3.000000 1.15363870 1.2628425 1.2113300 0.8574929 1.2649111
140 4.000000 0.75885576 0.7648905 0.8583598 0.8603661 0.9325048
141 3.500000 1.10692130 1.3847680 1.0271052 0.8644378 1.0801235
142 3.933333 0.91936830 1.0465362 0.8997354 0.8837151 0.5936168
143 3.312500 0.66432410 0.7899884 0.8091316 0.8861750 1.1697654
144 3.800000 1.17968920 1.1972190 1.2292726 0.9189366 1.3165612
145 3.296296 1.22427560 1.3047217 1.3412124 0.9278575 1.0308628
146 3.428571 0.62396500 0.9482242 0.5401177 0.9474586 1.3844373
147 3.057143 0.87834935 0.9752988 0.9440892 0.9640895 1.4939655
148 3.192308 1.36836170 1.5698305 1.2793677 0.9643055 1.2335066
149 3.428571 1.23607220 1.2916690 1.3954048 0.9678334 1.5324595
150 3.218750 1.30806460 1.4456077 1.3447692 0.9702155 1.2657735
151 4.083334 0.76709280 1.0675591 0.6963624 0.9900296 0.7810788
152 3.225806 0.88445354 0.9956896 0.8500474 0.9956896 1.5429339
153 3.277778 1.49316180 1.6095475 1.5578513 1.0116283 1.6379886
154 3.111111 1.40057380 1.4962073 1.4008346 1.0344708 1.3963114
155 3.606557 1.17485390 1.2631159 1.1904024 1.0421478 1.2685778
156 3.500000 0.91793525 1.0020332 0.9752709 1.0777130 1.2460464
157 3.222222 1.24521490 1.4528056 1.2571365 1.0824549 1.3862730
158 3.785714 1.01160850 1.0994504 1.1217138 1.0894096 1.3688047
159 2.857143 1.13476720 1.4337030 1.0766206 1.0962049 1.2010448
160 3.019608 1.21557450 1.3438947 1.1931890 1.1298854 1.2726381
161 3.090909 1.39316510 1.5075567 1.4333686 1.1677484 1.3003496
162 2.365854 1.39106610 1.4259879 1.5203170 1.1908744 1.3182583
163 2.454545 0.90864410 0.9780193 0.9990938 1.2128539 1.4384937
164 3.650000 1.17953560 1.5270939 1.0406748 1.2303796 1.0399899
165 2.861111 1.33897610 1.5147424 1.3484265 1.2305632 1.2224747
166 3.097561 1.33399600 1.4027390 1.4027390 1.3973279 1.0721450
167 4.368421 0.34199280 0.3153018 0.5129892 0.6306035 0.7608859
168 3.636364 0.80622580 0.9045340 0.9045340 0.6741999 0.9244163
169 3.400000 0.65828060 0.6749486 0.7071068 0.7071068 1.5776213
170 3.285714 0.51589980 0.6321988 0.6566344 0.7608522 1.0738933
171 3.705882 0.91604894 0.9883070 0.9905718 0.7935313 1.1070847
172 2.187500 0.17078250 0.2500000 0.2500000 0.8164966 1.5585784
173 3.828571 1.23789690 1.2746887 1.2343487 0.8181477 1.0427823
174 3.357143 1.19542130 1.2606535 1.2589465 0.8462441 1.3666473
175 3.833333 0.58348596 0.5417078 0.7510676 0.8473185 1.0494995
176 3.566667 1.06986810 1.2103504 1.0726652 0.8656989 1.1404232
177 3.466667 1.34518540 1.5055453 1.4573296 0.9154754 1.1872337
178 3.369565 0.98589080 1.1070699 0.9997584 0.9335403 1.1226694
179 3.692308 1.16161910 1.1929279 1.2557560 0.9540736 1.1094004
180 2.740741 1.05611770 1.2854655 1.0912759 0.9622504 1.1298654
181 3.483871 1.24482120 1.4465258 1.2622509 0.9631880 1.1509697
182 3.281250 1.29271770 1.6051831 1.2536238 0.9954534 1.3009767
183 3.590909 0.95940320 1.0413528 0.9847319 0.9989172 0.7341397
184 3.500000 0.96416175 1.0486219 1.0860975 1.0116963 1.1832160
185 4.714286 1.00227010 1.4459976 1.0787198 1.0269106 0.4879500
186 3.659574 1.21826220 1.3112807 1.2342522 1.0355666 1.1087909
