Use the following information from a multiple regression analysis.n=15b1=2b2=6Sb1=1.4Sb2=0.5a.Which variable has the largest slope, in units of a t statistic?b.Construct a90%confidence interval estimate of the population slope,β1.c.At the0.10level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the independent variables to include in this model.

Solution: Given information: n= 15 observation k= 2 independent variables b1= 2b2= 6Sb1= 1.4Sb2= 0.5 a) The variable X2 has the largest slope with tSTAT= 12 tSTAT= b2Sb2tSTAT= 60.5=12 b) The 90% confidence interval estimate of the population slope, β1 is b1±tα/2.n-(k+1)×Sb1At α=0.10tα/2,n-(k+1)=t0.05, 12=1.782 From t table ( 2±1.782×1.4)(2±2.4948)(2-2.4948, 2+2.4948)(-0.4948, 4.4948) The 90% confidence interval estimate of the population slope, β1 is ( -0.4948, 4.4948) c) Test for significance of β1 To test the hypothesis Ho:β1=0 VS Ha:β1≠0 Test statistic tSTAT= b1Sb1tSTAT=21.4tSTAT== 1.4286 Test statistic is 1.4286 To find p value p value = 2*P(t> 1.4286) p value = 0.1786 From Excel The p value for the test is 0.1786 Decision: p value > α=0.10 Fail to reject the null hypothesis Conclusion: There is insufficient evidence to conclude that the variable X1 contribute significant to the model. Test for significance of β2 To test the hypothesis Ho:β2=0 VS Ha:β2≠0 Test statistic tSTAT= b2Sb2tSTAT= 60.5=12 Test statistic is 12 To find p value p value = 2*P(t> 12) p value = 0.0000 From Excel The p value for the test is 0.0000 Decision: p value < α=0.10 Reject the null hypothesis Conclusion: There is sufficient evidence to conclude that the variable X2 contribute significantly to the model. Based on the results of hypothesis testing or test for significance of β1 and β2. The independent variable X2 is included in the model.

Answered: Use the following information from a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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a.	Which variable has the largest slope, in units of a t statistic?
b.	Construct a 90% confidence interval estimate of the population slope, β1.
c.	At the 0.10 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the independent variables to include in this model.