Discuss the strength and the significance of your regression model by using R-square and significance F where α = 0.05.
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.919011822 | |||||||
R Square | 0.844582728 | |||||||
Adjusted R Square | 0.834446819 | |||||||
Standard Error | 163.953479 | |||||||
Observations | 50 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 3 | 6719578.309 | 2239859.44 | 83.3257999 | 1.28754E-18 | |||
Residual | 46 | 1236514.191 | 26880.7433 | |||||
Total | 49 | 7956092.5 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 21.7335244 | 114.2095971 | 0.19029508 | 0.84991523 | -208.158471 | 251.62552 | -208.15847 | 251.62552 |
sqft | 0.546807448 | 0.076647924 | 7.13401509 | 5.738E-09 | 0.392523179 | 0.70109172 | 0.39252318 | 0.70109172 |
age | -3.075663237 | 2.263665569 | -1.3587092 | 0.18086435 | -7.632185699 | 1.48085922 | -7.6321857 | 1.48085922 |
features | 40.54881241 | 15.65468404 | 2.59020318 | 0.0128049 | 9.0375678 | 72.060057 | 9.0375678 | 72.060057 |
Multiple Regression
From the given output we can see that R Square is 0.844582728 which means approximately 84% of the total variation in the dependent variable can be explained by the set of independent variables. So the model is good enough strong for prediction.
We see that the significance F is 1.28754E-18 which is smaller than alpha 0.05. It indicates that at 95% level of significance the regression coefficients are significant. Thus we can say that the model is fine and we can continue with this set of independent variables.
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