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

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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%

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When Quarter = 4, the predicted Sales is:

146.6666667 + 64.5*Quarter

=146.6666667 + 64.5*4

=404.67

Rahul Sunny answered 2 years ago
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