Question

Regression model

Using gretl this has been estimated with the output below.

Model 1: OLS, using observations 1-57

coefficient	std. error	t-ratio	p-value
const	-0.6167	0.2360	-2.6130	0.0118
X1	-1.9892	0.0409	-48.6760	0.0000
X2	0.3739	0.0408	9.1686	0.0000
X3	1.3447	0.0368	36.5730	0.0000
X4	-0.4012	0.0320	-12.5220	0.0000
X5	-0.0478	0.1276	-0.3746	0.7095

Mean dependent var	-6.2529	S.D. dependent var	4.2151
Sum squared resid	6.8318	S.E. of regression	0.366
R-squared	0.99313	Adjusted R-squared	0.99246
F(5, 51)	1475.3	P-value(F)	0
Log-likelihood	-20.418	Akaike criterion	52.835
Schwarz criterion	65.094	Hannan-Quinn	57.599

Construct a complete ANOVA table for this regression. Please show working

Answer 1

Given: R² = 0.99313 and RSS = 6.8318

We know that,

R² = 1 - (RSS/TSS)

RSS/TSS = 1 - 0.99313

RSS/TSS = 0.00687

6.8318/TSS = 0.00687

TSS = 994.4396

and TSS = ESS + RSS

ESS = TSS - RSS

ESS = 994.4396 - 6.8318

ESS = 987.6078

Degrees of freedom are calculated as:

For regression, df = k - 1 = 6 - 1 = 5

For residual, df = n - k = 57 - 6 = 51

For total, df = n - 1 = 57 - 1 = 76

Thus, the ANOVA table is:

Source	df	SS	MS	F
Regression	5	987.6078	197.52156	1474.48
Residual	51	6.8318	0.13396
Total	56	994.4396

where, MS = SS/df

and F = MS_regression/MS_residual