4 30 02 252x0242c ECO252 QBA2 Name FINAL EXAM Hour of Class Registered Circle May 6 2002 I 16 points Do all the following 1 Hand in your fourth regression problem 2 points Remember Y Vol volatility std Deviation of return X1 CR Credit rating on a zero to 100 per cent scale X2 emd a dummy variable that is 1 if a country has an emerging market 0 if the country has a developed market X3 ecr the product of CR and emd X4 gdp per capita income in thousands of US dollars in the late 90 s X5 gd cr the product of CR and gdp We would expect foreign exchange rates to became less volatile as i credit rating improves ii markets became developed and iii per capita income rises Remember saying yes or no to a question is useless unless you cite statistical tests Use a significance level of 1 in this problem except when you are told otherwise 2 Answer the following questions a For the regression of Vol against CR emd ecr gdp and gd cr what coefficients are significant at the 5 level Why What about the 1 level 3 b Given the comments at the beginning of this page what signs would you expect the coefficients to have Do they have the expected signs 4 c For the same regression what does the ANOVA tell us Why 2 d In view of the analysis above is there a regression that seems to work better than the one mentioned in a above Why 2 3 The problem in the text says Write a model that describes the relationship between volatility Y and credit rating as two nonparallel lines one for each type of market Is there evidence to conclude that the slope of the linear relationship between volatility Y and credit rating X1 depends on market type a What equation did you fit that answers the questions in the text Given the coefficients that you found what are the two equations and coefficients that your equation implies for these two market types 3 b Using the 1 confidence level what evidence can you present as to whether the slope depends on market type 2 4 What equation was suggested by your stepwise regression Does this seem to work as well as the one suggested by the textbook authors Why If you compare the slope of the regression line relating volatility to the credit rating for countries with gdps of 2 thousand and 20 thousand what seems to be happening to the slope as per capita gdp rises 5 4 30 02 252x0242 II Do at least 4 of the following 7 Problems at least 15 each or do sections adding to at least 60 points Anything extra you do helps and grades wrap around Show your work State H 0 and H1 where applicable Use a significance level of 5 unless noted otherwise Do not answer questions without citing appropriate statistical tests 1 A researcher is investigating the behavior of the Dow Jones Transportation Industrial and Utility averages Data is presented below for closing numbers for 14 days in May 2001 Because the researcher believes that the underlying distributions are not Normal she computes rank correlations instead of standard correlations For your convenience ranks have been computed for Transportation and Industry a Check the utilities for rises and falls in value marking rises with and falls with Using a statistical test find out if the pattern of rises and falls is random 5 b Compute a rank correlation between industry and utility prices and test it for significance 5 c Compute a measurement of concordance between the three series and test it for significance Express it on a zero to one scale 6 Row Date Trans Indust x1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 5 5 5 5 5 5 5 5 5 5 5 5 5 5 07 08 09 10 11 14 15 16 17 18 21 22 23 24 2850 64 2865 54 2865 73 2899 76 2879 56 2874 59 2880 24 2925 50 2957 58 2978 95 3004 35 2990 97 2969 16 2951 01 r1 1 2 3 7 5 4 6 8 10 12 14 13 11 9 Util x2 10935 2 10888 5 10867 0 10910 4 10821 3 10877 3 10873 0 11215 9 11248 6 11301 7 11337 9 11257 2 11105 5 11122 4 r2 7 5 2 6 1 4 3 10 11 13 14 12 8 9 x3 383 93 378 74 383 74 383 52 386 64 391 04 385 70 387 52 387 84 391 54 394 43 394 67 398 31 397 68 2 4 30 02 252x0242 2 Pelosi and Sandifer A diaper company is testing three filler materials for diapers Eight diapers were tested with each of the three filler materials making a total of 24 diapers put on 24 toddlers Each column x1 x 2 and x 3 can be considered a random sample of eight taken from a Normally distributed population As each toddler played fluid was injected into the diaper until the product leaked Each number below in x1 x 2 and x 3 represents the capacity of the diaper The remaining columns r1 r2 and r3 are a ranking of the 24 numbers In this entire problem we assume that the underlying distributions are Normal Row x1 r1 x2 r2 x3 r3 1 2 3 4 5 6 7 8 791 24 0 3 5 811 13 5 872 The following are computed for you 792 790 797 803 811 791 801 5 0 2 0 6 0 8 5 13 5 3 5 7 0 809 818 803 781 813 808 805 12 0 17 0 8 5 1 0 15 5 11 0 10 0 826 813 854 843 846 847 835 18 0 15 5 23 0 20 0 21 0 22 0 19 0 x x x 1 3 2 2 6376 00 6736 00 5197954 x x 2 x12 2 3 6448 00 5082066 5673944 and n1 n 2 n 3 8 a Compute the sample variances of x1 and x 3 and test the hypothesis that the population variances for these two columns are equal 4 b Assume that the variances of the populations from which x 2 and x 3 come are equal and test the hypothesis that 3 is greater than 2 i First state your null and alternate hypotheses 2 and then test the hypotheses using a ii test ratio iii a critical value and iv a confidence interval 6 c Test if the hypothesis that the means of all three populations are equal holds water 7 d Use a test of goodness of fit to see if x 2 has the Normal distribution 5 3 4 30 02 252x0242 3 Data from the previous problem is repeated In this problem assume that the underlying distributions are not Normal Remember that each column is an independent sample Row x1 r1 x2 r2 x3 r3 1 2 3 4 5 6 7 792 790 797 …
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