Question

Exercise 14.23 (Self-Test) ED eBook Video Given are five observations for two variables, I and y. N 1 2 3 4 5 3 7 5 11 14 The estimated regression equation is ý = 0.2 +2.62 a. Compute the mean square error using the following equation (to 3 decimals). s? = MSE = SSE n - 2 b. Compute the standard error of the estimate using the following equation (to 3 decimals). 3 = VMSE SSE In-2 c Compute the estimated standard deviation by using the following equation (to 3 decimals). V2(x,- ) d. Use the t test to test the following hypotheses (0.05 ): H: 0 H. :D Compute the value of the test statistic (to 2 decimals), The value is Use Table 1 of Appendix B. What is your conclusion?

Answer 1

S.No х y (x-X) (4-7) 1 2 3 1 2 3 4 3 7 5 11 14 40 4.0000 1.0000 0.0000 1.0000 4.0000 10.0000 SSX 4 (x-x)(y-7) 10.0000 1.0000 0.0000 3.0000 12.0000 26.0000 25.00 1.00 9.00 9.00 36.00 80.0000 SSY 5 Total 5 15 Mean 3.000 8.0000 SXY sample size n. 5 3.0000 10.000 U 26.000 y = 8.0000 S. (X-X)= Sw Z(X-X)(y-7)= slopes . = S/S - intercepta B. = V-B,x= Least square line equation: û =0.2+2.6*X 2.6000 Cov 0.2000

SSE =Syy-(Sxy)2/Sxx=

12.400000

a)

s2 =SSE/(n-2)=

4.133

b )

std error σ              =

=se =√s2=

2.033

c)

std error of slope =se(β1) =s/√Sxx=

0.643

d)

test stat t =(b1-β1)/se(β1)=

4.04

the p value is between 0.025 and 0.05

we can conclude that relationship is significant

e)

Source	DF	SS	MS	F	p value
regression	1	67.6	67.600	16.35	0.0272
Residual error	3	12.4	4.133
Total	4	80.0

the p value is between 0.025 and 0.05

we can conclude that relationship is significant