The Effect of Grouping Data by using Arithmetic Mean on the Significance of the Multiple Linear Regression Model

Adil Mousa Younis Waniss, Abdulmajied Ali Balkash

Abstract: This paper is completely focused on the impact of data aggregation on the multiple linear regression estimation particularly on the significance of the model and the multiple coefficient of determination , we generate random numbers from Excel and built multiple linear regression model with two independent variables ,we compared ungrouped multiple linear regression model with different five aggregated linear regression models, we find that, both F test and R-square are increasing with the increase of aggregation, except in case of grouping by less than five grouped where a Sharpe decreases happened on both of them. Aggregation gives misleading results for the coefficient of determination, but doesn't affect the significance of the different models. We find that grouping should not goes above twenty groups nor below five groups. The most important flinging is that; all ANOVA tables gives same p- values.

Keywords: Aggregation, multiple linear regression. Coefficient of determination, F-test, ungrouped model