Homework 3

hw3

desriptive statistics

probability

Template of course blog qmd file

Author

Xiaoyan

Published

April 5, 2023

Code

library(tidyr)
library(dplyr)


Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

Code

library(readxl)
library(ggplot2)
library(alr4)

Loading required package: car

Loading required package: carData


Attaching package: 'car'

The following object is masked from 'package:dplyr':

    recode

Loading required package: effects

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

Code

library(smss)
library(stargazer)


Please cite as:

 Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.

 R package version 5.2.3. https://CRAN.R-project.org/package=stargazer

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.

Identify the predictor and the response.

Code

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

predictor is ppgdp and response is fertility and birth rate.

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?

Code

ggplot(UN11, aes(ppgdp, fertility)) +
  geom_point()

straight line doesn’t fit for summary this graph.

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.

Code

ggplot(UN11, aes(ppgdp, fertility)) +
  geom_point()+scale_y_log10()+scale_x_log10()

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). (a) How, if at all, does the slope of the prediction equation change? the slope will also divided by 1.33 (b) How, if at all, does the correlation change? correlation will not change # 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.)

Code

head(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

Code

pairs(water)

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.

Code

head(Rateprof)

  gender numYears numRaters numCourses pepper discipline              dept
1   male        7        11          5     no        Hum           English
2   male        6        11          5     no        Hum Religious Studies
3   male       10        43          2     no        Hum               Art
4   male       11        24          5     no        Hum           English
5   male       11        19          7     no        Hum           Spanish
6   male       10        15          9     no        Hum           Spanish
   quality helpfulness  clarity easiness raterInterest sdQuality sdHelpfulness
1 4.636364    4.636364 4.636364 4.818182      3.545455 0.5518564     0.6741999
2 4.318182    4.545455 4.090909 4.363636      4.000000 0.9020179     0.9341987
3 4.790698    4.720930 4.860465 4.604651      3.432432 0.4529343     0.6663898
4 4.250000    4.458333 4.041667 2.791667      3.181818 0.9325048     0.9315329
5 4.684211    4.684211 4.684211 4.473684      4.214286 0.6500112     0.8200699
6 4.233333    4.266667 4.200000 4.533333      3.916667 0.8632717     1.0327956
  sdClarity sdEasiness sdRaterInterest
1 0.5045250  0.4045199       1.1281521
2 0.9438798  0.5045250       1.0744356
3 0.4129681  0.5407021       1.2369438
4 0.9990938  0.5882300       1.3322506
5 0.5823927  0.6117753       0.9749613
6 0.7745967  0.6399405       0.6685579

Code

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

In this five parameters, quality, Clarity and helpfulness are positively correlated. while easiness and raterinterest were not significantly related. # 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

Code

head(student.survey)

Error in head(student.survey): object 'student.survey' not found

Code

ggplot(data = student.survey, aes(x = re,fill=pi)) +
    geom_bar(position = "dodge" )

Error in ggplot(data = student.survey, aes(x = re, fill = pi)): object 'student.survey' not found

Code

ggplot(data = student.survey, aes(x = hi, y = tv)) +
    geom_point()

Error in ggplot(data = student.survey, aes(x = hi, y = tv)): object 'student.survey' not found

Summarize and interpret results of inferential analyses.