The progress report of a research analyst to the supervisor stated: \"All the es

Question

The progress report of a research analyst to the supervisor stated: "All the estimated regression coefficients in our model with three predictor variables to predict sales are statistically significant. Our new preliminary model with seven predictor variables, which includes the three variables of our smaller model, is less satisfactory because only two of the seven regression coefficients are statistically significant. Yet in some initial trials the expanded model is giving more precise sales predictions than the smaller model. The reasons for this anomaly are now being investigated." Comment.

Explanation / Answer

In smaller model, all three predictors are significant, R^2 value would be higher, so fitting good in given test data.

In larger model with 7 predictors (including previous 3 predictors), only 2 variables are significant.

First of all, Need to verify assumptions for multivariate regression i.e

1. Linearity ( linear relationship between independent and dependent parameters)

2. Multivariate Normality (e.g QQ plot - test for normality)

3. No Multicollinearity ( no or less correlated independent parameters)

4. No Autocorrelation ( residuals are not dependent i.e Y(x) does not depend on y(x-1)

5. Homoscedasticity ( error term over the regression should be constant)

There might be chance of multicolinearity.

Also adj. R^2 for both models need to be compared, obviousley it would be greater than smaller and that could be reason

its predicting sales significantly for few test data.

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