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. decrease the intercept if B3 is negative **

b. decrease the intercept if B3 is positive

c. decrease the slope of (B1 + B2) is negative

d. increase the intercept and slope if B3 is positive

_____ 5. For the estimated regression equation: = 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. = 13 + 5X1 - 6X4

b. = 10 + 5X1 - 6X4

c. = 4 - 2X2 + 1X3

d. = 9 - 2X2 + 1X3 **

_____ 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.)

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 / 829.3697 / 19.66118 / 42.18311 / 0.0000
FSPCOM / -0.173837 / 0.060576 / [JX1] / 0.0046
R-squared / 0.040722 / Mean dependent var / 778.5051
Adjusted R-squared / [JX2] / S.D. dependent var / 121.3172
S.E. of regression / [JX3] / Akaike info criterion / 12.40841
Sum squared resid / 2753112. / Schwarz criterion / 12.44186
Log likelihood / -1214.024 / F-statistic / [JX4]
Durbin-Watson stat / 0.643963 / Prob(F-statistic) / 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]

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 / 5.757585 / 1.133735 / 5.078424 / 0.0000
D1 / 0.169699 / 0.284173 / 0.597168 / 0.5506
AGE / -0.049105 / 0.022571 / -2.175564 / 0.0300
D2 / -0.218983 / 0.344283 / -0.636057 / 0.5250
EDUC / 0.017989 / 0.058249 / 0.308823 / 0.7576
REL / -0.482513 / 0.111689 / -4.320151 / 0.0000
SAT_M / -0.716715 / 0.119977 / -5.973775 / 0.0000
YRSM / 0.171249 / 0.041211 / 4.155421 / 0.0000
R-squared / 0.129695 / Mean dependent var / 1.455907
Adjusted R-squared / 0.119421 / S.D. dependent var / 3.298758
S.E. of regression / 3.095527 / Akaike info criterion / 5.111015
Sum squared resid / 5682.295 / Schwarz criterion / 5.169565
Log likelihood / -1527.860 / F-statistic / 12.62428
Durbin-Watson stat / 1.004220 / Prob(F-statistic) / 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.

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)

UCFBusiness1 of 1

[JX1]1-2.869734

[JX2]10.035777

[JX3]1119.1272

[JX4]18.235372