help me to solve some questions.

d. Gonstruct a 959i. condence interval for the gender gap. Interpret your nding. e. Another researcher uses the same data, but regressea wages on Female1 a domes]r terriahle that is equal to one if the worker in female and sero it the worker is male. What are the regression estimates calculated trom this regression? .I''-\\. range = _____ + _____ a Female R: It. {It} points} Suppose that a random sample of 2m twent}r year old men is auected from a population and their height families} and weight [pounds] is recorded. A regression of weight on height yields _,_.-._._ weight = 9!.41+3.941-.heipht {2.15} {0.31} R' = s.s:1,.:;=1s.s a What is the regression's 1weight prediction for someone who is Tl} inches tall'.r as inches taLl'! 74 inches taut h. A person has a late growth spurt and grows 1.5 inches our the course of a year. 'What is the regressioo's prediction for the increase in the person's weight? c. Construct a 99% condecnoe interval for the weight gain in h}. 11 Suppose that instead. ofmeasoring weight and height in pounds and indies, the}r are measured in kilograms and centimeters. What are the regression estimates from this now kilogram-centimeter regression! {Hint 1 inch is equivalent to 2.54. cms and 1 pound is equivalent to [#4525 kgs} :L {It} points} Consider a simple linear regression model F=5n+ix+u {:1} uncles the identifying susumption E{u.iX} = EL Suppose we have a random sample {12-1 Xi} lior t = 1. ..,re and consider the following formulas for the OLE estimators ):[11- ?:I [xiTI l1: hilt1 in. =? 51? Z (Xiff i'l a. Show that in can be written as Six-ii1'i i1=i+": or Z [Xif}: 41 (Hint: average equation [1} to get ? = ,5. +if+ E, then euhstract this equation from equation [1} eeaitmtedats' to get 1'.- Y =,u:1I [357.- ?J +u.- e.rhich is then replaced in :1}. h. Show E (s: I] = [I implies that in and in are unbiased estimators of n and ,51 when conditioning on XE (In... K\") i.e. an" I] = ,6\" and E{t151l}= .51. 1. (10 points) Suppose that a researcher, using data on class size across schools (CS) and average test scores from 100 third-grade classes, estimates the OLE: regression where homoskedastic std errors are reported in brackets _,__,__._,__ Testsco're = 520 5.82 X OS {20.4) {2.21} R2 = 0.08, 8;,- = 11.5 a. A classroom has 22 students. \"that is the regressionts prediction for that classroomis average test score? 1). Last year a classroom had 19 students and this year it has 23 students. 1What is the regressions prediction for the percent change relative to last year in the classroom average test score? Is the change sizable in nlagnitude? c. Construct a 95% condence interval for .51, the regression slope coefficient. (Hint: use the std normal distribution to construct it) d. Calculate the j: value for the two sided test Ha : .31 = 0 vs. H1 : 51 g 0 . Do you reject the null hypothesis at the 5% level? At the 1% level? e. Calculate the sample std deviation of test scores across the 100 classrooms. (Hint: review the formulas for the R2 and 8a). 2. (10 points} Suppose that a researcher, using wage per hour data on 250 randomly selected male workers and 280 female workers, estimates the following 0L3 regression __,_.-._._,_ wage = 12.88 + 2.79 x Mole {0.18) {0.84) R2 = 0.08, a; = 3.10 where Ivfale is a dummy variable that takes the value 1 if the 1worker is male and 0 if female; in hrackets homoskedastic std errors are reported. a. \"rhat is the estimated gender wage 3313? h. Is the estimated gender wage gap signicantly different from zero? (Hint: compute the pvalue for testing the null hypothesis that there is no gender gap) c. How large in magnitue is the gender pay gap? (Hint: Compare the gap to the average wage per hour for women in the sample)