Question

Using 20 observations, the multiple regression model y = β₀ + β₁x₁ + β₂x₂ + ε was estimated. A portion of the regression results is shown in the accompanying table:

	df	SS	MS	F	Significance F
Regression	2	2.12E+12	1.06E+12	55.978	3.31E-08
Residual	17	3.11E+11	1.90E+10
Total	19	2.46E+12

	Coefficients		Standard Error		t Stat		p-value		Lower 95%	Upper 95%
Intercept	−986,892		130,984		−7.534		0.000		−1,263,244	−710,540
x1	28,968		32,080		0.903		0.379		−38,715	96,651
x2	30,888		32,925		0.938		0.362		−38,578	100,354

a. At the 5% significance level, are the explanatory variables jointly significant?

• No, since the p-value of the appropriate test is more than 0.05.

• Yes, since the p-value of the appropriate test is more than 0.05.

• Yes, since the p-value of the appropriate test is less than 0.05.

• No, since the p-value of the appropriate test is less than 0.05.

b. At the 5% significance level, is each explanatory variable individually significant?

• Yes, since both p-values of the appropriate test are less than 0.05.

• Yes, since both p-values of the appropriate test are more than 0.05.

• No, since both p-values of the appropriate test are not less than 0.05.

• No, since both p-values of the appropriate test are not more than 0.05.

c. What is the likely problem with this model?

• Multicollinearity since the standard errors are biased.

• Multicollinearity since the explanatory variables are individually and jointly significant.

• Multicollinearity since the explanatory variables are individually significant but jointly insignificant.

• Multicollinearity since the explanatory variables are individually insignificant but jointly significant.

Answer 1

a) To test whether the explanatory variables jointly significant,

P-value = 3.31E-08

Since P-value < 0.05, so we reject the null hypothesis.

ans-> Yes, since the p-value of the appropriate test is less than 0.05.

b) To test whether each explanatory variable is individually significant,

P-value for x₁ is = 0.379

P-value for x₁ is = 0.362

ans-> No, since both p-values of the appropriate test are not less than 0.05.

c) Multicollinearity since the explanatory variables are individually insignificant but jointly significant.