(18 points overall) Answer yes or no to each of the items (a)-(c). If yes, briefly justify the statement, if no, provide a counter-example or disprove the statement.

(6points) We have a sample of n individuals, indexed by i = 1, • • ,n. For the i-th individual, we can observe Xi and Y{. If we assume our sample is i.i.d. cross-sectionally, it implies Xi and Yi are independent with each other.
(6points) In multivariate OLS, we have three regressors Xi, XWe will maintain the OLS assumptions throughout this problem. You estimate the following regression using OLS:

birthweight = Po~~ Pi smoke + P2race + p^drink + p^smoke * drink + Pb og(weight) -1- U.

You obtain the following estimation results:

birthweight = 3 — 0.25smoke -1- .10 race — .1 drink — .05 smoke * drink — 3.5 log(weiqht)

(.01)        (.05)                            (.07)                 (.04)                       (.02)                  (.7)

(5 points) What is the interpretation of pb in this multivariate regression?
(5 points) You want to test that there is no effect of smoking on baby’s birthweight. Write down your Hq and Hi in terms of (/3o, • • • ,/3s).
(5 points) You choose to use F-test to conduct the above test and obtain a F-stat of 4. Based the Chi-square table, is the P-value of your F-test less than 1%, between 1% and 5%, or greater than 5%, and why?
(5 points) A mother drinks but does not smoke. Her weight is 70 KG. What is the expected change of her baby’s birthweight (in terms of pi, • • , if she starts to smoke and gain 1.4 kg of weight, given other variables unchanged?
(5 points) Based on the regression results, what is a valid estimate (number) of the above expected increase?
(5 points) In order to construct the confidence interval for the expected increase, you will run a F-test to recover the standard error of the estimator of the expected increase you proposed above. What is the null hypothesis of the F-test you are going to run?