A]Use the following data to fit a linear regression function of Y on X .Assume the regression model Y= a+bx+u is applicable

X 5 6 7 8 9 10 11 12 13 14 15

Y 1 4 3 8 7 7 13 10 16 17 13

N=11

B} Work out the 1TSS

2 RSS

3 ESS

C}FIND THE LINEAR CORRELATION COEFFICIENT {r}

d} what proportion of the total variation is explained by the fitted regression function

e}find the unbiased estimate of sigma squared

f}find the stardard error of b and a

g}test the following hypothesis

1]H0:b=0 against H1:b is not equal to 0

2]H0:b=1 against H1:b>1

3]H0:b=2 against H1:b<2

4}H0:b=1.8 against H1: b is not equal to 1.8

h]obtain the 95 %confidence interval use the interval to test the given hypothesis in g[1]and g{4]

i]use the given data to predict the value of y at 8.5

j]test the following hypothesis

1)H0:E[y]=5.8 GIVEN X=8.5 AGAINST H1:Y is not equal tp 5.8

2]H0:Y=5.8 GIVEN X =8.5 AGAINST H1:Y IS NOT EQUAL TO 5.8

3]H0:ALFA =O AGAINST H1:ALFA IS NOT EQUAL TO 0