STAT 310/270. Assignment II. After going through the previous communication, handle the assignment below and submit your work by 13/4/23 between 8 am to 9:30 am in the office a) Suppose a random sample of 200 twenty – year old men is selected from a population and their heights and weights recorded. A regression of weight on height is given as: Weight = −99.41 + 3.94 Height , R 2 = 0.81, SER = 10.2 ( 2.15) ( 0.31) Where weight is measured in pounds and height in inches. A man has a late growth spurt and grows 1.5 inches over the course of the year. i) Construct a 99% confidence interval for the person’s weight gain [6Mks] ii) Calculate p-value for the 2-sided test of H0 : 1 = 3.94 and determine whether 3.94 is contained in the 95% CI for 1 . b) Prove that F statistic is equal to the square of t statistic [7Mks] [6Mks] c) A researcher has international cross-section data on aggregate wages, W, aggregate profits, P, and aggregate income, Y, for a sample of n countries. By definition, Yi = Wi + Pi The regressions Wˆi = a1 + a2Yi Pˆ = b + b Y i 1 2 i are fitted using OLS regression analysis. Show that the regression coefficients will automatically satisfy the following equations: a2 + b2 = 1 a1 + b1 = 0 Explain intuitively why this should be so. A Seventh-day Adventist Institution of Higher Learning ©2021/22(2) [10Mks]
