Dec 11 2000 ECON 240A 1 Final L Phillips Answer all four questions 1 40 points There are several buy signals used by some stock investors One signal developed by Gerald Appel says a market bottom has been reached when the weekly close of the New York Stock Exchange NYSE is 4 points or more below its 10 week moving average Another buy signal based on bottoming out depends on a chart pattern As an experiment 100 weeks were selected at random and the week was classified as an Appel buy a chart buy or no buy Then the percentage change over the next 4 weeks was calculated for that week The data are shown in Table 1 Table 1 Percent Change on the NYSE Depending on Buy Signal Or Not Appel Buy 1 53 1 38 1 16 2 31 0 8 0 44 0 3 Chart Buy 1 26 1 21 1 14 1 68 0 55 2 38 0 47 1 61 0 23 No Buy 0 84 0 47 0 03 0 13 1 18 2 23 0 16 0 96 1 2 0 08 0 34 0 2 1 96 2 13 1 03 0 94 1 55 0 66 0 07 1 8 0 89 0 08 1 66 0 26 0 38 1 99 0 92 1 82 No Buy 1 29 0 98 0 45 1 78 0 53 1 47 2 09 0 68 0 71 0 15 0 22 0 21 0 78 1 17 0 43 0 93 2 04 0 09 1 49 0 74 0 57 0 84 0 16 1 92 0 86 1 65 0 95 1 37 No Buy 0 96 0 4 0 62 0 74 0 26 1 25 1 61 0 16 0 41 0 19 0 94 0 96 0 14 0 74 1 29 0 86 1 14 1 76 0 62 0 03 1 45 0 74 0 1 0 11 0 93 1 07 0 87 1 13 The average percentage increase for each class is listed in Table 2 along with the sample variance Dec 11 2000 ECON 240A 2 Final L Phillips Table 2 Mean Percentage Change of the NYSE in 4 Weeks Appel Buy Chart Buy No Buy Sample Mean 1 13 1 17 0 812 Sample Variance 0 4816 0 4608 0 4868 of Observations 7 9 84 The issue is whether one of the buy indicators is useful Four statisticians look at the data The first plots the three means plus or minus one standard deviation of that mean i e the sample standard deviation divided by the square root of the sample size as shown in Figure 1 The second pools the data for the Appel Buy and the Chart Buy since the means are close and tests whether there is a significant difference between the means for buy and no buy The data are shown in Table 3 You will have to conduct the test The third runs one way analysis of variance obtaining the results shown in Table 4 The fourth statistician runs a regression using the 100 observations for percentage change as the dependent variable and including as regressors a constant term and two dummy zero one indicator variables These dummy variables indicate whether the observation is an Appel buy a no buy or neither i e a chart buy The results are shown in Table 5 and Figure 2 a Is there any evidence from any of the analyses of the four statisticians that the buy signals are useful No b What is i the statistic its definition its value and its distribution used by the second statistician ii Is it significant i t x 1 x 2 1 2 sp2 1 n1 1 n2 where sp2 n1 1 s12 n2 1 s22 n1 n2 2 dof n1 n2 2 16 84 2 sp2 15 0 4388 83 0 4868 98 0 4795 dof 98 t 1 153 0 812 0 0 4795 1 16 1 84 1 80 Dec 11 2000 ECON 240A 3 Final L Phillips t distribution ii not significant c What is i the statistic its value and its distribution used by the third statistician ii Is it significant iii What is the null hypothesis i F2 97 1 62 EMS UMS F distribution ii Not significant iii 2 or more of the three means differ from one another d What is i the statistic its value and its distribution used by the fourth statistician ii Is it significant iii What is the null hypothesis i F2 97 1 62 EMS UMS F distribution ii Not significant iii 2 or more of the three means differ from one another Figure 1 Sample Mean One Standard Deviation of the Mean 1 600 1 400 1 200 Change 1 000 0 800 0 600 0 400 0 200 0 000 Appel Buy Chart Buy No Buy Table 3 Data for Pooled Sample Appel Buy Plus Chart Buy and Data for No Buy Buy Sample Mean No Buy 1 153 0 812 Dec 11 2000 ECON 240A 4 Final Sample Variance of Observations 0 4388 16 L Phillips 0 4868 84 Table 4 Anova Single Factor SUMMARY Groups Appel Chart No Count Sum Average Variance 7 92 1 131429 0 481614 10 53 1 17 0 4608 68 17 0 811548 0 48677 7 9 84 ANOVA Source of Variation Between Groups Within Groups SS 1 573971 46 97798 Total 48 55196 df MS F P value F crit 2 0 786986 1 624966 0 202233 3 090193 97 0 484309 99 Table 5 Regression of Pct Change in NYSE on a Constant and Dummy Indicators for Appel Buy Or No Buy Variable Coefficient Std Error t Statistic Prob APPEL NOBUY C 0 038571 0 358452 1 170000 0 350712 0 244085 0 231974 0 109980 1 468553 5 043660 0 9127 0 1452 0 0000 R squared 0 032418 Mean 0 866200 Adjusted R squared 0 012468 S D 0 700303 S E of regression 0 695923 Akaike 2 142386 Sum squared resid 46 97798 Schwarz 2 220541 Log likelihood 104 1193 F statistic 1 624966 Durbin Watson stat Fitted 2 068029 Prob F0 202233 Figure 2 Actual and Residuals from Regression of Pct Change In NYSE on Constant and Dummies For Appel Buy and No Buy 3 2 1 2 0 1 1 0 1 2 10 20 30 40 Res idual 50 60 Actual 70 80 90 100 Fitted Dec 11 2000 ECON 240A 5 Final L Phillips 2 40 points An increasing concern among environmentalists and others is that research results are for sale For example Robert Kennedy Jr has spoken to this issue pointing out that increasingly even public research universities are increasingly seeking funding from companies and that this jeopardizes the reliability of faculty as independent experts The New England Journal of Medicine published an article Conflict of Interest in the Debate over Calcium Channel Antagonists January 8 1998 The debate was whether the use of calcium channel blockers to treat hypertension increased the risk of heart disease The authors …
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