I'm trying to forecast sales of a product based on the other variables like Competitor sales, Fuel Price and CPI (Consumer Price Index).
The below given output (based on 1 to 44 months) gives me the lowest MAPE 11.62 when I validated with 45 to 48 actual sales
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2320.6320 496.3898 -4.675 3.83e-05 ***
Sales lag_1 0.2124 0.1119 1.898 0.065515 .
Competi_sales(1) lag1 -1.6535 0.8875 -1.863 0.070404 .
Competi_Sales(1)_lag3 -5.4108 0.8352 -6.478 1.42e-07 ***
Competi sales(2)_lag1 2.3004 0.5726 4.017 0.000277 ***
Fuel price -48.3714 17.5225 -2.761 0.008926 **
CPI 22.2696 3.4485 6.458 1.51e-07 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 212.7 on 37 degrees of freedom
Multiple R-squared: 0.7252, Adjusted R-squared: 0.6806
F-statistic: 16.27 on 6 and 37 DF, p-value: 4.58e-09
I understand that by removing Sales lag_1 and Competi_sales(1) lag1 from the model (since both are not significant at alpha 0.05), the Adjusted R squared can be improved from 0.6806 but when If I do that the MAPE is increasing. For business use, MAPE is often preferred because apparently managers understand percentages better than other accuracy parameters.
Should I go ahead and forecast the sales using this model or should I remove the insignificant variables?