Question

10. The following is the simple linear regression analysis output: E(Y) = Bo + B1 (ADV_X) The REG Procedure Model: MODELI Dependent Variable: SALES_T Analysis of Variance Sun of Mean Squares Square 4.90000 4.90000 1. 10000 0.36667 6.00000 Source Model Error Corrected Total F Value 13.36 Pr>F 0.0354 Root PSE Dependent Mean Coeff Var 0.60553 2.00000 30.27650 R-Square Ady A-se 0.8167 0.7556 Parameter Estimates Variable DF "estinato Value Pr > Itt 95% confidence Linite "Error .. 63503 0.19149 -0.10000 0.70000 What is the p-value of the two-tailed t-test with the null hypothesis: B. - 0? a) 0.0001 b) 0.0354 c) 0.0708 d) 0.5000

Answer 1

Solution :

The null and alternative hypotheses are as follows :

$\large H_{0}: \beta_{1}=0$

$\large H_{1}: \beta_{1}\neq0$

To test the hypothesis t-test will be used. The test statisical is given as follows :

$\large t = \frac{\hat{\beta}_{1}}{SE_{\hat{\beta}_{1}}}$

From the given output we have,

$\large \hat{\beta}_{1}=0.70000, SE_{\hat{\beta}_{1}}=0.19149$

0.70000 ==3.65554 0.19149

The value of the test statistic is 3.65554.

Degrees of freedom = (n - 2) = (5 - 2) = 3

The two-tailed p-value for the test statistic is given as follows :

p-value = 2.P(T > t)

p-value = 2.P(T > 3.65554)

Using R software we get,

p-value = 0.0354

The p-value is 0.0354.

Hence, option (b) is correct.

Please rate the answer. Thank you.