Question

1. In the simple regression model y = + β1x + u, suppose that E (u) 0. Letting oo-E(u), show that the model can always be rewrit ten with the same slope, but a new intercept and error, where the new error has a zero expected value 2. The data set BWGHT contains data on births to women in the United States. Two variables of interest are the dependent variable, nfan birth weight in ounces (bught), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy (cigs). The following simple regression was estimated using data on n-1,388 births a) What is the predicted birth weight when cigs 0? What about when cigs-20 (b) Does this simple regression necessarily capt ure the causal relationship between (c) To predict a birth weight of 125 ounces, what would cigs have to be? Com- (d) The proportion of women in the sample who do not smoke while pregnant is bwght-119.77 0.514cigs (one pack per day)? Comment on the difference. the child's birth weight and mot her's smoking habit? Explain ment about 0.85. Does this help reconcile your finding from part (c)? 3. Consider the standard simple regression model u = Ao + β +u under the Gauss- Markov Assumptions SLR.1 through SLR.5. The usual OLS est imators Bo and Bi are unbiased for their respective population parametrs. Let be the est imator of B obtained by assuming the intercept is zero (see Section 2.6) (a) Find E() in terms of the ris Boand Verify that B is unbiased for Bi when the population intercept (8o) is zero. Are there other cases where is unbiased? (b) Find the variance of Bi. (Hint: The variance does not depend on Bo.) (c) Show tha Var) Var(). Hint: For any sample of data, 2 ()2 with strict inequality unless -0.] Comment on the tradeoff beteen bias and variance when choosing betweern (d) and 4. The data set in CEOSAL2.dta contains information on chief executive officiesr for U.S. corporations. The variable salary is annual compensation, in thousands of dollars, and ceoten is prior number of years as company CEO. a) Find the average salary and the average tenure in the sample. (b) How many CEOs are in their first year as CEO (that is, ceoten-0)? What is the longest tenure as a CEO?

Answer 1

here Te nom into