I need to comment on the validity of the regression model and the significance o

Question

I need to comment on the validity of the regression model and the significance of individual coefficients. The relationship (positive or negative) between the dependent variable and each of the independent variables with significant coefficient needs to be briefly discussed and comment if those relationships are expected. Report the adjusted r-squared and briefly comment on the fitness of the model.

Quarters Revenue Seasonal 2008-01-01 10379 3.6 2008-04-01 12009 3.6 2008-07-01 14509 3.6 2008-10-01 11728 3.7 2009-01-01 9984 3.9 2009-04-01 11832 4.0 2009-07-01 13844 4.1 2009-10-01 11375 4.2 2010-01-01 10168 4.2 2010-04-01 12388 4.3 2010-07-01 14361 4.5 2010-10-01 11587 4.6 SUMMARY OUTPUT Regression Statistics Multiple R 0.111015934 R Square 0.012324538 Adjusted R Square -0.086443009 Standard Error 1606.474677 Observations 12 ANOVA df SS MS F Significance F Regression 1 322035.7872 322035.7872 0.124783272 0.731236691 Residual 10 25807608.88 2580760.888 Total 11 26129644.67 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 10056.85199 5558.889946 1.809147525 0.100541987 -2329.126675 22442.83065 -2329.126675 22442.83065 Seasonal 486.1651376 1376.276292 0.353246758 0.731236691 -2580.369539 3552.699815 -2580.369539 3552.699815

Explanation / Answer

SOlution-

Cofficient of the slope of seasonal explanatory variable = 486.165 which is positive. This is expected as more seasonal value rises, more sales and and thus more revenue is expected or vice versa.

To check the significance of sesonal variable, we have p-vallue from the table equal to = 0.7312

This is greater than 0.05 and thus null hypothesis- slope is not significant is not rejected

and thus slope is not significant.

Adjusted value of R2 = -0.0864

Value of R2 = 0.01232

This means that only 1.232% of the total variation in the revenue variable is explained by the model.

This low value indicates that model is poorly fit here!

Thanks!

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