In a multiple regression analysis, two independent variables are considered, and the sample size is 30. The regression coefficients and the standard errors are as follows. b1 = 2.815Sb1 = 0.75 b2 = −1.249Sb2 = 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 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) H0: β1 = 0H0: β2 = 0 H1: β1 ≠ 0H1: β2 ≠ 0 H0 is rejected if t < −2.074 or t > 2.074

There is a sufficient evidence that the coefficient b1 is not zero

There is a sufficient evidence that the coefficient b2 is not zero

Step-by-step explanation:

Given

Claim: Coefficient is zero

The null and alternate hypotheses are:

The test is two tailed because the alternate hypothesis contains

Calculate the rejection region

Calculate the degrees of freedom

On the student's T distribution table, the t value at 28 and column with (two tailed) is:

The rejection value will contain all value lesser than -2.048 and all values greater than 2.048.

So: We reject when and

Testing the first independent variable

Calculate test statistic

This implies that, we reject and accept

There is a sufficient evidence that the coefficient b2 is not zero

Testing the second independent variable

Calculate test statistic

This implies that, we reject and accept

There is a sufficient evidence that the coefficient b2 is not zero

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