Question

From the following MINITAB regression analysis, what can you conclude for the hypothesis test of Ho: β1=0 versus Ha: β1≠ 0 using α=0.10?
The regression equation is
Test2 = 27.8 + 0.583 Test1
  
Predictor Coef SE Coef T P
Constant 27.82 25.00 1.11 0.278
Test1 0.5825 0.3070 1.90 0.071
  
S = 22.9977 R-Sq = 14.1% R-Sq(adj) = 10.2%

The null hypothesis would not be rejected and the conclusion would be that the x variable is of no use in the regression model to predict y.

The null hypothesis would be rejected and the conclusion would be that the x variable is necessary for the regression model to predict y.

The null hypothesis would not be rejected and the conclusion would be that the slope of the regression line is equal to zero.

The null hypothesis would be rejected and the conclusion would be that the y-intercept of the regression model is equal to zero.

Answer 1

Solution:

Given:   Following is the MINITAB regression analysis:

Ho: β1=0 versus Ha: β1≠ 0

α=0.10

The regression equation is

Test2 = 27.8 + 0.583 Test1

Predictor	Coef	SE Coef	T	P
Constant	27.82	25	1.11	0.278
Test1	0.5825	0.307	1.9	0.071

We have make conclusion regarding the hypothesis test.

Decision Rule:
Reject H₀, if P-value < 0.10 level of significance, otherwise we fail to reject H₀

Since P-value for Slope coefficient is 0.071 < 0.10 level of significance, we reject null hypothesis H₀: β1=0.

Thus we accept its alternative hypothesis H_a: β1≠ 0 , that means slope of the regression equation is significantly different from 0.

Thus correct option is:

The null hypothesis would be rejected and the conclusion would be that the x variable is necessary for the regression model to predict y.