Question

# Regression model Using gretl this has been estimated with the output below. Model 1: OLS, using...

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

Given: R2 = 0.99313 and RSS = 6.8318

We know that,

6.8318/TSS = 0.00687

TSS = 994.4396

and TSS = ESS + 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 = MSregression/MSresidual