Question

Y=α+βX+u; parameters α and β has no economic interpretation. And that fitted regression always passes through the mean values of X and Y. T/F? explain your answer. b. regression equation is all about predicting the mean value of dependent variable. T/F ? explain your answer. c. OLS estimators are unbiased if and only if Cov(X,u)=0.T/F ? explain your answer. d. For a regression Y=α+β Xˉ+u the degree of goodness of fit is zero. T/F? explain your answer. e. For a regression Y=a+u the degree of goodness of fit is zero. T/F? explain your answer. f. We can not estimate the equation Y=a+bX 2+u with the help of OLS method. T/F? explain your answer. g. For a regression Y=βX+u; we may note that ∑ u^=∑u^2=0.T/F ? explain your answer.

Answer 1

a. False. The parameters α and β do have economic interpretations, representing the intercept and slope, respectively. The fitted regression always passes through the mean values of X and Y due to the nature of OLS estimation.

b. True. The regression equation estimates the mean value of the dependent variable for a given value of the independent variable.

c. True. OLS estimators are unbiased if and only if the covariance between the independent variable X and the error term u is zero.

d. False. The degree of goodness of fit is not zero; it is measured by the coefficient of determination (R-squared), indicating the proportion of the dependent variable's variance explained by the independent variable.

e. True. If Y=a+u, and there are no independent variables, the degree of goodness of fit is zero.

f. False. OLS can estimate equations with quadratic terms like Y=a+bX^2+u.

g. False. The sum of the residuals (∑u^) may not be zero, and the sum of squared residuals (∑u^2) is generally not zero in a regression with non-zero residuals.

Step-by-step explanation:

a. α and β have economic interpretations as the intercept and slope, and the fitted regression passes through the mean values due to OLS properties.

b. The regression equation predicts the mean value of the dependent variable for a given value of the independent variable.

c. Cov(X,u)=0 ensures unbiasedness of OLS estimators.

d. The degree of goodness of fit is measured by R-squared, not zero.

e. If there are no independent variables, the degree of goodness of fit is indeed zero.

f. OLS can estimate equations with quadratic terms.

g. The sums of residuals are not guaranteed to be zero in a regression.