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

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

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

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 \\e 0`

The test is two tailed because the alternate hypothesis contains
`\\e`

Calculate the rejection region

`P(t < -t_0) = P(t > t_0) = (\alpha)/(2)`

`P(t < -t_0) = P(t > t_0) = (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 = (b_1 - 0)/(Sb_1)`

`t = (2.815 - 0)/(0.75)`

`t = (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 = (b_2 - 0)/(Sb_2)`

`t = (-1.249 - 0)/(0.41)`

`t = (-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