Question

Which of the following statements is NOT true about multicollinearity?

a. We cannot use a model that contains multicollinearity
b. When there is a strong correlation between two predictors (X variables) in a model, multicollinearity exists
c. If two variables have a correlation of 1 or -1, we have perfect multicollinearity
d. If two variables have a correlation of 0, they are independent

Answer 1

Multicollinearity does not render a model unusable; it requires caution and mitigation techniques. A correlation coefficient near -1 or 1 indicates strong correlation, while a coefficient of 0 implies independence between variables.

Step-by-step explanation:

The statement that is NOT true about multicollinearity is that 'We cannot use a model that contains multicollinearity'. While multicollinearity can pose problems, such as unreliable estimates of coefficient values and difficulties in determining the specific effect of each independent variable, it does not make a model entirely unusable. Analysts can still employ various techniques to mitigate the effects of multicollinearity and use the model with caution.

For a correlation coefficient ('r'), values closer to -1 or 1 indicate a strong linear relationship, regardless of whether the relationship is positive or negative. Hence, both a coefficient of -1 and 1 imply perfect multicollinearity or a perfect linear relationship between two variables. A correlation of 0 indicates no linear relationship—meaning that as one variable changes, there is no predictable pattern in the change of the other variable, and they are considered independent.