Question

In a multiple regression equation, two independent variables are considered, and the sample size is 30. The regression coefficients and the standard errors are as follows.

b1 = 2.815 Sb1 = 0.75
b2 = -1.249 Sb2 = 0.41
Conduct a test of hypothesis to determine whether either independent variable has a coefficient equal to zero. Would you consider deleting either variable from the regression equation? Use the .05 significance level. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

H0: β1 = 0 H0: β2 = 0
H1: β1 ≠ 0 H1: β2 ≠ 0
H0 is rejected if t < -2.042 or t > 2.042
t for b1 coefficient =
t for b2 coefficient =
(Click to select)Neither the first nor secondThe first and secondThe second variable can be deleted.

Answer 1

Both the variables are important for the regression analysis and cannot be deleted.

Explanation:

(1)

The hypothesis for for the testing of coefficient β₁ are:

H₀: β₁ = 0 vs. Hₐ: β₁ ≠ 0

The test statistic is:

`t=\frac{b_(1)}{S_{b_(1)}} =(2.815)/(0.75)= 3.753`

It is provided that H₀ is rejected if t > 2.042.

The test statistic value, t = 3.753 > 2.042.

Thus, the null hypothesis is rejected.

Conclusion:

There is a significant relationship between the regression variable and the dependent variable.

(2)

The hypothesis for for the testing of coefficient β₂ are:

H₀: β₂ = 0 vs. Hₐ: β₂ ≠ 0

The test statistic is:

`t=\frac{b_(2)}{S_{b_(2)}} =(-1.249)/(0.41)= -3.046`

It is provided that H₀ is rejected if t < -2.042.

The test statistic value, t = -3.046 < -2.042.

Thus, the null hypothesis is rejected.

Conclusion:

There is a significant relationship between the regression variable and the dependent variable.

Thus, both the variables are important for the regression analysis and cannot be deleted.