252y0771t 11 28 07 Warning This document is 74 pages At most you need the first 16 pages and about 5 pages from the two appendices for your individual solutions 1 252y0771t 11 28 07 ECO252 QBA2 THIRD EXAM Nov 26 29 2007 TAKE HOME SECTION 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 t and 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 H0 and H1 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 x1 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 oil prices Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 GasPrice 1 25 1 38 1 30 1 24 1 21 1 20 0 93 0 95 0 96 1 02 1 16 1 14 1 13 1 11 1 11 1 15 1 23 1 23 1 06 1 17 1 51 1 46 1 36 1 59 1 88 2 30 3 10 CrudePrice 26 07 35 24 31 87 26 99 28 63 26 25 14 55 17 90 14 67 17 97 22 22 19 06 18 43 16 41 15 59 17 23 20 71 19 04 12 52 17 51 28 26 22 95 24 10 28 53 36 98 50 23 90 00 Yr 1979 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 x 2 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 n 17 observations The other row is the value for This data set also contains the year with 1979 subtracted from it the year 1980 a 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 to do the regression go to 3takehome072a Show your work it is legitimate to check your results by running the problem on the computer In fact I will 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 b0 b1 x to predict the price of gasoline on the basis of crude oil prices 3 R 2 2 c Compute s e 2 d Compute s b1 and do a significance test on b1 2 b Compute 2 252y0771t 11 28 07 e Compute a confidence interval for b0 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 massaged to make 1980 year 1 This involves a simultaneous equation solution Attempting to recycle work 7 b1 which has been from the previous page won t b Compute the regression sum of squares and use it in an ANOVA F test to test the usefulness of this regression 4 c Compute R 2 and R 2 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 R 2 here with the R 2 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 …
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