187 3.241935 1.17516610 1.3203248 1.2208527 1.0366117 1.1878850
188 2.923077 1.12944280 1.3634421 1.0127394 1.0500305 1.3204506
189 3.950000 1.26569100 1.5035047 1.2607433 1.0513150 0.9986833
190 4.266667 0.83037110 1.0467885 0.7006621 1.0701221 0.9802650
191 4.086957 1.54925720 1.5463843 1.6502485 1.0724727 0.6683115
192 2.870968 1.07787720 1.2460408 1.0937059 1.0825279 1.1232837
193 3.761905 0.66619470 0.8025077 0.7066960 1.0876244 0.8499505
194 2.708333 1.26548390 1.3014763 1.2846643 1.1293194 1.1970677
195 4.272727 1.64970860 1.7101507 1.6811168 1.2057554 1.1621744
196 3.833333 0.81067690 1.2431631 0.5149286 1.2060454 1.2673044
197 2.586207 1.33463480 1.4081416 1.3674647 1.2504032 1.0527936
198 3.100000 1.30290100 1.4568627 1.3425532 1.2779128 1.2152872
199 2.957447 1.24308870 1.3771770 1.2936610 1.3114591 1.3180593
200 3.307692 1.21694387 1.3732131 1.2459458 1.5946339 1.4366985
201 2.900000 0.18445101 0.0000000 0.3689020 0.5922892 1.3222238
202 3.333333 1.21797200 1.2776357 1.2718675 0.6642112 0.8164966
203 3.650000 1.38419940 1.3968564 1.4405203 0.7223151 1.2258188
204 3.333333 0.63296210 0.7762500 0.6405126 0.7679476 1.3228757
205 2.846154 1.21818480 1.1821319 1.3008873 0.8006408 0.9870962
206 2.444444 1.30390310 1.4652846 1.2935233 0.8023658 1.2472191
207 3.181818 0.15075567 0.3015113 0.0000000 0.8090398 1.4012981
208 4.043478 0.84238670 1.0228166 0.8086075 0.8236878 1.2239378
209 3.200000 1.46671000 1.6124516 1.3557637 0.8451543 1.3201731
210 3.320000 0.43493295 0.5228129 0.4760952 0.8698659 1.2819256
211 3.142857 1.46547570 1.6704718 1.3540064 0.8701396 1.1952286
212 3.047619 0.21630646 0.0000000 0.4326129 0.8817078 1.2484601
213 3.000000 0.59375840 0.7472827 0.6435197 0.8935499 1.3070323
214 2.909091 1.12815210 1.3003496 1.0954451 0.8944272 1.2210279
215 2.904762 0.31802452 0.2668803 0.5547002 0.9073929 1.3749459
216 3.028571 1.42965700 1.5773357 1.4431156 0.9079231 1.3169866
217 3.228571 1.20101500 1.4242793 1.2209653 0.9102590 1.2622509
218 3.107143 0.91612536 1.1733914 0.9364012 0.9151166 1.3968029
219 2.961538 0.80676025 1.2058288 0.6064784 0.9222661 1.1482428
220 3.642857 0.91504186 0.9164863 1.0408330 0.9371803 0.9440892
221 3.354839 0.60810500 0.6139169 0.7084447 0.9603898 1.4270806
222 3.346154 1.22798060 1.4991179 1.1379690 0.9670497 1.1642099
223 2.796610 1.15508210 1.2557641 1.2337789 0.9723844 1.1563865
224 3.894737 1.19394220 1.4423487 1.0640912 0.9733285 1.1806886
225 3.357143 0.91161615 1.1411388 0.9376145 0.9749613 1.2774459
226 3.896552 1.27813170 1.6822750 1.1838403 0.9775812 1.2913124
227 2.851064 1.00320000 1.1715584 1.0413763 0.9784634 1.3984265
228 3.882353 0.55901700 0.6805570 0.5871429 0.9787210 1.1114379
229 2.722222 1.42218820 1.5039630 1.5321942 0.9952267 1.2274103
230 3.375000 1.18693470 1.4667249 1.1137256 1.0076629 1.3716451
231 4.000000 1.39136530 1.5566236 1.4366985 1.0127394 1.2472191
232 3.611940 1.03199600 1.0770834 1.1120002 1.0139239 1.5270810
233 3.000000 1.01667380 1.2681432 1.2163602 1.0145145 1.3228757
234 2.875000 1.03077640 0.9195587 1.3585243 1.0145993 1.1474610
