120B Economics Professor Yongil Jeon Winter 2008
Name: _________________________ Student ID#: _________________________
Answer to Homework #1, Winter 2008 (Part of Exam 1, Summer 2006)
Answer all questions on separate paper. This problem set should be handed in to Professor Jeon at the beginning of your class on Wednesday, February 6th, 2008. Problem sets may not be handed in once solutions have been distributed. Please write down your name and PID clearly. Good luck!
1-a. (5 points) Analyzing the behavior of unemployment rates across 150 different countries in July of 2006 is an example of using a. b. c. d. Answer: c 1-b. (5 points) The least squares procedure minimizes the sum of A) B) C) D) Answer: D 1-c. (5 points) A residual is A) B) C) D) the difference between the mean of Y conditional on X and the unconditional mean. the difference between the mean of Y and its actual value. the difference between the regression prediction of Y and its actual value. the difference between the sum of squared errors before and after X is used to predict Y. the residuals. squared maximum error. absolute errors. squared residuals. time series data. panel data. cross-sectional data. experimental data.
Answer: C 1-d. (5 points) Income is used to predict savings. For the regression equation Y = 1,000 + .10X, which of the following is true? A) B) Y is income, X is savings, and income is the independent variable. Y is income, X is savings, and savings is the independent variable.
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Answer: D
Answer to HW #1, ECON 120B, Winter 2008 Y is savings, X is income, and savings is the independent variable. Y is savings, X is income, and income is the independent variable.
2. (10 points) Sketch a hypothetical scatterplot of data for an estimated regression with R 2 = 0.9 . Also sketch a hypothetical scatterplot of data for a regression with R 2 = 0.5 . Answer The value of the R 2 indicates how dispersed the points are around the estimated regression line. Note that the R 2 does not indicate whether the line has a positive or a negative slope. When R 2 = 0.9 , the scatter of points should lie very close to the regression line. When R 2 = 0.5 the points should be more dispersed about the line.
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Answer to HW #1, ECON 120B, Winter 2008
3. (35 points) A corporation administers an aptitude test to all new sales representatives. Management is interested in the extent to which this test is able to predict their eventual success. The accompanying table records average weekly sales (in thousands of dollars) and aptitude test scores for a random of sample eight representatives. Weekly sales Test score 10 55 12 60 28 85 24 75 18 80 16 85 15 65 12 60
Let y = weekly sales and x = test score
n = 8, y = 135 / 8 = 16.875, x = 565 / 8 = 70.625,
x
i =1
8
2 i
= 40925, xi y i = 9945
i =1
8
(a) (15 points) Estimate the linear regression of weekly sales (including a constant term) on aptitude test scores.
Answer
^ 1 =
x y - nxy =9945 - 8 * 70.625 *16.875 = 0.4018 40925 - 8 * 70.625 x - nx
i i 2 i 2 2
^ ^ 0 = y - 1 x = 16.875 - 0.4018 * 70.625 = -11.5046
(b) (10 points) Interpret the slope parameter of the regression line.
Answer:
A one unit increase in the test score is associated with a $401.80 increase in weekly sales.
(c) (10 points) What is the STATA command for running the regression of ^ ^ WeeklySalesi = 0 + 1TestScorei , i=1,2,...,n?
Answer:
reg WeeklySales TestScore
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Answer to HW #1, ECON 120B, Winter 2008
4 (35 points) The median starting salary for new law school graduates (over 136 different schools) is determined by
ln( salary ) = 0 + 1 LSAT + 2 GPA + 3 ln(libvol ) + 4 ln(cos t ) + 5 rank + u where LSAT is the median LSAT score for the graduating class, GPA is the median college GPA for the class, libvol is the number of volumes in the law school library, cost is the annual cost of attending law school, and rank is a law school ranking (with rank=1 being the best). ***
. des lsalary LSAT GPA llibvol libvol lcost cost rank storage display value variable name type format label variable label ------------------------------------------------------------------------------lsalary float %9.0g log(salary) LSAT int %9.0g median LSAT score GPA float %9.0g median college GPA rank int %9.0g law school ranking libvol int %9.0g no. volumes in lib., 1000s cost int %9.0g law school cost llibvol lcost float %9.0g float %9.0g log(libvol) log(cost)
*** (i) (10 points) Explain why we expect 5 0 .
Answer
A larger rank for a law school means that the school has less prestige; this lowers starting salaries. (ii) (15 points) What signs do you expect for the other slope parameters? Justify your answers.
Answer
1 > 0 , 2 > 0 . Both LSAT and GPA are measures of the quality of the entering class.
No matter where better students attend law school, we expect them to earn more, on average. 3 > 0 , 4 > 0 . The number of volumes in the law library and the tuition cost are both measures of the school quality.
(iii) (10 points) What is the STATA command for running the estimated regression?
Answer. reg lsalary LSAT GPA llibvol lcost rank
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