Question

Note: For this Question, it may be necessary to use R to avoid LONG calculations and achieve the required precisions in both answers.

1. For the following pairs of (x,y) observations,

(−2,−3),(3,3),(6,6),(7,6),(10,9)

we are interesting in fitting the population regression model μy=α+β1x. Carry out the hypothesis test

H0 β1=0

H1 β1≠0

Determine the value of the test statistic and the associated p-value.

Test Statistic =

p-Value =

2. For the data set we have the following (x,y) pairs of observations:

(−2,−1),(1,0),(6,6),(7,8),(10,12)

Please carry out the hypothesis test:

H0 β1=1

H1 β1≠1

Determine the value of the test statistic and the associated p-value.

Test Statistic =

p-Value =

Answer 1

1)

SSE =Syy-(Sxy)2/Sxx=

1.196

	s2 =SSE/(n-2)=	0.3986
std error σ              =	=se =√s2=	0.6313

estimated std error of slope =se(β1) =s/√Sxx=			0.069
test stat t =	(bo-β1)/se(β1)=	=	14.3092
p value:		=	0.0007

2)

test stat t =	(bo-β1)/se(β1)=	=	0.9751
p value:		=	0.4014