Econ 399 Winter 2015 Midterm Exam
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Econ 399
Winter 2015
Midterm Exam
Question 1 (60 marks)
Suppose we estimated a model to study the factors that affect the sales of a particular restaurant. The sample contains data on 33 branches for the restaurant, and we used the following variables:
Sales: Revenues to the restaurant measured in dollars.
Competition: number of competitors within the same location of the restaurant.
Population: number of people living in the restaurant`s surrounding area.
Income: average income of the population living in the restaurant`s area measured in dollars
The dependant variable and all the explanatory variables are expressed in the natural logarithmic form.
1. Report the results of model 1 in a full reporting form. ( 4 marks)
2. Interpret the meaning of the estimated coefficients and in Model 1. ( 4 marks)
3. Briefly explain the meanings of the calculated value of and in Model 1 . Of the
two, which do you recommend typically using? Why? (4 marks)
4. Suppose we change the unit of measurement of the dependant variable sales by multiplying the original variable sales by 10. Report the result of the new model in a full reporting form. ( 4 marks)
5. Develop and test appropriate hypothesis about the individual slope coefficient at the 5%
significance level. ( 4 marks)
6. Develop and conduct an overall significance test for model 1 at the 5% significance level. ( 4 marks)
7. Construct a 95% confidence interval estimate of the true coefficient and interpret its meaning. ( 4
marks)
8. Based on the results of Model 1, which of the three explanatory variables has more effect on the dependant variable? and why? ( 4 marks)
9. Suppose that all the Classical Assumptions hold. Does this mean that the true (marginal) effect of the competition on sales is -0.377 (i.e. the population parameter is -0.377)? ( 4 marks)
10. What are the consequences of adding an irrelevant variable to model 1? ( 4 marks)
11. Suppose we omitted a relevant explanatory variable like population from Model 1. And suppose the correlation between population and income is negative, while there is zero correlation between population and competition. What are the consequences of omitting population from our model? (4 marks).
12. Suppose now we estimated model 1 but without population and Income and we get model 2. Test the restriction of excluding both population and Income from model 1. ( 6 marks)
13. Which of the two models: model 1 or model 2 do you prefer and why? ( 10 marks)
Model 1
. reg sales competition population Income
Source |
SS df MS |
|
Model Residual |
703457412 .(.)294463032 |
3 .234485804 29 .010153898 |
Total |
.997920444 32 .031185014 |
Number of obs = 33
F( 3, 29) = 23.09
Prob > F = 0.0000
R-squared = 0.7049
Adj R-squared = 0.6744
Root MSE = .10077
sales |
Coef. |
Std. |
Err. |
t |
P>|t| |
[95% Conf. |
Interval] |
competition |
-.3779502 |
.064 |
9484 |
-5.82 |
0.000 |
-.5107846 |
-.2451157 |
population |
.352044 |
.055 |
9798 |
6.29 |
0.000 |
.2375525 |
.4665355 |
Income |
.1590619 |
.084 |
5355 |
1.88 |
0.070 |
-.0138326 |
.3319564 |
cons |
6.657826 |
.772 |
1623 |
8.62 |
0.000 |
5.078577 |
8.237076 |
Model 2
. reg sales competition
Source |
SS df MS |
|
Model Residual |
017734189 .(.)980186255 |
1 .017734189 31 .031618911 |
Total |
.997920444 32 .031185014 |
Number of obs = 33
F( 1, 31) = 0.56
Prob > F = 0.4596
R-squared = 0.0178
Adj R-squared = -0.0139
Root MSE = .17782
sales Coef. Std. Err. t P>|t| [95% Conf. Interval]
competition
cons
-.052729 .0704072
11.799 .1023621
-0.75
115.27
0.460
0.000
-.1963254
11.59023
0908675
1(.)2.00777
Question 2 ( 15 marks)
Under the classical linear model (CLM) assumptions, the OLS estimators have stronger properties than what they would have under the Gauss-Markov assumptions.
1) State the Classical Linear Model (CLM) assumptions. ( 10 marks)
2) Briefly explain the properties of the OLS estimators if these assumptions are satisfied. ( 5 marks)
Question 3 (25 marks)
Consider the following sample regression model without an intercept: and the corresponding
true population regression model is . Assume that the standard assumptions about this model
apply.
1) Derive the ordinary least squares (OLS) estimator of
2) Derive the expected value of the OLS estimator . Is an unbiased estimator of ?
2022-06-30