235 3.363636 0.89157915 0.9021379 1.0455016 1.0192944 1.3471507
236 2.812500 1.22304260 1.3647344 1.2500000 1.0246951 1.0468206
237 2.812500 1.22304260 1.3647344 1.2500000 1.0246951 1.0468206
238 3.200000 1.01596430 1.1624764 1.0496223 1.0301293 1.2319282
239 2.650794 0.97440100 1.0814835 1.0152612 1.0386036 1.2202423
240 3.645161 1.24819200 1.3233520 1.3578282 1.0427823 1.1704241
241 2.281250 1.31053040 1.3897667 1.3526408 1.0429293 1.1139692
242 3.810345 1.23102660 1.4605106 1.1826534 1.0436626 1.4244112
243 3.350000 1.01653000 1.1212238 1.0910895 1.0442587 1.2258187
244 3.000000 1.21465170 1.2880570 1.1934163 1.0552897 1.1832160
245 3.333333 1.35847510 1.4588635 1.3809673 1.0574412 1.2841818
246 3.000000 0.62568640 0.9492623 0.5345225 1.0716117 1.0377490
247 3.028571 1.21248590 1.5020311 1.1524100 1.0723805 1.3169866
248 2.700000 1.22927260 1.2866839 1.2516656 1.0749677 1.2516656
249 3.413793 0.76263310 1.0618786 0.7738544 1.0806554 0.9826074
250 4.117647 0.72571800 0.6782330 0.9183318 1.0847427 1.2187264
251 2.343750 1.33853150 1.4601822 1.3617468 1.1041826 1.1247760
252 2.333333 1.29379800 1.4996706 1.3082287 1.1051443 1.0846523
253 2.122807 0.97855616 1.2413160 0.9438567 1.1057107 1.2965638
254 3.078431 0.84032700 0.8403270 0.7948120 1.1271381 1.2139710
255 3.341463 1.20162490 1.2326850 1.2892615 1.1348149 1.2963363
256 3.076923 1.13933180 1.1266014 1.1821319 1.1435437 1.4411534
257 2.787234 1.20562260 1.2873383 1.2225878 1.1468364 1.2146957
258 3.303030 1.17944840 1.3342800 1.1256311 1.1489455 1.3574988
259 2.950000 1.30686450 1.5525870 1.1697953 1.1516578 1.1459310
260 4.153846 0.31521258 0.2773501 0.4385290 1.1657506 1.2810252
261 2.285714 1.25680650 1.3535886 1.2408033 1.1694644 1.3385315
262 3.050000 1.15849270 1.2732057 1.1876558 1.1742859 1.1459310
263 3.615385 1.20488770 1.3245324 1.2139540 1.1818465 1.1148610
264 2.978723 1.13765860 1.3147594 1.1938400 1.1865233 1.1700866
265 2.950000 1.17703720 1.2883571 1.2460823 1.2062056 1.1972190
266 3.891304 1.15064310 1.3034491 1.1686087 1.2412962 1.0160547
267 2.350877 1.35781870 1.5355030 1.2970470 1.2746320 1.2318863
268 4.090909 1.14724730 1.2004901 1.1472473 1.3117119 1.0444659
269 3.724138 1.34645130 1.5297810 1.3565507 1.3235272 1.2217245
270 3.692308 1.31558700 1.3301244 1.3445045 1.3634421 1.1094004
271 3.173913 1.25822410 1.4054784 1.1838403 1.3753638 1.0724727
272 2.962963 1.30506780 1.3645765 1.3491468 1.4054784 1.2241632
273 4.181818 1.64869094 1.6124516 1.8090681 1.4206273 0.9816498
274 2.090909 1.13066760 1.4433757 1.3026779 1.4222262 0.8312094
275 2.444444 1.36362650 1.4741786 1.4652846 1.4245742 1.3382263
276 3.000000 1.06904500 1.4864467 1.0997835 1.4375906 1.4142136
277 4.240000 0.16583124 0.0000000 0.3316625 0.5000000 0.8793937
278 3.000000 1.02198060 0.8755950 1.3374935 0.5270463 1.3333333
279 3.250000 0.59646390 0.4385290 0.8697185 0.7250111 1.1381804
280 2.914894 1.11129090 1.2131716 1.1661270 0.7362680 1.4269120
281 3.000000 1.45539750 1.6624188 1.3483997 0.9045340 1.4832397
282 3.588235 1.37466570 1.5550886 1.4061025 0.9217772 0.9393364
