Q2. The following data consists of the length of service call in minutes and the number of components\ repaired.\ i) Draw a scatter diagram and comment.\ ii) Estimate the simple linear model Minutes

=\\\\alpha +\\\\beta

. Unites

+e

\ iii) Plot the standardized residuals against units and comment.\ iv) Calculate multiple correlation coefficient

(R^(2))

and comment.\ v) Calculate

hat(Y)

and show that

\\\\sum_(i=1)^n (hat(Y)_(i)-Y_(i))=0

, also comment.\ vi) Find

hat(\\\\sigma )^(2),Var(hat(\\\\alpha )),Var(hat(\\\\beta )),Var(hat(\\\\sigma )^(2))

, and

Var(hat(P)_(4))

.\ vii) Test the hypotheses,

H_(0):\\\\alpha =0,20,30,40;H_(0):\\\\beta =0,5.0,10.0,15.0;H_(0):\\\\sigma ^(2)=0;H_(0):Y_(4)=60

and\

H_(0):\\\\mu _(4)=60

at

5%

and

2.5%

level of significance. Also find the confidence interval in each case.\ viii) Also estimate the simple parabola model Minutes

=\\\\beta _(0)+\\\\beta _(1)

. Unites

+\\\\beta _(2)

.

( Unites )^(2)+e

\ ix) Calculate multiple correlation coefficient

(R^(2))

for viii) and comment with iv).\ x) Find

hat(\\\\sigma )^(2),Var(hat(\\\\beta )_(0)),Var(hat(\\\\beta )_(1)),Var(hat(\\\\beta )_(2)),Var(hat(\\\\sigma )^(2))

, and

Var(hat(\\\\beta )_(4))

for viii).\ xi) Test the hypotheses,

H_(0):\\\\beta _(0)=0,20,30,40;H_(0):\\\\beta _(1)=0,5.0,10.0,15.0;H_(0):\\\\sigma ^(2)=0;H_(0):Y_(4)=60

at\

5%

and

2.5%

level of significance Also find the confidence interval in each case.

Q2. The following data consists of the length of service call in minutes and the number of components renaired ] i) Draw a scatter diagram and comment. ii) Estimate the simple linear model Minutes =+. Unites +e iii) Plot the standardized residuals against units and comment. iv) Calculate multiple correlation coefficient (R2) and comment. v) Calculate P^ and show that i=1n(Y^iYi)=0, also comment. vi) Find ^2,Var(^),Var(^),Var(^2), and Var(Y^4). vii) Test the hypotheses, H0:=0,20,30,40;H0:=0,5.0,10.0,15.0;H0:2=0;H0:Y4=60 and H0:4=60 at 5% and 2.5% level of significance. Also find the confidence interval in each case. viii) Also estimate the simple parabola model Minutes =0+1. Unites +2. (Unites)2+e ix) Calculate multiple correlation coefficient (R2) for viii) and comment with iv). x) Find ^2,Var(^0),Var(^1),Var(^2),Var(^2), and Var(Y^4) for viii). xi) Test the hypotheses, H0:0=0,20,30,40;H0:1=0,5.0,10.0,15.0;H0:2=0;H0:Y4=60 at 5% and 2.5% level of significance Also find the confidence interval in each case