Homework - 3

hw3

desriptive statistics

probability

Homework 3

Author

Hannah Rosenbaum

Published

May 4, 2023

Question 1

Code

library(alr4)

Loading required package: car

Loading required package: carData

Loading required package: effects

lattice theme set by effectsTheme()
See ?effectsTheme for details.

Code

library(smss)

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data(UN11)

a

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head(UN11)

                region  group fertility   ppgdp lifeExpF pctUrban
Afghanistan       Asia  other     5.968   499.0    49.49       23
Albania         Europe  other     1.525  3677.2    80.40       53
Algeria         Africa africa     2.142  4473.0    75.00       67
Angola          Africa africa     5.135  4321.9    53.17       59
Anguilla     Caribbean  other     2.000 13750.1    81.10      100
Argentina   Latin Amer  other     2.172  9162.1    79.89       93

Code

summary(UN11)

        region      group       fertility         ppgdp         
 Africa    :53   oecd  : 31   Min.   :1.134   Min.   :   114.8  
 Asia      :50   other :115   1st Qu.:1.754   1st Qu.:  1283.0  
 Europe    :39   africa: 53   Median :2.262   Median :  4684.5  
 Latin Amer:20                Mean   :2.761   Mean   : 13012.0  
 Caribbean :17                3rd Qu.:3.545   3rd Qu.: 15520.5  
 Oceania   :17                Max.   :6.925   Max.   :105095.4  
 (Other)   : 3                                                  
    lifeExpF        pctUrban     
 Min.   :48.11   Min.   : 11.00  
 1st Qu.:65.66   1st Qu.: 39.00  
 Median :75.89   Median : 59.00  
 Mean   :72.29   Mean   : 57.93  
 3rd Qu.:79.58   3rd Qu.: 75.00  
 Max.   :87.12   Max.   :100.00

Code

pairs(UN11)

Predictor: ppgdp, Response: fertility

b

Code

plot(UN11$ppgdp, UN11$fertility)

No, a linear model will not fit this curve.

c

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plot(log(UN11$ppgdp), log(UN11$fertility))

Yes, a simple linear regression will fit this dataset much better.

Question 2

a

The slope will not change, but the y-intercept will increase.

b

The residuals will change.

Question 3

Code

data(water)

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summary(water)

      Year          APMAM            APSAB           APSLAKE     
 Min.   :1948   Min.   : 2.700   Min.   : 1.450   Min.   : 1.77  
 1st Qu.:1958   1st Qu.: 4.975   1st Qu.: 3.390   1st Qu.: 3.36  
 Median :1969   Median : 7.080   Median : 4.460   Median : 4.62  
 Mean   :1969   Mean   : 7.323   Mean   : 4.652   Mean   : 4.93  
 3rd Qu.:1980   3rd Qu.: 9.115   3rd Qu.: 5.685   3rd Qu.: 5.83  
 Max.   :1990   Max.   :18.080   Max.   :11.960   Max.   :13.02  
     OPBPC             OPRC           OPSLAKE           BSAAM       
 Min.   : 4.050   Min.   : 4.350   Min.   : 4.600   Min.   : 41785  
 1st Qu.: 7.975   1st Qu.: 7.875   1st Qu.: 8.705   1st Qu.: 59857  
 Median : 9.550   Median :11.110   Median :12.140   Median : 69177  
 Mean   :12.836   Mean   :12.002   Mean   :13.522   Mean   : 77756  
 3rd Qu.:16.545   3rd Qu.:14.975   3rd Qu.:16.920   3rd Qu.: 92206  
 Max.   :43.370   Max.   :24.850   Max.   :33.070   Max.   :146345

Code

pairs(water)

Pairs of higher correlation: APMAM & APSAB, APSAB & APSLAKE, OPBPC & OPRC, OPBPC & OPSLAKE, OPBPC & BSAAM, OPRC & OPSLAKE, OPRC & BSAAM, OPSLAKE & BSAAM

Question 4

Code

data(Rateprof)

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pairs(Rateprof[, c('quality', 'helpfulness', 'clarity', 'easiness', 'raterInterest')])

Quality, Helpfulness, and Clarity have a strong correlation. Easiness compared to the prior three has a weak relation. raterInterest has little correlation to the other four.

Question 5

Code

data("student.survey")
summary(student.survey)

      subj       ge           ag              hi              co       
 Min.   : 1.00   f:31   Min.   :22.00   Min.   :2.000   Min.   :2.600  
 1st Qu.:15.75   m:29   1st Qu.:24.00   1st Qu.:3.000   1st Qu.:3.175  
 Median :30.50          Median :26.50   Median :3.350   Median :3.500  
 Mean   :30.50          Mean   :29.17   Mean   :3.308   Mean   :3.453  
 3rd Qu.:45.25          3rd Qu.:31.00   3rd Qu.:3.625   3rd Qu.:3.725  
 Max.   :60.00          Max.   :71.00   Max.   :4.000   Max.   :4.000  
                                                                       
       dh             dr               tv               sp        
 Min.   :   0   Min.   : 0.200   Min.   : 0.000   Min.   : 0.000  
 1st Qu.: 205   1st Qu.: 1.450   1st Qu.: 3.000   1st Qu.: 3.000  
 Median : 640   Median : 2.000   Median : 6.000   Median : 5.000  
 Mean   :1232   Mean   : 3.818   Mean   : 7.267   Mean   : 5.483  
 3rd Qu.:1350   3rd Qu.: 5.000   3rd Qu.:10.000   3rd Qu.: 7.000  
 Max.   :8000   Max.   :20.000   Max.   :37.000   Max.   :16.000  
                                                                  
       ne               ah             ve          pa    
 Min.   : 0.000   Min.   : 0.000   Mode :logical   d:21  
 1st Qu.: 2.000   1st Qu.: 0.000   FALSE:60        i:24  
 Median : 3.000   Median : 0.500                   r:15  
 Mean   : 4.083   Mean   : 1.433                         
 3rd Qu.: 5.250   3rd Qu.: 2.000                         
 Max.   :14.000   Max.   :11.000                         
                                                         
                     pi                re         ab              aa         
 very liberal         : 8   never       :15   Mode :logical   Mode :logical  
 liberal              :24   occasionally:29   FALSE:60        FALSE:59       
 slightly liberal     : 6   most weeks  : 7                   NA's :1        
 moderate             :10   every week  : 9                                  
 slightly conservative: 6                                                    
 conservative         : 4                                                    
 very conservative    : 2                                                    
     ld         
 Mode :logical  
 FALSE:44       
 NA's :16

Code

fita <- lm(hi ~ tv, data=student.survey)
#fitb <- lm(pi ~ re, data=student.survey)

Code

summary(fita)


Call:
lm(formula = hi ~ 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 ***
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: 0.03879

Code

AIC(fita)

[1] 77.53632

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BIC(fita)

[1] 83.81935