statistics homework
Exam 1 Econ 4400, Elementary Econometrics, Fall 2017
1 Multiple Choice
Table 1
id year y x1 x2 x3 1 2016 1 4 12 1 2 2016 3 16 12 1 3 2016 5 73 12 0 4 2016 8 155 12 0 5 2016 2 12 12 1
1. Given the data in table 1, what can we say about Cov(x1,x2)
(a) Cov(x1,x2) < 0
(b) Cov(x1,x2) = 0
(c) Cov(x1,x2) > 0
(d) Not enough information given
2. Using the data set in table 1, which variable likely has the highest standard deviation?
(a) y
(b) x1
(c) x2
(d) x3
3. Suppose we estimate the equation y = β0 + β1x1 + �. Which statement will be true?
(a) β̂1 > 0
(b) β̂1 = 0
(c) β̂1 < 0
(d) unable to tell
4. What is E[x2|x3 = 1] in table 1?
(a) 7.33
(b) 4.4
(c) 9.4
(d) 12
5. Which of the following problems would be present in the attempted regression: y = β0 + β1x1 + β2x2 + e
(a) Independent variables correlated with the error
(b) Perfect multicollinearity
(c) Heteroskedasticity
(d) B & C
6. Which is true of non-random sampling?
(a) β̂ is not necessarily unbiased in OLS
(b) It is a violation of our necessary assumptions for OLS to be BLUE.
(c) The probability of being chosen for the sample is different for different mem- bers of the population.
7. Which value is minimized in OLS, when estimating: yi = β̂0 + β̂1xi + ei
(a) ∑n
(yi − ȳ) (b) |
∑n ei|
(c) ∑n
ei
(d) ∑n
e2i
8. What is the difference between R2 and R̄2?
(a) R̄2 is the mean R2 of several regressions
(b) R̄2 is larger
(c) R̄2 is adjusted for number of independent variables
(d) They are the same thing.
9. Given that ŷi = yi for all observations, which is true?
(a) R2 = 0.5
(b) R2 = 0.67
(c) R2 = 1
(d) Not enough information is given to calculate
10. Which of the following can be tested with a t-test?
(a) H0 : β1 = β2
(b) H0 : β1 = β 2 2
(c) H0 : β1 = β2 = 0
(d) All of the above.
11. The figures below depict scatter plots with a fitted regression line. Suppose we estimated regressions with OLS for each data set. Which would have the lowest R̄2
(a) (b) (c)
(d)
12. Given the following scatter plots of y and x. Which dataset would most likely have homoskedastic errors in the regression y = β0 + β1x + e?
(a) (b) (c)
(d)
13. In the scatter plot ,the regression y = β0 + β1x + e would yield which result?
(a) β̂1 = 0
(b) β̂1 > 0
(c) β̂1 < 0
(d) More information would be needed.
14. Given the regression equation: yi = β0 + β1xi + ei, which is the independent variable?
(a) yi
(b) β0
(c) β1
(d) xi
(e) ei
15. Given the regression equation: yi = β0 + β1xi + ei, which is the constant?
(a) yi
(b) β0
(c) β1
(d) xi
(e) ei
2 Open Answer
t = β̂−βH0 se(β̂)
1. (5 pts) Name 5 of the assumptions of the Classical Linear Model. (Only your first 5 will be graded.)
2. (10 pts)Suppose you are working for the campus book store. You want to develop a model for the sale of textbooks for classes (Note the store only carries books that are recommended or required reading.). You have collected the following variables for each textbook last semester: Books Sold (S), price (P ), a dummy for being a required textbook (Q), a dummy for being a recommended textbook (M), a dummy variable indicating that previous editions of the textbook have been published.
(a) (5 pts)Write out an equation that you use to estimate book sales using the given variables. (You may use the abbreviations that are given in the description.)
(b) (5 pts) What is your predicted sign of each coefficient? Give a theoretical reason why you expect each sign.(You must be more descriptive than just saying ”I expect β̂ < 0, because x has a negative effect on y. Give a reason why.)
3. (5 Points)Suppose I want to estimate the effect of study time on GPA. I collect data and estimate the equation GPA = β0 + β1Hrs + �. My β̂0 = 2 and β̂1 = 0.2 Graph my estimated equation on the answer sheet:
4. (30 pts)Table 2 Shows regression results from the NLSY dataset that has been used in homeworks. Adult income is in dollars, Armed Services Aptitude Bat- tery (ASVAB) is an intelligence test, the omitted race/ethnicity group is ”non- white/non-hispanic”. Mother’s education is the years of schooling completed by the respondent’s mother, and HH Income as an adolescent is the household income when the individual was an adolescent (in dollars).
(a) (5 pts)How degrees of freedom in the regression?
(b) (5 pts)What is the predicted income of a white male, 30 years old, score of 50,000 on ASVAB, 12 years of education, whose mother had 12 years of education, and a household income of $100,000 as an adolescent.
(c) (5 pts)Interpret the coefficient on highest grade completed.
(d) (5 pts)Interpret the coefficient on female.
(e) (5 pts)Conduct a t-test on the null hypothesis that men and women earn the same income with a 0.05 significance level. (Conducting a test includes writing out hypotheses, calculating the appropriate test statistic, finding the correct critical value, and making the correct decision.)
(f) (5 pts) Typically in reporting regression results 1, 2, or 3 stars are put on coefficients if we can reject H0 : β = 0 at significance levels below 0.10, 0.05, and 0.01 respectively. How many stars would be put on the coefficient for Hispanic? (You must show how you get the answer.)
Table 2: Regression Results
(1) Adult Income
Armed Services Aptitude Battery 0.149 (0.0228)
Highest Grade COmpleted 2568.0 (217.4)
Age 1400.4 (351.1)
Female -14719.7 (988.1)
race ethnicity==black -1363.6 (1342.4)
race ethnicity==hispanic 2961.1 (1410.3)
race ethnicity==mixed race (non-hispanic) -1095.7 (5251.2)
Mother’s Education 921.7 (431.5)
HH Income as Adolescent 0.0963 (0.0132)
Constant -54431.2 (11154.1)
Observations 3426 R2 0.212 Adjusted R2 0.210 mss 7.47196e+11 rss 2.77885e+12
Standard errors in parentheses
Exam 1 Econ 44000
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