Homework 13.pdf

Homework 13Due on 2018-06-151.Consider a problem of multiple linear regression in which a patients response Y to anew drug B is to be related to her response X1to a standard drug A and her heartrate X2.Suppose that,for all values X1=x1and X2=x2,the regression function hasa form E(Y)=0+1x1+2x2,and the values of 10 sets of observations(xi1,xi2,Yi)are given the table below.ixi1xi2yi11.9660.720.862-1.031.164-0.240.161-1.25-0.163-0.164.4703.474.6680.081.6620.895.5683.7103.4662.0(a)Under the standard assumptions of multiple linear regression,determine the valuesof the M.L.E.s0,1,2and 2.(b)Carry out a test of the following hypotheses:H0:1=0,H1:16=0.(c)Carry out a test of the following hypotheses:H0:2=1,H1:26=1.(d)Carry out a test of the following hypotheses:H0:1=2=0H1:The hypothesis H0is not true.1(e)Determine the value of R-square.(f)Find the predicted value and the 95%prediction interval for a patients response Yto drug B given that her response to drug A is 4 and that her heart rate is 65.2