Question

The output below is from a study that used multiple linear regression analysis to link dependent variable y to x₁ and x₂.The sample consisted of 28 observations.   

	Coeff	Std Error	t Stat	P-value
Intercept	85	34.10	2.493	.0196
b1	-1.2	.88	-1.364	.1847
b2	3.5	1.12	3.125

Use the appropriate t tests to determine which, if any, of the individual coefficients are statistically significant at the 5% significance level. Report your conclusion. CHoose from A,B,C, and D below

		A) For b1, the p-value is .1847. Since .1847 > .05, we can reject the β1 = 0 null hypothesis. This coefficient is statistically significant. For b2, tstat = 3.125. From the t table, the critical t value, tc, for a .025 tail and 25 degrees of freedom is 2.060. Since tstat > tc, we can reject the β2 = 0 null hypothesis. This coefficient is statistically significant.
		B)For b1, the p-value is .1847. Since .1847 > .05, we can’t reject the β1 = 0 null hypothesis. This coefficient is not statistically significant. For b2, tstat = 3.125. From the t table, the critical t value, tc, for a .025 tail and 25 degrees of freedom is 1.711. Since tstat > tc, we can reject the β2 = 0 null hypothesis. This coefficient is statistically significant.
		C) For b1, the p-value is .1847. Since .1847 > .05, we can’t reject the β1 = 0 null hypothesis. This coefficient is not statistically significant. For b2, tstat = 3.125. From the t table, the critical t value, tc, for a .025 tail and 25 degrees of freedom is 2.060. Since tstat > tc, we cannot reject the β2 = 0 null hypothesis. This coefficient is not statistically significant.
		D) For b1, the p-value is .1847. Since .1847 > .05, we can’t reject the β1 = 0 null hypothesis. This coefficient is not statistically significant. For b2, tstat = 3.125. From the t table, the critical t value, tc, for a .025 tail and 25 degrees of freedom is 2.060. Since tstat > tc, we can reject the β2 = 0 null hypothesis. This coefficient is statistically significant.

Answer 1

p value corresponding to beta1 is 0.1847, which is greater than significance level of 0.05, failed to reject the null hypothesis

for beta2, sample size is n = 28

and degree of freedom = n-3

= 28-3

=25

using t distribution table with df(25) and alpha 0.05 for two tailed, we get

t critical = 2.060

and t statistic for beta2 is 3.125

this is clear that test statistic is less than t critical, means insignificant result and we again failed to reject the null hypothesis

therefore, none of the variable is significant at 0.05 significance level

option C is correct