The regression model
Y_{i} = β_{0} + β_{1}X_{1i} + β_{2}X_{2i} + β_{3}X_{3i} + β_{4}X_{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 |
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 R^{2} has been set to 0, which is clearly incorrect. Calculate the correct R^{2} for this estimated model. Show your working.
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