283 2.904762 1.19557330 1.4359334 1.1169687 0.9283883 1.0442587
284 3.459459 0.99885650 0.9160461 1.1305596 0.9358023 1.1924437
285 3.961538 0.79534630 0.8083372 0.9721501 0.9603898 0.8708970
286 3.407407 0.09622505 0.0000000 0.1924501 0.9798541 1.3376000
287 3.000000 0.73340220 0.6741999 0.8876254 0.9847319 1.6514456
288 3.850000 1.27009100 1.4238233 1.2581050 1.0110501 1.1220403
289 2.302326 1.20064120 1.3527498 1.2047948 1.0139335 0.9888638
290 3.656250 0.70710677 0.6946508 0.8432740 1.0642085 1.0957211
291 2.607843 1.06251160 1.2539247 1.0757475 1.0772081 1.2973578
292 2.320000 1.40084460 1.4225526 1.4255729 1.0944631 1.3453624
293 3.352941 1.23073390 1.3284223 1.2277430 1.1114379 1.2718675
294 3.366667 1.08860350 1.2452207 1.0618786 1.1121068 1.2726116
295 3.272727 1.40453820 1.5666989 1.3684763 1.1200649 1.4893562
296 2.470588 0.91454744 0.9393364 1.1599949 1.1726039 1.2307339
297 2.733333 1.09883430 1.3442329 1.0482052 1.2169036 1.2339054
298 3.421053 1.27296710 1.2852322 1.4227760 1.2178386 1.0813300
299 2.884615 1.02731920 1.3547637 0.9583640 1.2434443 1.4234303
300 4.068966 1.34365870 1.4418106 1.3993313 1.2614012 1.3074248
301 2.250000 1.35637750 1.4390636 1.4078071 1.2688132 1.0823902
302 2.875000 1.14336860 1.3102163 1.0935416 1.3400871 1.3102163
303 1.900000 1.07496770 1.3165612 0.9660918 1.3703203 1.1005049
304 2.714286 1.19580300 1.2924124 1.1507283 0.5135526 1.2043875
305 4.000000 0.28946713 0.2672612 0.3631365 0.5345225 1.1766968
306 3.416667 1.49443412 1.4298407 1.6329932 0.6992059 1.3540064
307 2.769231 1.24163870 1.5275252 1.0801234 0.8006408 1.4232502
308 2.909091 1.15009880 1.2060454 1.2135598 0.8090398 1.1361818
309 3.055556 0.76706850 0.8148421 0.8938234 0.8098583 1.1697239
310 3.593750 0.87399140 1.0957211 0.8775883 0.8327955 1.5420844
311 3.900000 0.78881064 0.6992059 0.6324555 0.8432740 1.2866839
312 3.894737 0.20118695 0.3585686 0.2182179 0.8728716 1.1969747
313 2.500000 1.32916010 1.5811388 1.4181365 0.8755950 0.9258201
314 3.500000 1.11464080 1.6422453 1.0552897 0.9003366 1.1677484
315 3.666667 1.26585190 1.3557637 1.2909944 0.9102590 1.5886502
316 3.133333 0.34287268 0.4112002 0.4658123 0.9206548 1.2720778
317 2.919355 1.06368230 1.1638203 1.2366939 0.9261587 1.1205734
318 3.348837 1.09459510 1.0766296 1.2070640 0.9339917 1.3252802
319 2.600000 1.02198060 1.3703203 1.3984118 0.9486833 1.3498971
320 3.114286 1.38551180 1.5743479 1.3333333 0.9803627 1.2312459
321 3.357143 0.79432510 0.9611501 0.7988086 1.0000000 1.4468609
322 3.093750 1.03954090 1.2374369 1.0544644 1.0080323 1.4448881
323 2.952381 0.91539320 0.8979555 1.0650762 1.0137396 1.2835961
324 4.000000 1.11987540 1.1411388 1.2043876 1.0271052 1.0377490
325 3.750000 1.41153260 1.8090681 1.1934162 1.0730867 0.7537783
326 2.741935 1.17564420 1.2529535 1.2759142 1.0766335 1.2101719
327 3.863636 0.86366886 0.8329709 1.0494995 1.0901403 1.0371873
328 3.285714 0.94998010 1.0615526 0.9623598 1.0923286 1.1818737
329 4.160000 0.63116350 0.8121526 0.5728554 1.0956314 0.8417668
330 3.636364 1.13618180 1.3618170 1.3684763 1.1037128 1.5015144
