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(ECON233)[2008](f)midterm~2047^_10246.pdf
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Econ 233 (L1) Introduction to Econometrics


Fall, 2008


Midterm Exam (1 Hour 35 Minutes, 8:45-10:20am)

Part I: Short Questions (8 points each)
Provide brief explanations to your answers.

1. Among all estimators that are weighted averages of , (the sample mean) is the most unbiased estimator of . T/F 1,...,nYY
Y
Y.

F. E( wiYi)=w1E Y1 +.+wnE Yn =Y wini=1 =ni=1Y for all wini=1=1
2. When binary variables enter into regression models on the RHS, their partial slope coefficients can be interpreted the same way as we interpret coefficients of other explanatory variables. T/F


F.
The coefficients of other regressors measure rate of change of Y given changes in X. The coefficients of binary variables are differences in means (or intercepts) of different groups or categories.
3. In multiple regression models, the t-statistics are not appropriate candidates for doing joint test (that all slope coefficients = 0 simultaneously under the null). They are therefore useless in statistical inference. T/F


F.
F-stat should be used to do the joint test. But the t-stat can still be used to study the significance of an individual explanatory variable.
4. What is the intuition behind the fact that R2 never declines as the number of explanatory variables increases?


The worst case of including an extra regressor in the regression model is that it does not improve the proportion of variation of the dependent variable explained, which would leave the R-square same as before. If it adds explanatory power to the regression model, R-square will increase.
5. What is the major implication of the Central Limit Theorem on Y ?


The sampling distribution of is approximately normal. YYY...


Part II: Analytical Questions (20 points each)
1. The development office and the registrar have provided you with anonymous matches of starting salaries and GPAs for 108 graduating economics majors. Your sample contains a variety of jobs, from church pastor to stockbroker.

a. The average starting salary for the 108 students was $38,644.86 with a standard deviation of $7,541.40. Construct a 95% confidence interval for the starting salary of all economics majors at your university/college. (Hint: the critical t value concerned is 1.96)



38,644.861.96= 38,644.861,422.32 = (37,222.54, 40,067.18). .
7,541.40108.

b. You wonder if it pays (no pun intended) to get good grades by calculating the average salary for economics majors who graduated with a cumulative GPA of B+ or better, and those who had a B or worse. The data is as shown in the accompanying table.




Cumulative GPA

Average Earnings

Standard Deviation
Ys

n

B+ or better
$39,915.25
$8,330.21
59

B or worse
$37,083.33
$6,174.86
49



Conduct a t-test for the hypothesis that the two starting salaries are the same in the population. Given that this data was collected in 1999 (a boom year), do you