Question

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 = 2.815 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 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) H0: β1 = 0 H0: β2 = 0 H1: β1 ≠ 0 H1: β2 ≠ 0 H0 is rejected if t < −2.074 or t > 2.074

Answer 1

Answer:

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

$n = 30$

$b_1 = 2.815$

$Sb_1 = 0.75$

$b_2 = -1.249$

$Sb_2 = 0.41$

$\alpha = 0.05$

Claim: Coefficient is zero

The null and alternate hypotheses are:

$H_0: \beta_1 =0\\\\H_1: \beta_1 \ne 0$

The test is two tailed because the alternate hypothesis contains $\ne$

Calculate the rejection region

$P(t < -t_0) = P(t > t_0) = \frac{\alpha}{2}$

$P(t < -t_0) = P(t > t_0) = \frac{0.05}{2}$

$P(t < -t_0) = P(t > t_0) = 0.025$

Calculate the degrees of freedom

$df = n -2$

$df = 30 -2$

$df = 28$

On the student's T distribution table, the t value at 28 and column with $\alpha = 0.05$ (two tailed) is:

$t\ value = 2.048$

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

So: We reject $H_0$ when $t < -2.048$ and $t >2.048$

Testing the first independent variable

Calculate test statistic

$t = \frac{b_1 - 0}{Sb_1}$

$t = \frac{2.815 - 0}{0.75}$

$t = \frac{2.815 }{0.75}$

$t = 3.753$

$t = 3.753 > 2.048$

This implies that, we reject $H_o$ and accept $H_1$

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

Testing the second independent variable

Calculate test statistic

$t = \frac{b_2 - 0}{Sb_2}$

$t = \frac{-1.249 - 0}{0.41}$

$t = \frac{-1.249 }{0.41}$

$t = -3.0463$

$t = -3.0463 < -2.048$

This implies that, we reject $H_o$ and accept $H_1$

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