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 = 1.331	Sb1 = 0.80
b2 = −2.922	Sb2 = 0.64

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 < −2.052 or t > 2.052

Answer 1

H₀: β₁ = 0, H₁: β₁ ≠ 0

Test statistic: t = b₁/S_b1 = 1.331/0.80 = 1.664

Critical value (Using Excel function T.INV.2T(probability,n-2)) = T.INV.2T(0.05,28) = 2.048

Since t < 2.048, H₀ is not rejected. So, β₁ = 0.

H₀: β₂ = 0, H₁: β₂ ≠ 0

Test statistic: t = b₂/S_b2 = -2.922/0.64 = -4.566

Critical value (Using Excel function T.INV.2T(probability,n-2)) = T.INV.2T(0.05,28) = 2.048

Since t < - 2.048, H₀ is rejected. So, β₂ ≠ 0.

X1 should be removed since its cofficient is zero.