331 3.421053 0.71838840 0.7723284 0.8200699 1.1160708 1.5024347
332 3.000000 1.41317940 1.5949482 1.4749368 1.1239030 1.1547005
333 3.092593 1.04803190 1.1538863 1.1036508 1.1498066 1.2017051
334 3.030303 1.29796560 1.4367224 1.3644976 1.1516090 1.1315048
335 2.769231 1.34008700 1.3768926 1.3647344 1.1528949 1.4232502
336 4.000000 1.30558240 1.4832397 1.3483997 1.2210279 0.8944272
337 3.184211 1.00277390 1.0135446 1.0917505 1.2239198 1.3326516
338 3.444444 1.15778930 1.3645163 1.1608700 1.2382784 1.0416176
339 3.200000 0.92646280 1.1005049 0.9189366 0.3162278 1.5491933
340 4.600000 0.24152295 0.3162278 0.4216370 0.3162278 0.6992059
341 4.647059 0.41322106 0.5144958 0.3233808 0.5745131 0.6063391
342 4.200000 0.33747430 0.4216370 0.3162278 0.6666667 0.6324555
343 3.875000 1.54650140 1.5776213 1.7288403 0.6749486 1.3562027
344 3.437500 1.44769930 1.5370426 1.4127397 0.7187953 1.0935416
345 3.187500 0.57373047 0.6191392 0.5773503 0.8164966 0.9810708
346 4.250000 1.64654520 1.7126977 1.6465452 0.8232726 0.8864053
347 3.000000 1.48644670 1.5886502 1.4242793 0.9411239 1.4638501
348 3.034483 0.96042377 1.2614012 0.9001916 0.9813532 1.0850529
349 2.625000 0.68630000 0.7172800 0.8297000 1.0072200 1.0959400
350 3.363636 1.30905940 1.4893562 1.2210279 1.0357255 0.6741999
351 3.636364 0.80750000 0.9625004 0.9714540 1.0568269 1.3988245
352 2.966102 1.37152520 1.4525821 1.4169220 1.0669052 1.3641481
353 3.428571 0.80622580 1.0757057 0.7464200 1.0712698 1.0281745
354 2.825000 1.14243270 1.2315400 1.2074394 1.0734965 1.0594508
355 2.000000 1.43745890 1.5050420 1.4034589 1.1381804 1.4142136
356 2.727273 1.67738970 1.7002674 1.7529196 1.1677484 1.4206273
357 2.823529 1.14777600 1.2363048 1.2610817 1.2119016 1.1407225
358 2.906977 0.97585590 1.0081791 1.0534049 1.2176242 1.1508579
359 2.200000 1.02198060 1.1005049 1.1972190 1.2292726 1.1352924
360 2.562500 1.18241190 1.3593477 1.1726039 1.2740441 1.3149778
361 2.555556 1.32958880 1.4935760 1.2787993 1.3397283 1.4232502
362 3.411765 1.54842470 1.5537972 1.6917165 1.4309504 1.0036697
363 2.533333 1.28822500 1.3345233 1.3557637 1.4474937 1.1254629
364 2.700000 1.20761480 1.4757296 1.0593499 1.5634719 0.9486833
365 2.545455 1.37510340 1.5782614 1.3003496 1.6180797 1.6348478
366 2.272727 0.91701096 0.9244163 1.0357255 1.6292776 1.4206273selected_data <- Rateprof[, c("quality", "helpfulness", "clarity", "easiness", "raterInterest")]
pairs(selected_data)
According to the scatter plot matrix of average professor evaluations for the themes of quality, clarity, helpfulness, easiness, and rater interest, the variables quality, clarity, and helpfulness appear to have substantial positive connections. Helpfulness, clarity, and quality appear to have a significantly less positive link with variable ease. Rater interest does not appear to be related to any of the other factors. As a result, we may conclude that Quality, helpfulness, and clarity have the most obvious linear links with one another, although Easiness and raterInterest do not appear to have linear ties with the other factors.
