Section 1: True/False, & explain why three or more sentences:
2. In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, β3 has no meaning since (Xi×Di) = 0 when Di= 0.
ANSWER:
Yes, it is true when =0,
= 0 then
Yi becomes
so here in the above equation, there is no , so when
=0:
has no
meaning
The effect of X depends on D
=increment
to the effect of X, when D= 1 then Yi becomes
here increment
to the effect of X
and when these two =1
and
=0 indicates the
difference in slopes of two regression lines
Section 1: True/False, & explain why three or more sentences: 2. In the regression model Yi...
Suppose that we have data on ECON 333 test scores (Yi), duration for which student i studies for exam (Xi), and the major of the student, call it Di, where Di =( 1, if economics major 0, if non economics major Consider the following model: Yi = β0 + β1Xi + β2Di + β3DiXi + ui (1) where Assumption 1 holds: E (ui|Xi,Di) = 0. (2) Yi is the score between 0 and 100. Xi is the duration studied in...
Consider the regression model: yi = β0 + β1Xi + εi for…. i = 1 Where the dummy variable (0 = failure and 1 = success). Suppose that the data set contains n1 failure and n2 successes (and that n1+n2 = n) Obtain the X^T(X) matrix Obtain the X^T(Y) matrix Obtain the least square estimate b
1. If a true model of simple linear regression reads: yi −y ̄ = β0 +β1(xi −x ̄)+εi for i = 1, 2, · · · , n, showβ0 =0andβˆ0 =0. (1pt) (hint: use the formula of estimator βˆ0 = y ̄ − βˆ1x ̄.)
Consider the following regression model: Xi = Bo + Bixi + y; where yi is individual i's University GPA and xi is the individual's high school grades. a. What do you think is in ui? Do you think E[ulx) = 0? Suggest a variable that you think might affect University GPA that isn't included in the regression equation but should be. c. What sign of bias would you expect in an OLS regression of y on x? Briefly explain. d....
Testing the equality of two regression coefficients. Suppose that you
are given the following regression model:
Yi = β1 + β2X2i + β3X3i + ui
and you want to test the hypothesis that β2 = β3. If we assume that the ui
are normally distributed, it can be shown that
t = βˆ
2 − βˆ
3
var (βˆ
2) + var (βˆ
3) − 2 cov (βˆ
2, βˆ
3)
follows the t distribution with n − 3...
TRUE or FALSE and Explain why: In a multiple regression model, the inclusion of a variable
TRUE or FALSE and Explain why: If the error term in a simple regression model is heteroskedastic, the estimated OLS coefficients are biased.
Log-lin model in simple regression:
yi=B0.B1Xi.eui
take natural log of both sides
lnyi=lnB0 + (lnB1)xi +
ui . Take lnyi = wi,
lnB0= B*0 and
lnB1=B*1 so the former equation
equals to wi= B*0 +
B*1 + ui. It is said that, when
you increase x by 1 unit, you expect B*1 %
change in y.
B*1
=(dyi/yi) / dxi =
= (((yi-yi-1)/yi) /
(xi- xi-1))*100 . question is about the
numerator, (yi-yi-1)/yi)*100:
1)It is said that the numerator reflects...
12. (Ch13.5) True or False? The effect of a binary predictor in a multiple regression with three predictors (two of them are continuous, one is binary) is to shift the regression fitting plane up or down 13. (Ch13.5) True or False? Unlike other predictors, the student's t for testing the significance of a binary predictor is either 0 or l1 14. (Ch13.5) In a multiple regression model of student grades, we would code the nine categories of business courses taken...