Quantitative Methods for Decision-Making

1. Suppose you have generated three alternative multiple regression models to explain the variation of a particular variable. The regression output for each model can be summarised as follows:

Model 1 Model 2 Model 3

Number of independent variables 3 5 8

R2 0.75 0.77 0.80

Adj. R2 0.71 0.71 0.69

Which of these models would you select as the “best” option? Fully explain your choice.

The coefficient determination R2 is the percentage of variation of the dependent variable explained by the regression. It explains the percentage of variation and the best fit model for regression analysis.

Adjusted R2 is a modification of R2 that adjusts for the number of explanatory terms in a model. Adjusted-R-Squared value is a measure of the explanatory power of a regression model that takes into consideration the number of independent variables in the model. Adjusted R2 increases only if the new variable which has been added improves the model more than it would be expected by chance.

The best model is a statistically significant model with a high r² and few variables. However, r² will always increase as more variable are added to a regression model even when the new variables have no real predictive capability. The adjusted r² takes into account the number of independent variable in the model. When variables are added to the equation, adjusted r² doesn't increase unless the new variables have additional predictive capability.

The numbers of independent variables are increasing from Model 1 to Model 3. Given the regression output for this questions and considering the R2 value only, the best model is ‘Model 3’ as it explains 80% of the variation in model. However the Adjusted-R-Squared value is decreasing from 0.71 to 0.69. This has shown that more independent variables has added to the model has inflated the R-Squared value and extra variables should be omitted.

Generally, a variable should not be added to the model if it causes the adjusted r² to...