PPOL 506
SPRING 2024 MIDTERM
Part 1: Conceptual and theoretical exam (50 points)
Use only handwritten notes on one, 8.5 by 11-inch piece of paper and a calculator to complete part 1 of the midterm. You must work by yourself. Show work if you want partial credit. If an answer is wrong and you do not show work, you will lose all points associated with the question.
Part 2: Computational exam (20 points)
You may use material from the class and outside material to complete part 2 of the midterm. You must work by yourself. You must submit your R code as well as your responses for full points.
Your final submission should have two parts: submission of R code and written answers. Your R code should be clean and run from start to finish without breaking. All R output/calculations included in your written answers should be in your R code upload file. Your written answers should be submitted as a doc or pdf file. This document should contain all answers. If you are asked to generate R output (tables, regressions, ANOVA, figures, etc.) these outputs should be included in your written submissions.
Question 1 (17 points)
The following regression output regresses annual weeks worked on age, an indicator for male, an indicator for married, a factor variable of education (bachelor’s degree or higher omitted category), and indicator for born in the United States. Using the regression output, answer the following questions.
a) What is the unit of analysis for this regression? (1 point)
b) What is the sample size for this regression? (1 point)
c) Write the prediction equation. Define each variable (outcome and explanatory) and specify the units. If a variable is binary or categorical, define each value. (4 points)
d) Conduct a hypothesis test for the estimated effect of age. Specify the hypotheses you are testing, calculate the test statistic, and draw a conclusion using either the test statistic critical value or associated p-value. Assume α = 0.05. (4 points)
e) Calculate a 95% confidence interval for the effect of age. Interpret. (3 points)
f) Conduct a global test of independence (i.e., test if any of the explanatory variables are statistically related to the outcome variable). Assume α = 0.05. Clearly write out the hypotheses, solve for the test statistic, and draw a conclusion. (4 points)
Question 2 (6 points)
An article reports results from a multivariate regression of climate change beliefs. The model used a response variable with a four-point scale in which climate change beliefs were scaled from 1 (climate change is not happening) to 4 (climate change, caused by human behavior, is happening). The explanatory variables used in the model include x1 = education (in years), x2 = age (in years), x3 = politically conservative (1=yes), x4 = religious fundamentalist (1=yes), and x5 = live in same city as when age 16 (1=yes). The prediction equation is as follows
Report the prediction equations for political conservatives and nonconservatives (you may assume all estimated relationships in the prediction equation are statistically significant). Interpret what these prediction equations suggest about the effect of education on climate change beliefs for those of differing political ideologies.
Question 3 (21 points)
A researcher is examining the effect of an affordable housing program on child mental health. Model 1 predicts the mental health score (values ranging from 1-10, higher values indicating poorer mental health) as a function of participation in the housing program (0=not in the housing program and 1=in the program, and race). Model 2 includes several additional explanatory variables and an interaction between the housing program and child’s race.
a) Why is the race/ethnicity category White omitted from the regression? (2 points)
b) Using Model 1, interpret the coefficients on Housing program and Black. Is the relationship between Housing program and Mental health score statistically significant? (4 points)
c) Using Model 1, what is the predicted mean mental health score for a White child from a family that participates in the affordable housing? How about for a Black child, a Latino child, and a child of other race? (4 points)
d) Using Model 2, what is the prediction equation for the child mental health score for a White child whose family participates in the affordable housing program? How about for a Black child whose family participates in the affording housing program? (4 points)
e) Using the partially created two-way ANOVA table and your knowledge of F-statistics, test the null hypothesis of identical mean mental health scores across race/ethnicity groupings (raceth) controlling for the affordable housing program (affordhouse). (4 points)
f) Using Model 2, interpret the coefficients on Housing program, Latino, and Number of children. (3 points)
Question 4 (6 points)
The following table reports the results of a two-way ANOVA test with an interaction. The response variable is Earned Income Tax Credit (measured in $). The factor variables include male (male=1, female=0) and married (married=1, not married=0).
a) Do the results of this test provide evidence for identical mean earned income tax credit dollars among men and women, controlling for marriage? Why or why not? (2 points)
b) Do the results of this test provide evidence that the size of the effect of marital status on the amount of earned income tax credit received varies by sex? Why or why not? (2 points)
c) Is there a significant interaction between sex and marital status on the amount of earned income tax credit received? (2 points)