Multiple Linear Regression

Question

What are the conditions needed to conduct inferences when dealing with Multiple Linear Regression?

Answer 1

When conducting inferences in Multiple Linear Regression, there are several conditions that must be met in order to ensure the validity of the results:

1. Linearity: The relationship between the dependent variable and the independent variables should be linear.
2. Independence of observations: The observations should be independent of each other, meaning that the value of the dependent variable for one observation should not affect the value of the dependent variable for any other observation.
3. Homoscedasticity: The variance of the errors should be constant across all levels of the independent variables. This means that the spread of the residuals should be constant, regardless of the value of the independent variables.
4. Normality of residuals: The residuals (i.e., the differences between the observed values and the fitted values) should be approximately normally distributed.
5. No multicollinearity: The independent variables should not be highly correlated with each other. This can lead to unstable and unreliable regression coefficients.
6. No omitted variable bias: All relevant independent variables should be included in the model. Omitting important variables can lead to biased and inefficient regression coefficients.
7. No autocorrelation: The residuals should not be autocorrelated, meaning that the value of the residual for one observation should not be related to the value of the residual for any other observation.

Satisfying these conditions is important for ensuring that the regression results are trustworthy and meaningful. If any of these conditions are not met, the results of the regression may be biased, inconsistent, or otherwise unreliable.