Question

The regression model

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

has been estimated using Gretl. The output is below.

Model 1: OLS, using observations 1-50

	coefficient	std. error	t-ratio	p-value
const	-0.6789	0.9808	-0.6921	0.4924
X1	0.8482	0.1972	4.3005	0.0001
X2	1.8291	0.4608	3.9696	0.0003
X3	-0.1283	0.7869	-0.1630	0.8712
X4	0.4590	0.5500	0.8345	0.4084

Mean dependent var	4.2211	S.D. dependent var	2.3778
Sum squared resid	152.79	S.E. of regression	1.8426
R-squared	0	Adjusted R-squared	-0.08889
F(4, 45)	9.1494	P-value(F)	2e-05
Log-likelihood	-98.873	Akaike criterion	207.75
Schwarz criterion	217.31	Hannan-Quinn	211.39

1. Construct the ANOVA table for this estimated model. Your answer should include a table consisting of columns for the sum of squares, degrees of freedom, and mean square, and rows labelled 'Estimated', 'Residual' and 'Total'. In addition to providing the completed table, you should provide an explanation of how you computed each element.

2. Notice that the R² has been set to 0, which is clearly incorrect. Calculate the correct R² for this estimated model. Show your working.

Answer 1