252x0761 11/16/07 ECO252 QBA2THIRD EXAMApril 16, 2007TAKE HOME SECTION Name: _________________________ Student Number: _________________________ Class days and time : _________________________Please Note: Computer problems 2 and 3 should be turned in with the exam (2). In problem 2, the 2 way ANOVA table should be checked. The three F tests should be done with a 1% significance level and you should note whether there was (i) a significant difference between drivers, (ii) a significant difference between cars and (iii) significant interaction. In problem 3, you should show on your third graph where the regression line is. You should explain whether the coefficients are significant at the 1% level. Check what your text says about normal probability plots and analyze the plot you did. Explain the results of the tand F tests using a 5% significance level. (3)III Do the following. (22+ points) Note: Look at 252thngs (252thngs) on the syllabus supplement part of the website before you start (and before you take exams). Show your work! State 0H and 1H where appropriate. You have not done a hypothesis test unless you have stated your hypotheses, run the numbers and stated your conclusion. (Use a 95% confidence level unless another level is specified.) Answers without reasons or accompanying calculations usually are not acceptable. Neatness and clarity of explanation are expected. This must be turned in when you take the in-class exam. Note that from now on neatness means paper neatly trimmed on the left side if it has been torn, multiple pages stapled and paper written on only one side. Show your work!1) The Lees, in their book on statistics for Finance majors, ask about the relationship of gasoline prices y in cents per gallon to crude oil prices 1x in dollars per barrel and present the data for the years 1975 - 1988. I have obtained most of the data for the years 1980 – 2007. It is presented below. Row Year GasPrice CrudePrice Yr-1979 1 1980 1.25 26.07 1 2 1981 1.38 35.24 2 3 1982 1.30 31.87 3 4 1983 1.24 26.99 4 5 1984 1.21 28.63 5 6 1985 1.20 26.25 6 7 1986 0.93 14.55 7 8 1987 0.95 17.90 8 9 1988 0.96 14.67 9 10 1989 1.02 17.97 10 11 1990 1.16 22.22 11 12 1991 1.14 19.06 12 13 1992 1.13 18.43 13 14 1993 1.11 16.41 14 15 1994 1.11 15.59 15 16 1995 1.15 17.23 16 17 1996 1.23 20.71 17 18 1997 1.23 19.04 18 19 1998 1.06 12.52 19 20 1999 1.17 17.51 20 21 2000 1.51 28.26 21 22 2001 1.46 22.95 22 23 2002 1.36 24.10 23 24 2003 1.59 28.53 24 25 2004 1.88 36.98 25 26 2005 2.30 50.23 26 27 2006 * * 28 2007 3.10 90.00 1252x0761 11/16/07 This data set also contains the year with 1979 subtracted from it 2x. You may need to use this later. Ignore it in Problem 1. Note that the numbers for 2006 have not yet been published in my source, Statistical Abstract of the United States, and that the numbers for 2007 are my estimates for third quarter prices. These are unleaded prices, which the Lees did not use. You are supposed to use only the numbers for 1990 through 2006 and one other observation for your data. You will thus have 17nobservations. The other column is the value for the year a1980, where a is the second to last digit of your student number. If you are unsure of the data that you are using or if you want help with the sums that you need todo the regression go to 3takehome072a. Show your work – it is legitimate to check your results by running the problem on the computer. (In fact, Iwill give you 2 points extra credit for checking it and annotating the output for significance tests etc.) But I expect to see hand computations for every part of this problem.a. Compute the regression equation Y b b x 0 1to predict the price of gasoline on the basis of crude oil prices. (3)b. ComputeR2. (2)c. Compute se. (2)d. Compute 1bs and do a significance test on 1b(2)e. Compute a confidence interval for 0b. (2)f. You have a crude price for 2007 Using this, predict the gasoline price for 2007 and create a prediction interval for the price of gasoline for that year. Explain why a confidence interval for the price is inappropriate and check to see if my estimated price is in the interval. (3)g. Do an ANOVA for this regression. (3)f) Make a graph of the data. Show the trend line and the data points clearly. If you are not willing to do this neatly and accurately, don’t bother. (2) [19]2) Now we can use the date to see if there is a trend line in addition to the effect of crude oil.a. Do a multiple regression of the price of gasoline against crude prices and the data variable, which has been massaged to make 1980 year 1. This involves a simultaneous equation solution. Attempting to recycle 1b from the previous page won’t work. (7)c. Compute the regression sum of squares and use it in an ANOVA F test to test the usefulness of this regression. (4)b. Compute R2 and R2 adjusted for degrees of freedom for both this and the previous problem. Compare the values of R2 adjusted between this and the previous problem. Use an F test to compare R2 here with the R2 from the previous problem. The F test here is one to see if adding a new independent variable improves the regression. This can also be done by modifying the ANOVAs in b.(4)d. Use your regression to predict the price of gasoline in 2007. Is this closer to the estimated gasoline price? Do a confidence interval and a prediction interval. (3) [37]e. Again there is extra credit for checking your results on the computer. Use the pull-down menu or try Regress GasPrice on 2 CrudePrice Yr-1979 (2)3) According to Russell Langley, three sopranos were discussing their recent performances. Fifi noted that she got 36 curtain calls at La Scala last week, but Adalina put her down with the fact that she got 39. Could one of the singers really say that she had more curtain calls than another or could the differences just be due to chance?Personalize the data below by adding the last digit of your student number to each number in the first row. Use a 10% significance level throughout this question.Row Fifi Adelina Maria 1 36 39 21 2 22 14 32 3 19 20 28 4 16 18 222252x0761 11/16/07 a) State your hypothesis and use a method to compare means
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