Question

7)

Consider the following regression model

Y_i = β₀ + β₁X_1i + β₂X_2i + β₃X_3i + β₄X_4i + β₅X_5i + u_i

This model has been estimated by OLS. The Gretl output is below.

Model 1: OLS, using observations 1-52

	coefficient	std. error	t-ratio	p-value
const	-0.5186	0.8624	-0.6013	0.5506
X1	0.1497	0.4125	0.3630	0.7182
X2	-0.2710	0.1714	-1.5808	0.1208
X3	0.1809	0.6028	0.3001	0.7654
X4	0.4574	0.2729	1.6757	0.1006
X5	2.4438	0.1781	13.7200	0.0000

Mean dependent var	1.3617	S.D. dependent var	3.6435
Sum squared resid	128.39	S.E. of regression	1.6707
R-squared	0.81036	Adjusted R-squared	0.78975
F(5, 46)	39.312	P-value(F)	0
Log-likelihood	-97.285	Akaike criterion	206.57
Schwarz criterion	218.28	Hannan-Quinn	211.06

Use an F-test with the critical value method and a significance level of 5% to test H0:β2+β1=0H0:β2+β1=0 against H1:β2+β1≠0H1:β2+β1≠0.

1. Derive the restricted regression model.

2. The restricted model has been estimated and its residual sum of squares is SSRr=128.59SSRr=128.59. Compute the value of the F-statistic.

3. Do you reject the null hypothesis?

Answer 1