Question 5:
For the student.survey data file in the smss package, conduct regression analyses relating (by convention, y denotes the outcome variable, x denotes the explanatory variable) (i) y = political ideology and x = religiosity, (ii) y = high school GPA and x = hours of TV watching. (You can use ?student.survey in the R console, after loading the package, to see what each variable means.) (a) Graphically portray how the explanatory variable relates to the outcome variable in each of the two cases (b) Summarize and interpret results of inferential analyses.
Answer:
data(student.survey)
student.survey subj ge ag hi co dh dr tv sp ne ah ve pa pi
1 1 m 32 2.2 3.5 0 5.00 3.0 5 0 0 FALSE r conservative
2 2 f 23 2.1 3.5 1200 0.30 15.0 7 5 6 FALSE d liberal
3 3 f 27 3.3 3.0 1300 1.50 0.0 4 3 0 FALSE d liberal
4 4 f 35 3.5 3.2 1500 8.00 5.0 5 6 3 FALSE i moderate
5 5 m 23 3.1 3.5 1600 10.00 6.0 6 3 0 FALSE i very liberal
6 6 m 39 3.5 3.5 350 3.00 4.0 5 7 0 FALSE d liberal
7 7 m 24 3.6 3.7 0 0.20 5.0 12 4 2 FALSE i liberal
8 8 f 31 3.0 3.0 5000 1.50 5.0 3 3 1 FALSE i liberal
9 9 m 34 3.0 3.0 5000 2.00 7.0 5 3 0 FALSE i very liberal
10 10 m 28 4.0 3.1 900 2.00 1.0 1 2 1 FALSE i slightly liberal
11 11 m 23 2.3 2.6 253 1.50 10.0 15 1 1 FALSE r slightly conservative
12 12 f 27 3.5 3.6 190 3.00 14.0 3 7 0 FALSE d liberal
13 13 m 36 3.3 3.5 245 1.50 6.0 15 12 5 FALSE d very liberal
14 14 m 28 3.2 3.2 500 6.00 3.0 10 1 2 FALSE i moderate
15 15 f 28 3.0 3.5 3500 1.00 4.0 3 1 0 FALSE d very liberal
16 16 f 25 3.8 3.3 210 10.00 7.0 6 1 0 FALSE i liberal
17 17 f 41 4.0 3.0 1000 15.00 6.0 7 3 10 FALSE i slightly liberal
18 18 m 50 3.8 3.8 0 3.00 5.0 9 6 10 FALSE d liberal
19 19 m 71 4.0 3.5 5000 3.00 6.0 12 2 2 FALSE i liberal
20 20 f 28 3.0 3.8 120 1.00 25.0 0 0 2 FALSE d very liberal
21 21 f 26 3.7 3.7 8000 8.00 4.0 4 4 1 FALSE i moderate
22 22 f 27 4.0 3.7 2 2.50 4.0 2 7 0 FALSE i liberal
23 23 m 31 2.7 3.5 1700 5.00 7.0 7 2 0 FALSE r very conservative
24 24 f 23 3.7 3.7 2 2.00 7.0 4 2 0 FALSE i moderate
25 25 m 23 3.2 3.8 450 4.00 0.0 7 7 3 FALSE i very liberal
26 26 f 44 3.0 3.0 0 2.00 2.0 3 2 3 FALSE i slightly liberal
27 27 m 26 3.7 3.0 1000 3.00 8.0 2 7 0 FALSE d liberal
28 28 f 31 3.7 3.8 850 10.00 10.0 3 7 0 FALSE r slightly conservative
29 29 m 24 3.3 3.1 420 2.00 10.0 6 5 0 FALSE d moderate
30 30 f 26 3.3 3.3 1200 0.75 10.0 0 3 0 FALSE r liberal
31 31 m 26 3.3 3.5 1000 1.50 0.0 3 3 3 FALSE d liberal
32 32 f 32 3.5 3.9 150 12.00 10.0 2 0 0 FALSE d liberal
33 33 m 26 3.4 3.4 2000 1.50 2.0 7 14 0 FALSE d liberal
34 34 f 22 3.2 2.8 316 2.00 10.0 3 5 2 FALSE i liberal
35 35 f 24 3.5 3.9 900 1.75 8.0 0 0 1 FALSE d very liberal
36 36 m 24 3.6 3.3 250 2.00 4.0 6 3 1 FALSE r slightly conservative
37 37 m 23 3.8 3.7 180 0.50 10.0 5 7 0 FALSE i liberal
38 38 m 33 3.4 3.4 6000 1.50 8.0 5 6 2 FALSE i liberal
39 39 m 23 2.8 3.2 950 2.00 37.0 10 5 0 FALSE r slightly conservative
40 40 m 31 3.8 3.5 1100 0.75 0.5 3 5 2 FALSE r conservative
41 41 m 26 3.4 3.4 1300 1.20 0.0 8 2 0 FALSE i liberal
