1. Letkidsdenotethenumberofchildreneverborntoawoman,andleteducdenoteyearsof educationforthewoman.Asimplemodelrelatingfertilitytoyearsofeducationis kids=B0+B1*educ+u

whereuistheunobservederror. (i)Whatkindsoffactorsarecontainedinu?Aretheselikelytobecorrelatedwithlevel ofeducation? Please explain it to me in simple terms (ii)Willasimpleregressionanalysisuncovertheceterisparibuseffectofeducation onfertility?Explain. Please explain it to me in simple terms 2. In the simple linear regression model y = ₀+₁x+u, suppose that E(u)does not = 0 (E stands for expected). Letting ₀= E(u), show that the model can always be rewritten with the same slope, but a new intercept and error, where the new error has a zero expected value. Please explain it to me in simple terms 3. The following table contains the ACT scores and the GPA ( grade point average) for eight college students. Grade point average is based on a four- 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 (A) Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and slope estimates in a linear equation. Here use GPA as your dependent variable (y) ACT as your independent (x) variable. Comment on the direction of the relationship. Does the intercept have a useful inter-pretation here? Explain.| GPA = B0hat + B1hatACT. (B) Compute the fitted values and residuals for each observation, and verify that the residuals ( approximately) sum to zero. (C) What is the predicted value of GPA when ACT 20? (D) How much of the variation in GPA for these eight students is explained by ACT? Explain.