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ECO 6416
TEST I
5/25/1999
NAME______________________________
I. MULTIPLE CHOICE (select single best answer and enter in underlined space at start of question, three
points per question)
_____ 1. Ordinary Least Squares, OLS
a. it minimizes the sum of the deviations
b. it minimizes the sum of the absolute value of the residuals
c. it maximizes the sum of the squared residuals
d. it minimizes the sum of the squared vertical deviations **
_____ 2. The probability of committing a Type II Error is
a. equal to the probability of rejecting the null hypothesis given it is false
b. equal to the probability of accepting the null hypothesis given it is true
c. equal to the probability of accepting the null hypothesis given it is false **
d. equal to the probability of rejecting the null hypothesis given it is false
__ ___ 3. Two conditions of least squares are
a. ei = 0 and ei2 = 0
b. ei is minimized and ei2 = 0
c. ei = 0 and ei2 is minimized **
d. ei = 0 and ei2 is maximized
_____ 4. For the following model, the dummy variable D will
Y = B0 + B1X1 + B2X2 + B3D + 
a.
b.
c.
d.
decrease the intercept if B3 is negative **
decrease the intercept if B3 is positive
decrease the slope of (B1 + B2) is negative
increase the intercept and slope if B3 is positive
_____ 5. For the estimated regression equation: Y = 10 + 5X1 - 2X2 + 1X3 - 6X4, both X1 and X4 are dummy variables.
These variables are defined as follows:
X1 = 1 if female and X1 = 0 otherwise AND X4 = 1 if student and X4 = 0 otherwise
For a female student, the regression equation reduces to
a.Y = 13 + 5X1 - 6X4
b.Y = 10 + 5X1 - 6X4
c.Y = 4 - 2X2 + 1X3
d.Y = 9 - 2X2 + 1X3 **
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_____ 6. The Gauss-Markov Theorem proves that OLS esimators are BLUE as long as Classical Assumptions I through VI
hold. BLUE means best linear unbiased estimator. In this context "best" means
a. most likely
b. least efficient
c. maximum mean value
d. minimum variance **
_____ 7. An unbiased estimator is one for which
a. the sampling distribution of the estimator collapses on the population parameter being estimated.
b. the sampling variability is at a minimum.
c. there is no sampling variation.
d. the most likely value of the estimator is the population parameter being estimated **
_____8. Serial correlation, sometimes referred to as autocorrelation, is a violation of which of the following Classical
Assumptions of the OLS Model?
a. The regression model is linear in the coefficients and the error term.
b. The error term has a zero mean.
c. The error term has a constant variance.
d. Observations of the error term are uncorrelated with each other. **
_____ 9. Heteroskedasticity is a violation of which of the following Classical Assumptions of the OLS Model?
a. No explanatory variable is a exact linear function of other explanatory variables.
b. The error term has a zero mean.
c. The error term has a constant variance. **
d. Observations of the error term are uncorrelated with each other.
_____ 10. The Dummy Variable Trap results if you
a. have a categorical variable with more than two levels
b. create your dummy variables in such a way that one is a linear combination of the others **
c. try using Alpha variables in a regression equation
d. are dumb enough to incorporate categorical variables in a regression equation
III.
A. Explain the logic of OLS (least squares) as a method for fitting a line to a bivariate (Y versus X) dataset.(5 pts)
B. What are three properties of good estimators and how does OLS fare with respect to these?(5 pts.)
C. Are there any instances in which least squares will provide a poor fit? Explain.(5 pts.)
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IV.
The following Eviews output has 5 entries that have been deleted and replaced with an underline or never were
dispalyed. Please show your work and determine the appropriate values for each of the missing statistics. The dependent
variable is new car sales and the independent variable is the S&P 500. (30 points, 6 points each)
Dependent Variable: RCAR6T
Method: Least Squares
Date: 05/24/99 Time: 13:59
Sample: 1980:01 1996:04
Included observations: 196
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
FSPCOM
829.3697
-0.173837
19.66118
0.060576
42.18311
0.0000
0.0046
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.040722
2753112.
-1214.024
0.643963
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
778.5051
121.3172
12.40841
12.44186
0.004564
A. S.E. of Regression SEE)
B. F - statistic
C. Explained Sum of Squares (ESS, never displayed in output)
D. Adjusted R-squared
E. t-statistic [for independent variable, FSPCOM]
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Based on the following regression output, answer the following questions and provide the basis for your response.(20 points,
5 points each) The above data is a sample dataset on EViews, so treat results as hypothetical and do not be offended by any
of the implications of your analysis.
Variable Definitions:
NUM_AFF = the number of affairs
Dependent Variable: NUM_AFF
Method: Least Squares
Date: 05/25/99 Time: 13:16
Sample: 1 601
Included observations: 601
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
D1
AGE
D2
EDUC
REL
SAT_M
YRSM
5.757585
0.169699
-0.049105
-0.218983
0.017989
-0.482513
-0.716715
0.171249
1.133735
0.284173
0.022571
0.344283
0.058249
0.111689
0.119977
0.041211
5.078424
0.597168
-2.175564
-0.636057
0.308823
-4.320151
-5.973775
4.155421
0.0000
0.5506
0.0300
0.5250
0.7576
0.0000
0.0000
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.129695
0.119421
3.095527
5682.295
-1527.860
1.004220
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
1.455907
3.298758
5.111015
5.169565
12.62428
0.000000
A. Without performing any hypothesis tests, describe the “fit” of the regression equation.
B. Is the (full) model statistically significant at the 5 percent level? State your hypotheses(null and alternate) and
perform the test at the 5% level of significance.
C. The researcher expects that GNP and M1 are directly related. Formulate the researcher's hypotheses(null and
alternate) and perform the appropriate test at the 5% level of significance.
D. The researcher expects that GNP and PRICE are inversely related. Formulate the researcher's hypotheses(null and
alternate) and perform the appropriate test at the 5% level of significance.
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VI. Bruggink and Rose(Southern Economic Journal) estimated a regression equation for the annual team revenue for Major
League Baseball franchises:
Ri = -1552.5 + 53.1Pi + 1469.4Mi + 1322.7Si - 7376.3Ti
where
R = team revenue (in thousands of dollars)
P = the percentage of games that the team won (in thousands, so 1000 means won all games, 250 means won 25% of games)
M = the population of the metropolitan area for the team
S = a dummy variable: S = 1 if team’s stadium was buit before 1940, S = 0 therwise
T = a dummy variable: T = 1 if team’s city has two Major League Baseball teams, T = 0 otherwise
Assume that your team is in last place with P = 350. According to this regression equation, would it be profitable to pay $4
million a year to a free agent superstar who would raise the team’s winning percentage, P, to 500? Assume all other factors
are constant and show your work. (10 points)
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