Consider the following multiple regression model: y = 0 + 1 x 1 + …+ k x k + u .
ID: 1139752 • Letter: C
Question
Consider the following multiple regression model: y = 0 + 1x1 + …+ kxk + u. Which of the following statements is correct?
a. MLR.1, the first assumption of multiple linear regression model, is about how the data used to estimate the parameters j‘s are obtained from a random sample.
b. MLR.2, the second assumption of the multiple linear regression model, is about the sample outcomes on any xj, {xij, where i = 1, …, n} not all being the same value, the sample containing at least j+1 observations, and there be no exact linear relationships among the independent variables xj’s.
c. MLR.3, the third assumption of the multiple linear regression model, is about the population model being linear in the parameters k’s.
d. MLR.6, the sixth assumption of the multiple linear regression model, is the error u being independent of the explanatory variables and being normally distributed with zero mean and constant variance 2.
Consider the following multiple regression model: y = 0 + 1x1 + …+ kxk + u. Which of the following statements is correct?
a.
The CLM assumptions can be summarized as, conditional on (x1, … xk), y has a normal distribution with mean linear in x1, …, xk and a constant variance.
b.
Whether normality of error u, and thus normality of y conditional on (x1, … xk) can be assumed, is an empirical matter. For example, past empirical evidence suggests that normality is not a good assumption for wages.
c.
Normality of error u translates into normal sampling distributions of the OLS estimators. Any linear combination of the OLS estimators is also normally distributed, and any subset of them has a joint normal distribution.
d.
All of the above.
a.
The CLM assumptions can be summarized as, conditional on (x1, … xk), y has a normal distribution with mean linear in x1, …, xk and a constant variance.
b.
Whether normality of error u, and thus normality of y conditional on (x1, … xk) can be assumed, is an empirical matter. For example, past empirical evidence suggests that normality is not a good assumption for wages.
c.
Normality of error u translates into normal sampling distributions of the OLS estimators. Any linear combination of the OLS estimators is also normally distributed, and any subset of them has a joint normal distribution.
d.
All of the above.
Explanation / Answer
answer:
part i.)
part c correct as regression model is assumed to be linear in parameter and may or may not be linear in explanatory varibales.
part d is correct as it is about homogeneity and endogeneity ( i.e. error variance is constant ; and errors and X's have 0 correlation )
part b is correct as it is about multicollinearity ( i.e. there should be no perfect linear relationship among explanatory variables)
part a is incorrect as CLRM assumptions are regarding the population and not sample.
part ii.)
given a k variable linear regression model the correct answer is part a and c
reason:
part a is correct as it says about homoscedasticity and since u~N(0,sigma^2) and y is a linear combimation of normally distributed variable, it is also normally distributed with mean
E(Y/X)= b1+b2X2+...... +bkXk i.e. nothing but linear in X1 ,...... , Xk
part c is correct since u is normal that implies Y is normal and because of that ols estimators are normal as they are linear combinations of X's and Y where X's are fixed . thus, applying normal distribution property ols estimators are also normally distributed.
part b is incorrect as normality of u and further y is a theoritical concept and the CLRM assumption which will hold true in all cases . it is not an empirical matter as these population assumptions cannot be checked using the sample data.