19. Interpret the results of the multiple regression shown below SUMMARY OUTPUT

Question

19. Interpret the results of the multiple regression shown below SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.14219048 0.02021813 0.00831795 16.1730108 251 ANOVA Significance sS MS 3 1333.18478 444.3949 1.698976 0.167797233 Regression Residual Total 247 64606.871 261.5663 250 65940.05578 UpperLowerUpper tStat p.value Lower 95% 95% 95.0% 95.0% Standard Intercept X Variable1 X Variable 2 X Variable 3 Coefficients ErrorStat P value 81.9293186 5.961063779 13.74408 2.62E-32 70.18831939 93.67032 70.18832 93.67032 0.04068006 0.061794765 0.658309 0.510953 0.08103183 0.162392 0.08103 0.162392 0.3941406 0.18642299 2.11423 0.035498 0.76132213 0.02696 0.76132 0.02696 0.16716363 0.308115478 0.542536 0.587939 0.43970517 0.774032 0.43971 0.774032 of 10 1342 words L

Explanation / Answer

This is a multiple regression output:

The R^2 which is tte coeff of determination is 0.02 which means the model does not fit well with the regression equation, The Regression equation is Y= 81.929 +0.04 X1 -0.039X2 +0.167X3.

So for different values of X1, X2 and X3, Y can be predicted

The R which is the correlation is 0.14 which shows there is a weak correlation between the dependent and the independent variable

The t stat and p values give us how significant the intercept and parameters are in predicting the trend for the population and the total observation on which this multiple regression is done is 251

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