in this analysis, we will use data from the 2018 GSS to examine factors associated with income for people who were working full time and between ages 30 and 49 at the time of the survey. Please note this is a highly selective sample – only those working full time and aged 30-49 are included in the analysis.

The variables used in this analysis are:

• income: respondent’s income in $1,000
• age: respondent’s age in years
• educ: respondent’s education in years
• race: respondent’s race in 3 categories (White, Black, and Other)
• marital: respondent’s marital status in 3 categories (Current married, Never married, and Other)

1) We are interested to know if marital status is associated with income. Using the summary statistics provided in the table below. Interpret the 95% confidence intervals for Current Married and Never Married. Do they tell us whether there is a statistically significant difference between these two groups in their average income? Why or why not? (3 points)

2) We use ANOVA to assess if there are income difference across people with different marital statuses. Using the ANOVA results in the table below to answer the following questions.
a. What is the null hypothesis and the research hypothesis in this ANOVA analysis? (2 points)
b. There are three missing numbers (labelled with a/b/c) in the table. Fill them in – show your calculations. (3 points)
c. Calculated the R-squared for this ANOVA analysis. What does it tell you about the relationship between marital status and income variation? (2 points)
d. Cite number(s) from this ANOVA analysis to assess if the average income is different across three marital status groups. (2 points)

3) We are interested in understanding the relationship between racial identity and marital status. The cross-tabulation below shows the frequencies of marital status by race, and column-based percentages. Also included in the table (last row) is the result of the ${?}^2$ (chi2) test.
a. Based on the cross-tabulation, do you see a relationship between the two variables? Cite numbers from the table to support your argument. (2 points)
b. We can use chi-squared test to test if the relationship between two categorical variables are statistically significant. What is the null hypothesis for such a test, and what is the alternative hypothesis? Based on the ${?}^2$ test, what can we conclude about the relationship between racial identity and marital status. (3 points)

4) Age and education are known to affect income. The scatterplot and correlation matrixes below show the relationship across these three variables. Cite features in the graph or numbers in table to describe the relationships between age and income, and between education and income. Make sure that you talk about the direction and strength of each relationship.

5) We use simple regression model to investigate the effect of age on income. Interpret the model result by answering the following questions.
a. Explain the effect of age on income. Is it statistically significant? What is the null hypothesis? (2 points)
b. Explain the intercept. Is it meaningful in this case? (2 points)
c. Explain the R-squared. What does it tell you about the relationship between age and income? (2 points)

6) We use multiple regression model to investigate the effects of age, education, and marital status on income. Interpret the model results by answering the following questions.
a. Explain the effect of age on income. Is it statistically significant? What is the null hypothesis? (2 point)
b. Why is the age effect not the same in this model as in the simple regression model above? (1 point)
c. Explain the effects of marital status on income. Please note the omitted (reference) category is “current married”. (4 point)
d. Explain the intercept. Is it meaningful in this case? (2 point)
e. Explain the R-squared. What does it tell us about the model? (2 point)
f. Explain the F-test. What does it tell us about the model? (2 point)