42 42 m 28 2.0 3.0 360 0.25 10.0 8 3 0 FALSE d slightly liberal
43 43 f 24 3.8 3.9 1800 2.00 2.0 5 4 1 FALSE r conservative
44 44 m 23 3.0 3.6 900 15.00 12.0 0 5 0 FALSE r slightly conservative
45 45 f 25 3.0 4.0 5000 5.00 1.5 0 4 0 FALSE i moderate
46 46 f 24 3.0 3.5 300 1.00 10.0 5 5 0 FALSE d liberal
47 47 f 27 3.0 3.8 2000 20.00 28.0 7 14 2 FALSE r slightly liberal
48 48 m 24 3.3 3.8 630 1.30 2.0 3 5 0 FALSE r very conservative
49 49 f 26 3.8 4.0 1200 1.00 0.0 4 3 1 FALSE d liberal
50 50 f 27 3.0 4.0 580 2.00 5.0 15 1 2 FALSE d very liberal
51 51 m 32 3.0 3.0 2000 5.00 5.0 5 2 1 FALSE r slightly conservative
52 52 f 41 4.0 4.0 0 8.00 8.0 4 2 2 FALSE r moderate
53 53 f 29 3.0 3.9 300 3.70 2.0 5 1 11 FALSE d liberal
54 54 f 50 3.5 3.8 6 6.00 7.0 3 7 0 FALSE d liberal
55 55 f 22 3.4 3.7 80 7.00 10.0 1 2 2 FALSE i liberal
56 56 f 23 3.6 3.2 375 1.50 5.0 10 5 0 FALSE r conservative
57 57 m 26 3.5 3.6 2000 0.30 16.0 8 3 0 FALSE d moderate
58 58 m 30 3.0 3.0 1 1.10 1.0 4 3 0 FALSE i slightly liberal
59 59 f 23 3.0 3.0 112 0.50 15.0 3 3 0 FALSE i moderate
60 60 f 22 3.4 3.0 650 4.00 8.0 16 7 1 FALSE i moderate
re ab aa ld
1 most weeks FALSE FALSE FALSE
2 occasionally FALSE FALSE NA
3 most weeks FALSE FALSE NA
4 occasionally FALSE FALSE FALSE
5 never FALSE FALSE FALSE
6 occasionally FALSE FALSE NA
7 occasionally FALSE FALSE FALSE
8 occasionally FALSE FALSE FALSE
9 occasionally FALSE FALSE NA
10 never FALSE FALSE FALSE
11 occasionally FALSE FALSE FALSE
12 occasionally FALSE FALSE NA
13 occasionally FALSE FALSE FALSE
14 occasionally FALSE FALSE FALSE
15 never FALSE FALSE FALSE
16 every week FALSE FALSE FALSE
17 every week FALSE NA FALSE
18 never FALSE FALSE FALSE
19 never FALSE FALSE FALSE
20 occasionally FALSE FALSE FALSE
21 occasionally FALSE FALSE FALSE
22 occasionally FALSE FALSE FALSE
23 every week FALSE FALSE FALSE
24 never FALSE FALSE FALSE
25 never FALSE FALSE FALSE
26 most weeks FALSE FALSE FALSE
27 occasionally FALSE FALSE NA
28 most weeks FALSE FALSE FALSE
29 occasionally FALSE FALSE NA
30 occasionally FALSE FALSE NA
31 occasionally FALSE FALSE FALSE
32 occasionally FALSE FALSE FALSE
33 never FALSE FALSE FALSE
34 occasionally FALSE FALSE NA
35 occasionally FALSE FALSE NA
36 every week FALSE FALSE FALSE
37 never FALSE FALSE NA
38 never FALSE FALSE FALSE
39 most weeks FALSE FALSE FALSE
40 most weeks FALSE FALSE NA
41 occasionally FALSE FALSE FALSE
42 never FALSE FALSE NA
43 every week FALSE FALSE FALSE
44 never FALSE FALSE FALSE
45 occasionally FALSE FALSE FALSE
46 never FALSE FALSE FALSE
47 occasionally FALSE FALSE FALSE
48 every week FALSE FALSE FALSE
49 never FALSE FALSE FALSE
50 occasionally FALSE FALSE FALSE
51 every week FALSE FALSE FALSE
52 occasionally FALSE FALSE FALSE
53 occasionally FALSE FALSE FALSE
54 occasionally FALSE FALSE NA
55 never FALSE FALSE NA
56 every week FALSE FALSE FALSE
57 occasionally FALSE FALSE NA
58 every week FALSE FALSE FALSE
59 most weeks FALSE FALSE FALSE
60 occasionally FALSE FALSE FALSE(i)
## plot(student.survey$re, student.survey$pi, main="Political Ideology vs Religiosity", xlab="Religiosity", ylab="Political Ideology")
student.survey %>%
