Question
In: Economics
A company is interested in forecasting sales in the final quarter of the year based on...
A company is interested in forecasting sales in the final quarter of the year based on the first three quarters by fitting a linear regression model.
Sales: 215 268 344
Quarter: 1 2 3
What proportion of the variability in sales can be explained by the model?
Also predict the sales for the fourth quarter
Solutions
Expert Solution
The data provided is:
| Sales | Quarter |
| 215 | 1 |
| 268 | 2 |
| 344 | 3 |
On regressing Sales on Quarterly time period in excel, the result is:
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.994743578 | |||||||
| R Square | 0.989514786 | |||||||
| Adjusted R Square | 0.979029573 | |||||||
| Standard Error | 9.389710681 | |||||||
| Observations | 3 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 1 | 8320.5 | 8320.5 | 94.37240076 | 0.065302626 | |||
| Residual | 1 | 88.16666667 | 88.16666667 | |||||
| Total | 2 | 8408.666667 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 146.6666667 | 14.34301998 | 10.22564752 | 0.062059825 | -35.57868177 | 328.9120151 | -35.57868177 | 328.9120151 |
| Quarter | 64.5 | 6.639528096 | 9.714545834 | 0.065302626 | -19.86320334 | 148.8632033 | -19.86320334 | 148.8632033 |
Thus, the OLS regression equation is:
Predicted_Sales = 146.6666667 + 64.5*Quarter
-------------------------------------------------------------------------------------------------------------------------------------------------------
It shall be noted that R-squared value measures the proportion of the variability in sales can be explained by the model
Thus, the proportion of the variability in sales can be explained by the model is 0.989514786331563 or 98.95%
------------------------------------------------------------------------------------------------------------------------------------------------------
When Quarter = 4, the predicted Sales is:
146.6666667 + 64.5*Quarter
=146.6666667 + 64.5*4
=404.67
Rahul Sunny answered 2 years agoRelated Solutions
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