In: Statistics and Probability
8) Consider the following regression model
Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i + β5X5i + ui
This model has been estimated by OLS. The Gretl output is below.
Model 1: OLS, using observations 1-52
coefficient | std. error | t-ratio | p-value | |
const | -0.5186 | 0.8624 | -0.6013 | 0.5506 |
X1 | 0.1497 | 0.4125 | 0.3630 | 0.7182 |
X2 | -0.2710 | 0.1714 | -1.5808 | 0.1208 |
X3 | 0.1809 | 0.6028 | 0.3001 | 0.7654 |
X4 | 0.4574 | 0.2729 | 1.6757 | 0.1006 |
X5 | 2.4438 | 0.1781 | 13.7200 | 0.0000 |
Mean dependent var | 1.3617 | S.D. dependent var | 3.6435 |
Sum squared resid | 128.39 | S.E. of regression | 1.6707 |
R-squared | 0.81036 | Adjusted R-squared | 0.78975 |
F(5, 46) | 39.312 | P-value(F) | 0 |
Log-likelihood | -97.285 | Akaike criterion | 206.57 |
Schwarz criterion | 218.28 | Hannan-Quinn | 211.06 |
Use an F-test with the critical value method and a significance level of 5% to test H0:β2+β1=0H0:β2+β1=0 against H1:β2+β1≠0H1:β2+β1≠0.
Derive the restricted regression model.
The restricted model has been estimated and its residual sum of squares is SSRr=128.59SSRr=128.59. Compute the value of the F-statistic.
Do you reject the null hypothesis?
Let me know in the comment section if anything is not
clear. I will reply ASAP!
If you like the answer, please give a thumbs-up. This will be quite encouraging for me.Thank-you!