Question

In determining if this regression is significant, I observed the following, am I taking the correct approach?

To check if your results are reliable (statistically significant), look at Significance F (0.00). If this value is less than 0.05, the regression is acceptable. If Significance F is greater than 0.05, it's advisable to stop using this set of independent variables.

As part of the hypothesis test, we should evaluate R-squared as it measures the strength of the relationship between the model and the dependent variable. This is not a formal test for a relationship but can be used in conjunction with an f-test. The F-test of overall significance is the hypothesis test for this relationship. If the overall F-test is significant, you can conclude that R-squared does not equal zero, and the correlation between the model and dependent variable is statistically significant.

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.9613 0.9241 0.9222 1425.3397 200 ANOVA Significance df MS Regression Residual Total 479410417802.47 95882083560.49 472.4892 39368362197.53 518778780000.00 0.00 194 199 202929702.05 Upper 95% CoefficientsStandard Erro t Stat P-value Lower 95% 45482.366 -10383.543 11.088 738.388 0.014 2.546 19403.8863 3153.7202 10.4859 175.8223 0.0023 1.2209 Intercept 2.340.0201 7217.90 83746.83 -3.290.0012 16602.68 -4164.41 31.77 391.67 1085.11 0.02 0.14 v2 1.06 0.2916 0.0000 0.0000 0.0383 -9.59 4.20 6.37 2.09 V4 V5 4.95

Answer 1

Yes, your approach is right

In your problem, there are 5 predictor variables. The global p- value for your regression is 0 (< 0.05). This means at least one of the 5 predictor variables is statistically significant. Further, if you look at the individual p- values, all except v2 are < 0.05. This means v1, v3, v4, v5 are statistically significant while v2 is not.