vANSWER ALL QUESTIONS: 50 MARKS IN TOTAL

Question # 00080157 Posted By: kimwood Updated on: 07/07/2015 01:18 AM Due on: 08/06/2015
Subject Mathematics Topic General Mathematics Tutorials:
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vANSWER ALL QUESTIONS: 50 MARKS IN TOTAL

Econometrics Practice Final Exam

Question 1 (30 MARKS)

A research has estimated the following multiple regression model for cinema gross box office:

GBO =

Where GBO is the gross box office, NOA is the number of admissions, NFS is the number of films screened and TPC is the top price of cinema ticket.

An (incomplete) regression output is shown as follow:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.984698

R Square

0.969631

Adjusted R Square

0.964272

Standard Error

48.06609

Observations

21

ANOVA

df

SS

MS

F

Significance F

Regression

3

1254015

418004.9

180.9272

4.27E-13

Residual

17

39275.93

2310.349

Total

20

1293290

Coefficien

Standard

t Stat

P-value

Lower

Upper

ts

Error

95%

95%

Intercept

-279.29 108.9081 -2.56445 0.020103 -509.066 -49.5137

NOA

8.673796

1.174789

7.383281

1.07E-06

6.195208

11.15238

NFS

-0.10242

0.515111

TPC

21.59475

13.0633

1.653085

0.11666

-5.96641

49.1559

(a) Perform a one-sided significance test for the coefficient for NFS. Use a 5% significance level. It might be useful to note that “=T.INV.2T(0.05,17)” = 2.11, “=T.INV.2T(0.5,17)”= 0.69 and “=T.INV.2T(0.1,17)” = 1.74.

(5 Marks)

(b) Interpret the estimated coefficients for NOA and NFS. Do they make sense or have the sign that you would expect? Explain

(5 Marks)


Page 1 of 3


(c) Construct a 95% confidence interval for NFS. Interpret this interval.

Once again, it might be useful to note that “=T.INV.2T(0.05,17)” = 2.11, “=T.INV.2T(0.5,17)”= 0.69 and “=T.INV.2T(0.1,17)” = 1.74.

(5 Marks)

(d) What are the F-statistic and corresponding p-value testing in the above regression? Sketch (roughly) the F distribution, and indicate the relative locations of the F-stat, F-crit (which is, in this case, 3.01), and the rejection region for an F-test on this model. What would your conclusion be?

(5 Marks)

(e) The researcher has also estimated a quadratic relationship between the number of admissions and the gross box office. Where the regression output is shown as follow. What are the major differences you have found from the previous model? Can you think of any reasons to these differences?

(10 Marks)

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.998288

R Square

0.996579

Adjusted R Square

0.995723

Standard Error

16.62989

Observations

21

ANOVA

df

SS

MS

F

Significance F

Regression

4

1288866

322216.4

1165.115

1.68E-19

Residual

16

4424.853

276.5533

Total

20

1293290

Coefficient

Standard

t Stat

P-value

Lower

Upper

s

Error

95%

95%

Intercept

26.01854

46.46992

0.559901

0.583302

-72.4933

124.5304

No. of admissions (millions)

-8.10597 1.549022 -5.23296 8.21E-05 -11.3898 -4.82219

No. of admissions (millions)^2

0.124897

0.011126

11.22584

5.37E-09 0.101311 0.148483

No of films screened

-0.10448

0.178218

-0.58626

0.56588

-0.48229

0.273323

Top price of cinema ticket ($)

38.03865

4.751088

8.006303

5.49E-07

27.96679

48.11051

Page 2 of 3


Question 2 (20 MARKS)

(a) What is the rationale behind the OLS estimation method?

(5 Marks)

(b) Explain why the parameters of a Simple Regression model have a sampling distribution. Feel free to use a diagram to help you.

(5 Marks)

(c) Under what circumstances would we consider using dummy variables, and how would we enter these into our Excel regression?

(5 Marks)

(d) Under what circumstances would we consider using interaction effects, and how would we enter these into our Excel regression?

(5 Marks)

**** End of Examination ****


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Tutorials for this Question
  1. Tutorial # 00074845 Posted By: kimwood Posted on: 07/07/2015 01:18 AM
    Puchased By: 2
    Tutorial Preview
    number of films screened (NOS) increases by 1unit, we predict ...
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    2080011-Solution-docx.docx (13.94 KB)
    2080012-solution.docx (35.27 KB)

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