Introduction

In the realm of regression analysis, model specification holds paramount importance. Accurate model specification ensures reliable results and meaningful interpretations of relationships between variables. This chapter delves into the consequences of two common model specification errors: excluding a relevant explanatory variable and including an irrelevant regressor. We will explore how each error impacts regression outcomes, examine the resulting biases, and discuss strategies to mitigate such errors.

Consequences of Excluding a Relevant Explanatory Variable

Excluding a relevant variable from a regression model can lead to biased parameter estimates, inefficient coefficient estimates, and omitted variable bias. Omitted variable bias occurs when a relevant variable is not included in the model, leading to an incorrect estimation of the relationship between the included variables and the response variable. This bias may misrepresent the true nature of the relationship and affect the predictive power of the model.

Example: Consider a real estate market analysis where the price of a house is regressed against its size but not the number of bedrooms. If the number of bedrooms significantly affects the price, excluding it may lead to underestimating the true impact of house size on price.

Consequences of Including an Irrelevant Regressor

Including irrelevant variables in a model introduces multicollinearity, which can lead to unstable coefficient estimates and increased standard errors. Multicollinearity occurs when two or more regressors are highly correlated, making it difficult to disentangle their individual effects. This can lead to difficulties in interpreting the relationships between variables and may reduce the model’s predictive accuracy.

Example: In a sales analysis, including a variable like “day of the week” as a regressor might introduce multicollinearity if it’s unrelated to sales. This can lead to inflated standard errors and misleading coefficient interpretations.

Mitigation Strategies

To address the consequences of model specification errors, practitioners can adopt various strategies. For excluding relevant variables, thorough domain knowledge and exploratory analysis are vital to identify all potential predictors. For irrelevant regressors, conducting correlation analysis and using techniques like stepwise regression can help avoid multicollinearity and enhance model accuracy.