Name. Department of Economics Ohio Wesleyan University Delaware, Ohio. Robert J. Gitter Econometrics Economics 355 Spring, ZOO6.

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The exam is worth 15 percent of your grade. The exam is closed book, but calculators are permitted.

1 Name Department of Economics Ohio Wesleyan University Delaware, Ohio Robert J. Gitter Econometrics Economics 355 Spring, ZOO6 Exam I You have one hour for this exam. The exam is worth 15 percent of your grade. The exam is closed book, but calculators are permitted. Please do all your work carefully and check your calculations before handing your work in. PLEASE SHOW ALL YOUR WORK TO AID IN THE AWARDING OF PARTIAL CREDIT WHERE APPLICABLE.

1. (20 points) Data were gathered on the change in unemployment and the change in Real GDP from w-2004. The regression was run and the results are presented below.

2 1. (20 points) Data were gathered on the change in unemployment and the change in Real GDP from w The regression was run and the results are presented below. i4w Regression Analysis: ChUnem versus %chgdp The regression equation is ChUnern = %chgdp Predictor Coef SE Coef T Constant %chgdp Analysis of Variance Source DF SS MS F P Regression Residual ~ rror Total a) Whoops, I accidentally cut out the R2. From the output above, please calculate the R2. L f Re5/ I y. 7 t6 roo o T,A/ - i7..iur YO, 3'2 b) In terms of the variables, please explain what the R2 tells us. c) At a.05 level please test whether the slope is > 0. Show your work

Analysis: Wins versus PtsFor, PtsAgst The regression equation is Wins = 10.3 + 0.0272 PtsFor - 0.0340 PtsAqst Predictor Coef SE Coef T P Constant 10.267 1.932 5.31 0.000 PtsFor 0.027159 0.003257 8.

3 2. (44 points) Once again, neither the Cleveland Browns nor the Detroit Lions made it to the Superbowl. I gathered data for all 32 teams for the 2005 season on Wins =Number of Games Won PtsFor = Points Scored by the Team PtsAgst= Points Scored against the Team I ran a regression and found, Regression Analysis: Wins versus PtsFor, PtsAgst The regression equation is Wins = PtsFor PtsAqst Predictor Coef SE Coef T P Constant PtsFor PtsAgst Analysis of Variance Source DF SS MS Regression Residual Error Total Source DF Seq SS PtsFor PtsAgst a) In terms of the variables, please explain what the slope on PtsFor tells us. b) The Cleveland Browns won G games this past season. They scored 232 points and gave up 301. How many games did the model predict they would win? LJ,,, =,J,] +, 0271(231) - i o 3 ~ ( 3 u / J 01 r 11; 3 d- C:?) - I0.277 the Browns. (No points for saying the error was that their fans thought they would do better.) '4 C,: r:-y = 6- L 176 ' 1-,376/ (This problem continues on the next page.)

4 d) The Browns scored the fewest points of any team in the league; 232. (Ouch!) That was 108 points less than the league average. How many additional games would they have been predicted to win, compared to your answer in part b), had they scored the league average number of points? lo8 + su,i1 = 2. 7 a e) Suppose that the Coach claims that offense doesn't win games, defense does. He goes on to state that the number of points scored does not matter. Based on the formal model above, test the idea that the number of points scored does not affect the number of games won. Please use a.05 level,,025 under each tail.,#:. 1?,= ~4 (-,*>< - ~i i A-1 =Z PWA hi/,027, 4 ~ 3 -, 5 - : "'j A-x's-5 C-1."4~- c_ X. X ~ 4 2. ~ ~ 1 f) In terms of the variables, please explain what your results in part e) mean. >.,,. 1 4,,q,, Dj&6+&, ppje tl g) Suppose your roommate says that points scored and allowed don't matter, all that matters is wins. You claim that these two variables do in fact matter as they determine wins. Your roommate still says they don't matter. Formally, test the idea at the.05 level that % Ho:Bz= B,=O < Jl*, VS. 0' HA : Ho is false,p 5 (,21 './$ c /+jberl I $Irrr 3", / )i 17l.Y'

$+A4 s* vh,/f +~llrr, I I C'J /v\ L.nI, 4 1 4 A C,~/J* rhe*~*,~j - b) What would be an example of a biased one?$

5 0 3-5 are worth 12 points each. 3.a) Suppose I wanted to find the mean of a population. What would be an example of unbiased estimator from a sample? (Formula of one, please.) 5Y4-.+A4 s* vh,/f +~llrr, I I C'J /v\ L.nI, A C,~/J* rhe*~*,~j - b) What would be an example of a biased one?,- \ 53, 41 ) c&%i/&m~ b A d l ~ & 7 /, 4 J-46'9 /%' L1 64 c) What does it mean for an estimator to be biased? 4. Suppose we look at the probability distribution of males and females that were admitted to an Ivy League graduate school. There are two programs; Arts and Sciences. 69 Bivariate Probability Distribution of Admissions by Program and Gender Program Male Female Arts.06.20,ZL Sciences I J7 I, 08 a) What does the figure.20 mean in terms of the variables? 2 e~ / 5JZ/d+37~~ ~k k$ &-A b) Calculate the marginal probabilities. c) Are gender and program independent? Demonstrate.

5. Check your OWU e-mail. There should be a file that has been mailed to you as an Excel iile. Cut and paste the variables into Minitab.

6 5. Check your OWU . There should be a file that has been mailed to you as an Excel iile. Cut and paste the variables into Minitab. The variables are: DEMAND FOR CHICKENS, UNITED STATES, Y = Per Capita Consumption of Chickens, Pounds X2 = Real Disposable Income Per Capita, $ XS = Real Retail Price of Chicken Per Pound. Cents X4 = Real Retail Price of Pork Per Pound, Cents X5 = Real Retail Price of Beef Per Pound, Cents X6 = Composite Real Price of Chicken Substitutes Per Pound, Cents a) Run a regression of Y on all of the X's. Write the regression equation below. P 1 n,,p,,t.j,fp~ b) Please nm a test to see if we can drop all of the those variables (together) that are not statistically significant at a.05 level. Show your work and any relevant test statistics. s- 1~d4y7 V*, 5-/ ' t 4 --f

Statistical Models of Stocks and Bonds. Zachary D Easterling: Department of Economics. The University of Akron

Statistical Models of Stocks and Bonds Zachary D Easterling: Department of Economics The University of Akron Abstract One of the key ideas in monetary economics is that the prices of investments tend to