Problem 1 A researcher wants to investigate the relationship between the annual income of a father (Fli) and the annual income of his oldest child (CI;) measured in thousands of dollars. Having collected that data on Fli, CI, their age differences (ADi), and the gender of the child (Gi = 1 if the child is a daughter and zero otherwise). The researcher estimates the following regressions assuming homoskedasticity: CI; = 3.62 + 0.325 FI; + 2.1 In (ADi) (1) (0.2) (0.014) (0.36) In (Cli) = 0.23 + 0.0047FI; + 0.35 In (AD;) - 0.56 Gi (2) (0.19) (0.002) (0.71) (0.06) CI; = 4.03 + 0.25 FI; + 2.3 In (AD;) - 0.14G; - 0.10 Flix Gi (3) (0.19) (0.003) (0.14) (0.34) (0.12) P-values are provided in the parentheses. The dataset contains 500 observations. The R2's of the first, second, and third regressions are 0.25, 0.18, and 0.26, respectively. Answer the following questions: (a) What is the interpretation for the coefficient on Fli in regressions (1) and (2)? (b) What is the interpretation for the coefficient on Fli in regression (3)? c) What is the interpretation for the coefficient on Flix G; in regression (3)? d) What is the interpretation for the coefficient on In(AD;) in regressions (1) and (2)? e) Test at the 5% significance level the null hypothesis that gender has no effect on the child's income in regression specification (2). (f) Test at the 5% significance level the null hypothesis that gender has no effect on the child's income in regression specification (3)