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MGT5380
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
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

= + + ,

where is the intercept, is the slope, and is the error term. Equivalently, we have the matrix
notation of

= + ,
where
= [

].

(1) Calculate ’, ’, and the inverse of (’), that is (’)?1. Then, Calculate the OLS estimate
for and . Show each step of derivation process.
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(2) Based on the OLS estimate derived in (1), calculate the error term for each observation.
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(3) Calculate 2 and SE(?). Show each derivation process.
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(4) Test the hypothesis that 0: = 0 with the two-sided alternative of 1: ≠ 0 at the 5 percent
significance level.
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A2
Suppose that and satisfy the assumptions of a classical linear regression model:

= + + .

The OLS estimation with a random sample size of n = 30 yields:

? = 43.2 + 61.5
(10.2) (7.4)

R2 = 0.54 =1.52

where the numbers in parentheses are standard errors.

(1) Construct a 95% confidence interval for the estimate of the intercept coefficient.
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(2) Test H0: 1 = 55 vs. H1: 1 ≠ 55 at the 5% significance level. Furthermore, Test H0: 1 = 55 vs. H1: 1 > 55
at the 5% significance level.
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(3) In another scenario, the error terms satisfy the normality assumption: is normally distributed as (0,
2),
and it is independent of . Discuss how the normal distribution assumption of changes the analyses of (2).
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(4) Interpret R2.
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B1
A researcher estimates the following econometric model, which includes a lagged dependent variable:

= 1 + 22 + 33 +
= 1 + 22 + 33 + 44 +

where and are i.i.d. disturbances and 3 is an irrelevant variable, which does not enter into the
data generating process for .

(1) If the researcher runs a regression for the second model with a large sample size, what estimate of 3
is she/he likely to obtain? Explain.
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(2) If the researcher runs regressions for both models, will the 2 values be the same for both models?
Discuss.
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(3) Furthermore, if the researcher runs regressions for both models, will the adjusted-2 values be the
same for both models? Discuss.
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(4) What are the units of 2 and adjusted-2? Explain
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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.
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(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.
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(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.
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(4) Discuss if the sings of the coefficients agree with the priori expected signs.
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