MGT5380

 Academic Year 2020-2021 

Practice In-Course Exam

Version 1: Updated on 2021 June 11

Instruction: 

Choose ONE question out of A1 and A2.

 Choose ONE question out of B1 and B2.

A1 

In this question, you are supposed to show all steps in your matrix algebra and calculations.

We have the five observations from firm A to E, described by

Firm               𝒚 𝒊                       x 𝒊

A                     4                          5 

B                     7                          6 

C                     9                          7

D                     6                          8

E                    10                         9

You are interested in running an ordinary least squares (OLS) estimation with the specification of

A2

 Suppose that x𝑖 and y 𝑖 satisfy the assumptions of a classical linear regression model:

B1

B2 

We consider the hedonic model, in which

Dependent Variable:

 - Rental Value for a building 

12 Explanatory Variables:

 - LnAGE: log of the apparent age of the property 

- NBROOMS: number of bedrooms 

- AREABYRM: area per room (in square meters)

 - ELEVATOR: dummy variable = 1 if the building has an elevator; 0 otherwise

 - BASEMENT: dummy variable = 1 if the unit is located in a basement; 0 otherwise 

- OUTPARK: number of outdoor parking spaces 

- INDPARK: number of indoor parking spaces 

- NOLEASE: dummy variable = 1 if the unit has no lease attached to it; 0 otherwise

 - LnDISTCBD: log of the distance in kilometres to the central business district

 - SINGLPAR: percentage of single parent families in the area 

- DSHOPCNTR: distance in kilometres to the nearest shopping centre 

- VACDIFF1: vacancy difference between the building and the census figure The regression outcome is reported in the following table:

The Residual Sum of Squares (RSS) for this regression is 152.56.

(1) Briefly explain the hedonic model.

(2) State the null and alternative hypothesis that all slopes are zero. Then, by using the F Statistic reported at the bottom of the table, report the test result of this hypothesis with 5% significance.

(3) We would like to test if the coefficients of OUTPARK, NOLEASE, LnDISTCBD, and VACDIFF1 are zero. We run the regression without these explanatory variables, and obtain the restricted Residual Sum of Squares (RRSS) of 158.23. Using F-statistic, show if the coefficients of these four variables match the hypothesis.

(4) Discuss if the sings of the coefficients agree with the priori expected signs