Omitted Variable Bias and Inclusion of Irrelevant Variables In multiple linear regression (MLR), the omitted variable bias occurs when the dependent va...
In multiple linear regression (MLR), the omitted variable bias occurs when the dependent variable is not included in the regression model. This can happen for several reasons, including:
Omitted variable error: This occurs when the relevant variable is not included in the model due to measurement error, sampling bias, or other factors.
Measurement error: When the independent variables are measured with error, this can also lead to omitted variable bias.
Multicollinearity: When the independent variables are highly correlated with each other, this can also cause omitted variable bias.
The inclusion of irrelevant variables is another type of bias that can occur in MLR. This occurs when the independent variables are not selected into the model based on their significance. This can happen for several reasons, including:
Sampling bias: This occurs when the relevant independent variables are not sampled correctly, leading to biased estimates.
Model selection bias: This occurs when the best model is not selected based on the data, leading to biased estimates.
Computational bias: This occurs when the independent variables are highly non-normally distributed, which can bias the estimates.
Both omitted variable bias and the inclusion of irrelevant variables can lead to ** biased and inefficient estimates**. This can result in misleading conclusions about the relationship between the dependent and independent variables.
Examples:
Imagine a study that aims to predict house prices based on various factors, including location, size, and number of bedrooms. If the "location" variable is omitted from the model due to measurement error, the resulting estimate of house price may be biased.
Imagine a regression where the "number of bedrooms" is highly correlated with the other independent variables. Including this variable in the model may lead to omitted variable bias, even though it is not a relevant factor in determining house price