Q. 4 (26 points) We will use the dataset, "kidiq.csv" that was used in Assignment 2 to model the children's test scores. Here is the description of all variables:

kid_score Child's IQ score mom_hs Indicator for whether the mother has a high school degree mom_iq Mother's IQ score mom_work 1 = did not work in first three years of child's life 2 = worked in 2nd or 3rd year of child's life 3 = worked part-time in first year of child's life 4 = worked full-time in first year of child's life mom_age Mother's age

(a) (2 pts) We start by modeling the children's test scores given an indicator for whether the mother graduated from high school (coded as 1) or not (coded as 0). Interpret the estimated intercept and the slope. (b) (3 pts) We consider a linear regression of child test scores on two predictors: the maternal high school indicator and maternal IQ. Interpret the estimated intercept, the coefficient of maternal high school completion, and the coefficient of maternal IQ. (c) (9 pts) We include interaction term between two predictors. Interpret the esti- mated intercept, the coefficient of maternal high school completion, the coefficient of maternal IQ, and the coefficient on the interaction term. Write down two separate regression lines for children of mothers who completed high school and those whose mothers did not. Plot these two lines on the scatter plot of test scores and mother's IQ scores. (d) (2 pts) Test whether the slopes relating mother's IQ to child test scores depends on maternal high school indicator. (e) (10 pts) We will use all independent variables in the data set. Please note the description of variables. Construct a linear regression of child test scores on mom's high school indicator, mom's IQ score, and their interaction, mom's work status, and mom's age. Test whether mom's work status is a significant predictor with = 0.05. Test whether both mom's work status and mom's age are significant predictors with = 0.05.