Question

If one or more of the relevant predictor variables are excluded, then the resulting OLS estimators are biased. The extent of the bias depends on the degree of the ____________ between the included and the excluded predictor variables.

Answer 1

In regression analysis, if predictor variables are excluded, the resulting OLS estimators can be biased. The extent of the bias depends on the correlation between the included and excluded variables.

Step-by-step explanation:

In regression analysis, if one or more relevant predictor variables are excluded, the resulting Ordinary Least Squares (OLS) estimators become biased. The extent of this bias depends on the degree of the correlation between the included and excluded predictor variables.

To understand why bias occurs, consider that predictor variables are used to explain the variation in the response variable. When a relevant predictor variable is excluded, the model fails to capture its contribution to the response variable. This leads to biased estimates of the regression coefficients.

For example, let's say we are studying the relationship between a person's height and their weight. If we exclude an important predictor variable like gender, which is correlated with both height and weight, the estimated coefficients for height may be biased due to the omitted gender variable.