Question

Consider the following set of deependent and independent variables. Complete parts a through c below. 11 14 14 21 24 26 31 Y X1 1 8 10 15 21 4 4. 7 X2 16 9 13 11 2 8 8 4 CO b. Test the significance of each independent variable using a 0.10. Calculate the appropriate test statistic The test statistic (Round to two decimal places as needed.) What is the critical t-score? Use the t-test to determine the significance of the relationship between x 2 and y. Use technology to determine t, rounding to two decimal places. c. Interpret the p-value for each independent (x1 and x2) variable. C Compare each p-value to alpha equals 0.05 Use the information from the previous steps to determine if the relationship between each independent variable and the dependent variable is statistically significant.

Answer 1

Following is the output of multiple regression analysis generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.952718261
R Square	0.907672085
Adjusted R Square	0.870740919
Standard Error	2.835799962
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	2	395.2911929	197.6455964	24.5774011	0.0025902
Residual	5	40.20880712	8.041761423
Total	7	435.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	14.56188966	4.234494556	3.438873156	0.01845781	3.67677487	25.4470044
X1	0.928970703	0.211020378	4.402279595	0.00700692	0.38652555	1.47141585
X2	-0.443986852	0.303407342	-1.46333589	0.20324461	-1.22392025	0.33594655

(b-c)

For variable x1:

Hypotheses are:

Ho B10, Ha : 0

The test statistics is:

t = 4.40

The p-value is: 0.0070

The critical value of t using excel function "=tinv(0.05,5)" is: +/- 2.571

Since t > 2.571, reject H0

That is we can conclude that independent variable X1 is significant to the model.

For variable x2:

Hypotheses are:

Ho B20, Ha :B20

The test statistics is:

t = -1.46

The p-value is: 0.2032

The critical value of t using excel function "=tinv(0.05,5)" is: +/- 2.571

Since -2.571 < t < 2.571, fail to reject H0

That is we can conclude that independent variable X2 is not significant to the model.