Question

True or False: Please specify your reasons.

(i) If an independent variable in a multiple linear regression model is an exact linear combination of other independent variables, we can still calculate the least square estimators of the intercept.

(ii) For the multiple linear regression y = β0 + β1x + β2x 2 + u, β1 can be interpreted as the effect of one unit increase in x on y.

(iii) In the multiple linear regression with an intercept, (the sum of the residuals equals zero) may not hold as in the simple regression.

(iv) When adding an irrelavent regressor, R2 will decrease

Answer 1

(i) False. If there is an exact linear combination between independent variables then regression model will suffer from perfect multicollinearity and it becomes impossible to calculate the OLS estimators.

(ii)False.β1 can be interpreted as the effect of one unit increase in X1 on Y,keeping other factors constant.

(iii) False. Sum of residuals is always zero in the case of multiple regression model with an intercept.

(iv)False.R2 always increases with an addition of new variables no matter whether its relevant or irrelevant.

If you have any doubt,feel free to ask.