Question

PROVIDE EXPLANATION PLS!

1. The owner of a construction firm, upon seeing the regression result, disagrees because the model suggests that the number of bathrooms does not contribute information in the prediction of home price. He explains that when he adds another bathroom, it increases the value of the home. How might you explain this apparent paradox?
A, If it is determined that bigger homes tend to have more bathrooms, then multicollinearity may be a problem. That would lead to an inflation of the standard error of the estimate and lower F value.
B. If it is determined that bigger homes tend to have more bathrooms, then multicollinearity may be a problem. That would lead to an inflation of the standard error of the coefficients and lower t values.       
C. If the owner of the construction firm is correct in his observation, then it means that heteroscedasticity is a problem with the model. In that case, the model should be abandoned.
D. If the owner of the construction firm is correct in his observation, then it means that the model residuals are not normally distributed. In that case, the model should be abandoned

Answer 1

option B) is correct

t = coefficient/ standard error

the more correlated the X variables are with each other, the bigger the standard errors

become, and the less likely it is that a coefficient will be statistically significant. This is known as the problem of multicollinearity.

Intuitively, the reason this problem occurs is as follows: The more highly correlated independent variables are, the more difficult it is to determine how much variation in Y each X is responsible for. For example, if X1 and X2 are highly correlated (which means they are very similar to each other) it is difficult to determine whether X1 is responsible for variation in Y, or whether X2 is. As a result, the standard errors for both variables become very large.