Regression Analysis and Change
Updated: November 11, 2011
Lecturer: Thilo Klein
Contact: tk375@cam.ac.uk
Contest Quiz 6
Question Sheet
In this quiz we will review non-linearity and model transformations covered in lectures 6 and 7.
Question 1: Logarithms
(i) The interpretation of the slope coefficient in the model Yi = β0 + β1 ln(Xi ) + ui is as follows:
(a) a 1% change in X is associated with a β1 % change in Y.
(b) a 1% change in X is associated with a change in Y of 0.01 β1 .
(c) a change in X by one unit is associated with a β1 100% change in Y.
(d) a change in X by one unit is associated with a β1 change in Y.
(ii) The interpretation of the slope coefficient in the model ln(Yi ) = β0 + β1 Xi + ui is as follows:
(a) a 1% change in X is associated with a β1 % change in Y.
(b) a change in X by one unit is associated with a 100β1 % change in Y.
(c) a 1% change in X is associated with a change in Y of 0.01β1 .
(d) a change in X by one unit is associated with a β1 change in Y.
(iii) The interpretation of the slope coefficient in the model ln(Yi ) = β0 + β1 ln(Xi ) + ui is as follows: (a) a 1% change in X is associated with a β1 % change in Y.
(b) a change in X by one unit is associated with a β1 change in Y.
(c) a change in X by one unit is associated with a 100β1 % change in Y.
(d) a 1% change in X is associated with a change in Y of 0.01β1 .
(iv) To decide whether Yi = β0 + β1 X + ui or ln(Yi ) = β0 + β1 X + ui fits the data better, you cannot consult the regression R2 because
(a) ln(Y) may be negative for 0 < Y < 1.
(b) the TSS are not measured in the same units between the two models.
(c) the slope no longer indicates the effect of a unit change of X on Y in the log-linear model. (d) the regression R2 can be greater than one in the second model.
1
(v) The exponential function
(a) is the inverse of the natural logarithm function.
(b) does not play an important role in modeling nonlinear regression functions in econometrics.
(c) can be written as exp(ex ).
(d) is ex , where e is 3.1415...
Lecturer: Thilo Klein
Contact: tk375@cam.ac.uk
Contest Quiz 6
Question Sheet
In this quiz we will review non-linearity and model transformations covered in lectures 6 and 7.
Question 1: Logarithms
(i) The interpretation of the slope coefficient in the model Yi = β0 + β1 ln(Xi ) + ui is as follows:
(a) a 1% change in X is associated with a β1 % change in Y.
(b) a 1% change in X is associated with a change in Y of 0.01 β1 .
(c) a change in X by one unit is associated with a β1 100% change in Y.
(d) a change in X by one unit is associated with a β1 change in Y.
(ii) The interpretation of the slope coefficient in the model ln(Yi ) = β0 + β1 Xi + ui is as follows:
(a) a 1% change in X is associated with a β1 % change in Y.
(b) a change in X by one unit is associated with a 100β1 % change in Y.
(c) a 1% change in X is associated with a change in Y of 0.01β1 .
(d) a change in X by one unit is associated with a β1 change in Y.
(iii) The interpretation of the slope coefficient in the model ln(Yi ) = β0 + β1 ln(Xi ) + ui is as follows: (a) a 1% change in X is associated with a β1 % change in Y.
(b) a change in X by one unit is associated with a β1 change in Y.
(c) a change in X by one unit is associated with a 100β1 % change in Y.
(d) a 1% change in X is associated with a change in Y of 0.01β1 .
(iv) To decide whether Yi = β0 + β1 X + ui or ln(Yi ) = β0 + β1 X + ui fits the data better, you cannot consult the regression R2 because
(a) ln(Y) may be negative for 0 < Y < 1.
(b) the TSS are not measured in the same units between the two models.
(c) the slope no longer indicates the effect of a unit change of X on Y in the log-linear model. (d) the regression R2 can be greater than one in the second model.
1
(v) The exponential function
(a) is the inverse of the natural logarithm function.
(b) does not play an important role in modeling nonlinear regression functions in econometrics.
(c) can be written as exp(ex ).
(d) is ex , where e is 3.1415...