How can multicollinearity affect regression analyses?

Multicollinearity occurs when two or more independent variables in a regression analysis are highly correlated, meaning they provide redundant information about the response variable. This situation can lead to unreliable coefficient estimates, which significantly affects the interpretation of the model.

When multicollinearity is present, it becomes difficult to ascertain the individual effect of each independent variable on the dependent variable. This can manifest in several ways, such as inflated standard errors for the coefficients; as a result, the estimates become unstable and sensitive to small changes in the data. This instability can cause the signs of the coefficients to change, complicating the understanding of relationships between variables. This unreliability can also lead to difficulties in hypothesis testing, making it hard to determine which variables are statistically significant.

Consequently, the primary issue with multicollinearity is that it compromises the regression model's ability to effectively estimate the relationships between the variables, impeding the reliability and interpretability of the analysis.