1. Let kids denote the number of children ever born to a woman, and let educ denote yeals of education for the woman. A simple model relating fertility to years of education is Kids = 0 + 1 educ + where is the unobserved error. i) What kinds of factors are contained in ?? Are these likely to be correlated with level of education? ii) Will a simple regression analysis uncover the ceteris paribus effect of education on fertility? Explain 2. The following table contains the ACT scores and the GPA for 8 college students. Grade point average is based on a 4 point scale and has been rounded to one digit after the decimal. Student GPA ACT 1 2.8 21 2 3.4 24 3 3.0 26 4 3.5 27 5 3.6 29 6 3.0 25 7 2.7 25 8 3.7 30 i) Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and slope estimates in the equation ^ GPA = 0 ^ + ACT 1 Comment on the direction of the relationship. Does the intercept have a useful interpretation? Explain! How much higher is the GPA predicted to be if the ACT score is increased by five points? Compute the fitted values and residuals for each observation, and verify that the residuals (approximately) sum to zero. What is the predicted value of GPA when ACT = 20? How much of the variation in GPA for these eight students is explained by ACT? Explain