[SOLVED] Problem set 2 soc-ga 2332 intro to stats

Load multiple packages to your environment using the following code (you can add more packages to the
current list as per your need):
knitr::opts_chunk$set(echo = TRUE)
library(pacman)
p_load(tidyverse, foreign, corrplot, stargazer, coefplot, effects)This week, we will begin familiarizing ourselves with the replication exercise. Download and save the paper
that we will be replicating. Make sure to download and save the Online Appendix (you will find it on the
ASR website).1. Read the paper closely and respond to the following questions:(a) What are the authors’ research questions?
(b) What is the gap in the literature that the authors aim to fill? How does their analysis advance the
literature?(c) What is the population that they are making inferences about? Be specific and make sure to identify
the geographical region that they are focusing on, the time period, demographic characteristics, and so on.(d) Do they have data on all individuals in the population? If they don’t, how do they solve this?
(e) Did the authors collect the data themselves? If they did, describe their sampling procedure. If they
didn’t, identify and describe the data source and discuss the sampling procedure that was used to
collect this data.2. As you read the text, make a list of all variables or characteristics of the population that
the authors mention throughout the paper (e.g., gender, age, wages, occupation, . . . ). Submit
a list with all the variables and characteristics that you have identified in the text. Note: Make
sure to read footnotes and table notes; they contain important information to understand who is in the
sample.3. Based on your answers to prior questions, select the samples and variables that you think
you will need to replicate the paper in your IPUMS account. Submit a screenshot of the page
where you can see the samples and variables that you have selected. Note: you can obtain this
from your “Data Cart”.Import the dataset sat_math.dta to your R environment and examine the effect of IQ and other variables
on SAT math score. Hint: use read.dta()
Variable Name Variable Detail
sat_math SAT Math Score
female The Female Dummy (Male = 0)
black/other Two Racial Dummies (White as the Reference Group)
meduy Mother’s Years of Schooling
feduy Father’s Years of Schooling
hours Average Weekly Study Hours
IQ IQ Score (0 to 100)1. Report descriptive statistics:
(a) Create a table that reports descriptive statistics (you should at least report the means) of all the
variables grouped by gender. Its structure should look similar to the “1970” column of Table A1a in
the replication paper, except that we are using gender instead of race as the grouping variable.Note:
You can either use tidyverse (group_by() and summarise) then transpose the table, or search other
R packages that can generate descriptive statistics table for you. At this point, don’t worry too much
about the specific formatting issues of the table. In practice, we will format the table in LaTeX instead
of R Markdown.(b) Create a correlation matrix and display it. Then visualize the matrix using any one plot option
that you think can effectively communicate the result from the corrplot package as demonstrated in
this webpage.2. Create scatter plots:
• Besides the key dependent variable (DV) sat_math, choose one numeric independent variable (IV) that
seems to have a meaningful relation to the DV based on the correlation matrix you created, and then
create the following plots. Note: Make sure to add appropriate titles, axis labels, and plot legend for
each plot.(a) A scatter plot of the DV and IV
(b) A scatter plot of the DV and IV with a fitted linear regression line
(c) A scatter plot of the DV and IV, and each observation is color coded by gender (make sure to coerce
your gender variable to a character or factor using as.character() or as.factor(), or recode your
gender variable to a character variable with values “Male” and “Female” using mutate() and ifelse().)
(d) On top of plot (c), fit a linear regression line for each gender group, the lines should also be color coded3. Additional exploratory data analysis:
(a) What are your preliminary findings/reflections on the data based on the descriptive statistics, the
correlation matrix, and the scatter plots?
(b) What other exploratory data analysis will be useful for you to better understand the data before
modeling? Please implement some additional exploratory data analysis and discuss your preliminary
findings.4. Nested models:
• Build five nested models that use sat_math as the DV and report regression results in a table using
stargazer() from the stargazer package.Note: You can set type = “text” in stargazer() when
viewing the table in R, but before knitting to PDF you should set type = “latex”
(a) Model 1: Baseline (only add “IQ” as the independent variable)
(b) Model 2: Model 1 + Demographic Characteristics
(c) Model 3: Model 2 + Parental Education
(d) Model 4: Model 3 + Weekly Study Hours
(e) Model 5: Model 4 + An Interaction Between IQ and the Female Dummy5. For the result of Model 1:
(a) What are the hypotheses that you are testing in this model with your t-values in the (Intercept) and
IQ row of the modeling results?
(b) Create a 95% confidence interval for the parameter βIQ based on Model 1 result.6. Interpret regression coefficients:
(a) How does the coefficient of “IQ” change across models? What could be the possible reason(s) for such
changes?
(b) Interpret the coefficient of “black” in Model 4.(c) Interpret the coefficient of “meduy” in Model 4.
(d) Interpret the coefficient of the interaction effect between IQ and the Female Dummy in Model 5.7. Create a coefficient plot for Model 5 with appropriate title and labels.
8. On the basis of Model 5, by holding other variables at their means, create a figure demonstrating the predicted SAT math score by gender and IQ levels (with confidence interval).Part 3 (Bonus) Data Simulation
Simulation is a fun and effective way to learn about statistical inference. You will get a better understanding
of how each population parameter affects the shape of the distribution.Now that we have learned about how to identify interactions from a given sample, you can try simulate a
data whose true data generating process involves interaction between two variables. For example, you can try
to reproduce a similar scatter plot we saw in class (the right panel) by simulating a data whose variables
have such associations:Or, you can try to reproduce a scatter plot that demonstrates the Simpson’s Paradox:
Note: Your output does not need to replicate the exact layout of the example graphs. You will get extra
credit as long as you generate a similar graph that illustrates the relationship (either a positive or negative
interaction, or the Simpson’s Paradox) clearly. Remember to use set.seed() for any random process.