In: Statistics and Probability
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 |
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.
Notice that the R2 has been set to 0, which is clearly incorrect. Calculate the correct R2 for this estimated model. Show your working.