select(c(pi, re)) %>%
ggplot() +
geom_bar(aes(x = re, fill = as.factor(pi)), position = "dodge") +
xlab("Religiosity") +
ylab("Political Ideology") +
scale_fill_manual(values = c("#FF0000", "#FF8000", "#FFFF00", "#80FF00", "#00FF00", "#00FF80", "#00FFFF", "#0080FF", "#0000FF", "#8000FF", "#FF00FF", "#FF0080")) +
labs(fill = "Political Ideology")
Religiosity and political ideology seem to have a positive relationship.
(ii)
student.survey %>%
select(tv, hi) %>%
ggplot(aes(x = tv, y = hi)) +
geom_point(color = "steelblue", alpha = 0.6) +
geom_smooth(method = "lm", se = FALSE, color = "red", linetype = "solid", size = 1) +
labs(title = "High School GPA vs Hours of TV Watching",
x = "Hours of TV Watching",
y = "High School GPA") +
theme_minimal() +
theme(panel.grid.major = element_line(color = "gray", linetype = "dotted"))Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.`geom_smooth()` using formula = 'y ~ x'
High school GPA and TV-watching appear to have a negative relationship.
(a)
model1 <- lm(as.numeric(pi) ~ as.numeric(re), data=student.survey)
summary(model1)
Call:
lm(formula = as.numeric(pi) ~ as.numeric(re), data = student.survey)
Residuals:
Min 1Q Median 3Q Max
-2.81243 -0.87160 0.09882 1.12840 3.09882
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.9308 0.4252 2.189 0.0327 *
as.numeric(re) 0.9704 0.1792 5.416 1.22e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.345 on 58 degrees of freedom
Multiple R-squared: 0.3359, Adjusted R-squared: 0.3244
F-statistic: 29.34 on 1 and 58 DF, p-value: 1.221e-06There is a statistically significant link between religion and political ideology at a significance level of 0.01. The association is modest and positive, implying that as weekly church attendance grows, political ideology shifts toward the right.
(b)
model2 <- lm(as.numeric(hi) ~ as.numeric(tv), data=student.survey)
summary(model2)
Call:
lm(formula = as.numeric(hi) ~ as.numeric(tv), data = student.survey)
Residuals:
Min 1Q Median 3Q Max
-1.2583 -0.2456 0.0417 0.3368 0.7051
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.441353 0.085345 40.323 <2e-16 ***
as.numeric(tv) -0.018305 0.008658 -2.114 0.0388 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.4467 on 58 degrees of freedom
Multiple R-squared: 0.07156, Adjusted R-squared: 0.05555
F-statistic: 4.471 on 1 and 58 DF, p-value: 0.03879There is a negative relationship between weekly TV viewing hours and high school GPA, with a slope of -0.018, indicating that as weekly TV viewing hours increase, a student’s GPA tends to fall. At a significance threshold of 0.05, there is a statistically significant association between weekly television viewing and GPA. The R-squared value, however, is close to zero, indicating that the regression model does not make a strong forecast for the observed variables. This is not surprising given that there does not appear to be a linear trend in the data when looking at the scatter plot with hours of television viewed and GPA.