Question

# The regression model Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i + ui...

The regression model

Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i + ui

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.