Question

For the data set shown below, complete parts (a) through (d).

X	Y
20	102
30	97
40	93
50	83
60	72

(a) Find the estimates of Bo and B1.
Bo=bo= _____ (Round to three decimal places as needed.)
B1=b1= ______(Round to four decimal places as needed.)

(b) Compute the standard error the point estimate for
se= ____

(c) Assuming the residuals are normally distributed, determine

Sb1=____
(Round to four decimal places as needed.)

(d) Assuming the residuals are normally distributed, test HoB1=0 versus H1:B1/=0 at the a=0.05 level of significance. Use the P-value approach.
The P-value for this test is _____.
(Round to three decimal places as needed.)
Make a statement regarding the null hypothesis and draw a conclusion for this test. Choose the correct answer below.

A. Reject Ho. There is sufficient evidence at the a= 0.05 level of significance to conclude that a linear relation exists between x and y.

B. Reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that a linear relation exists between x and y.

C. Do not reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that a linear relation exists between x and y.

D. Do not reject Ho. There is sufficient evidence at the a= 0.05 level of significance to conclude that a linear relation exists between x and y.

Answer 1

a)

bo =119.000

b1= -0.7400

b)

SSE =Syy-(Sxy)2/Sxx=

25.600

	s2 =SSE/(n-2)=	8.5333
se	=se =√s2=	2.9212

(please try 2.921 or 2.92 if required less number of decimals)

c)

std error of slope =se(β1) =s/√Sxx=

0.0924

d)

test stat t =(b1-β1)/se(β1)=		-8.011
p value =	0.004	(from excel:tdist(-8.011,3,2)

A. Reject Ho. There is sufficient evidence at the a= 0.05 level of significance to conclude that a linear relation exists between x and y.