Question

In a multiple regression analysis, two independent variables are considered, and the sample size is 26. The regression coefficients and the standard errors are as follows.

b1 = 1.468	Sb1 = 0.89
b2 = −1.084	Sb2 = 0.88

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 < −2.069 or t > 2.069

Answer 1

Answer:

Given data

b1 = 1.468	Sb1 = 0.89
b2 = −1.084	Sb2 = 0.88

Null hypothesis  H₀ : β₁ = 0

Alternative hypothesis H1: β₁ ≠ 0

test statIstic t1 = b₁/ S_b1

t1 = 1.468 / 0.89

  t1 = 1.649

Therefore the value of test statistic t1 is 1.649

Now,

Null hypothesis  H₀ : β₂= 0

Alternative hypothesis H1: β₂ ≠ 0

test statIstic t2 = b2 / S_b2

test statIstic t2  = −1.084 / 0.88

test statIstic t2  = -1.232

Therefore the value of test statistic t2 is -1.232