In a multiple regression equation, two independent variables are considered, and

Question

In a multiple regression equation, two independent variables are considered, and the sample size is 27. The regression coefficients and the standard errors are as follows.

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.)

rev: 03_18_2016_QC_CS-46019

Explanation / Answer

For the first hypthesis -

H0: 1 = 0

H1: 1 0

Sample size , n = 27

Number of independent variable including intercept = 3

Degree of freedom for the test statistic = 27 - 3 = 24

For two tail test, significance level = 0.05/2 = 0.025

Rejection region for significance level = 0.025 and degree of freedom is given as,

t < -2.064 or t > 2.064

t for b1 coefficient = coeff/Std error = 1.027/0.58 = 1.771

As, t does not lie in the rejection region, we accept the null hypothesis and conclude that 1 = 0 and first independent variable can be deleted from the model.

For the second hypthesis -

H0: 2 = 0

H1: 2 0

Sample size , n = 27

Number of independent variable including intercept = 3

Degree of freedom for the test statistic = 27 - 3 = 24

For two tail test, significance level = 0.05/2 = 0.025

Rejection region for significance level = 0.025 and degree of freedom is given as,

t < -2.064 or t > 2.064

t for b2 coefficient = coeff/Std error = -2.529/0.7 = -3.613

As, t does lie in the rejection region, we reject the null hypothesis and conclude that 2 0 and second independent variable cannot be deleted from the model.

So, The first variable can be deleted, and

The second variable cannot be deleted.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.