Question

You may need to use the appropriate technology to answer this question. Consider the following data for a dependent variable y and two independent variables, x, and x, V X1 y 30 92 12 47 10 108 25 17 112 51 16 178 40 5 94 51 19 175 74 7 170 36 12 117 59 13 142 16 210 The estimated regression equation for these data is -18.74 2.01x, 4.73x Here, SST 15,229.6, SSR 14,077.25 0.2495, and 0.9575. (a) Test for a significant relationship among x, x, and y. Use a 0.05. State the null and alternative hypotheses Ho: P>Pz 76 The estimated regression equation for these data is 2.01x,+ 4.73x2 y=-18.74 + Here, SST 15,229.6, SSR 14,077.2, s 0.2495, and 5 2 = 0.9575. (a) Test for a significant relationship among x,, x, and y. Use a 0.05. State the null and alternative hypotheses. Ho: P>A2 0 and P2 = 0 = 0 and # 0 Ho H # 0 # 0 and One or more of the parameters is equal to zero. H One or more of the parameters is not equal to zero. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value State your conclusion. O Do not reject Ho. There is sufficient evidence to conclude that there is a significant relationship among the variables. Reject Ho There is insufficient evidence to conclude that there is a significant relationship among the variables. O Do not reject Ho. There is insufficient evidence to conclude that there is a significant relationship among the variables. Reject Ho. There is sufficient evidence to conclude that there is a significant relationship among the variables. (b) Is B significant? Use a 0.05. State the null and alternative hypotheses. Hoi By

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.961422643
R Square	0.924333499
Adjusted R Square	0.902714499
Standard Error	12.83060262
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	2	14077.22945	7038.614727	42.75560781	0.000119169
Residual	7	1152.370546	164.6243636
Total	9	15229.6
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-18.73506579	18.14254204	-1.032659356	0.336115885	-61.63536067	24.1652291	-61.63536067	24.1652291
x1	2.014081562	0.249470879	8.073413489	8.59808E-05	1.424176671	2.603986454	1.424176671	2.603986454
x2	4.728069085	0.957466177	4.938105594	0.001678746	2.464021343	6.992116827	2.464021343	6.992116827

a)

Hypothesis:

Ho: Py-Pz=O H:One or more of the parameters is not equal to zero.

Test statistic = F = 42.76

P value = 0.000 < 0.05 (significance level)

Reject Ho There is sufficient evidence to conclude that there is a significant relationship among the variables.

b)

Hypothesis :

Ho By O HB o

Test stat : t = 8.07

P value = 0.000 < 0.05 (significance level)

Reject H. There is sufficient evidence to conclude that B, is significant.

c)

Hypothesis :

Ho-B2-O

Test stat : t = 4.94

P value = 0.002 < 0.05 (significance level)

Reject Ho. There is sufficient evidence to conclude that B, is significant.