An analyst observes a positive relationship between digital marketing expenses and online sales for a firm. However, she intuitively feels that she should add an additional predictor variable, one that has a high correlation with marketing expenses.If the analyst adds this independent variable to the model, which of the following can happen?Note: Multiple options can be correct.The model’s R-squared could decrease.The model’s adjusted R-squared could decrease.The beta-coefficient for the predictor digital marketing expenses will remain the same.The relationship between marketing expenses and sales could become insignificant.
Question
An analyst observes a positive relationship between digital marketing expenses and online sales for a firm. However, she intuitively feels that she should add an additional predictor variable, one that has a high correlation with marketing expenses.If the analyst adds this independent variable to the model, which of the following can happen?Note: Multiple options can be correct.The model’s R-squared could decrease.The model’s adjusted R-squared could decrease.The beta-coefficient for the predictor digital marketing expenses will remain the same.The relationship between marketing expenses and sales could become insignificant.
Solution
When an additional predictor variable is added to a model, several things can happen:
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The model's R-squared could decrease: This is unlikely. The R-squared value of a model generally increases or stays the same when a new predictor variable is added, because R-squared measures the proportion of the variance in the dependent variable that is predictable from the independent variables. Adding another variable can only increase or leave this proportion unchanged.
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The model's adjusted R-squared could decrease: This is possible. The adjusted R-squared takes into account the number of predictors in the model. If the new variable does not significantly improve the model's predictive power, the adjusted R-squared could decrease.
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The beta-coefficient for the predictor digital marketing expenses will remain the same: This is unlikely. The beta-coefficient of a variable can change when other variables are added to the model, because the coefficients are calculated based on the relationships between all the variables in the model.
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The relationship between marketing expenses and sales could become insignificant: This is possible. If the new variable is highly correlated with marketing expenses, it could absorb some of the explanatory power that was previously attributed to marketing expenses. This could make the relationship between marketing expenses and sales appear less significant in the model.
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