Appel BuyChart BuyNo BuyBuyNo BuyFinancial TiesNo Financial TiesFavorableNeutralCriticalFinancial TiesNo Financial TiesFavorableNeutralCriticalDec. 11, 2000 ECON 240A-1 L. PhillipsFinalAnswer 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 NotAppel Buy Chart Buy No Buy No Buy No Buy1.53 1.26 0.84 1.29 0.961.38 1.21 -0.47 0.98 0.41.16 1.14 0.03 -0.45 0.622.31 1.68 0.13 1.78 0.740.8 0.55 1.18 0.53 0.260.44 2.38 2.23 1.47 1.250.3 0.47 -0.16 2.09 1.611.61 0.96 0.68 -0.160.23 1.2 0.71 0.410.08 -0.15 -0.19-0.34 0.22 0.940.2 -0.21 0.961.96 0.78 0.142.13 1.17 0.741.03 0.43 1.290.94 0.93 0.861.55 2.04 1.140.66 0.09 1.760.07 1.49 0.621.8 0.74 0.030.89 -0.57 1.450.08 0.84 0.741.66 0.16 -0.10.26 1.92 -0.110.38 0.86 0.931.99 1.65 1.070.92 0.95 0.871.82 1.37 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 L. PhillipsFinal------------------------------------------------------------------------------------------------------Table 2: Mean Percentage Change of the NYSE in 4 WeeksAppel Buy Chart Buy No BuySample Mean 1.13 1.17 0.812Sample 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 percentagechange 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 = [(x1 - x2) – (1 - 2)]/[sp2{(1/n1) +(1/n2)}, where sp2 =[(n1-1)s12 + (n2- 1)s22]/[n1 +n2 –2] , dof = n1 + n2 –2 = 16+84-2sp2 = [15*0.4388 + 83*0.4868]/98 = 0.4795, dof =98t = [(1.153 – 0.812) – 0]/[0.4795{(1/16) +(1/84)}= 1.80Dec. 11, 2000 ECON 240A-3 L. PhillipsFinalt-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 __________----------------------------------------------------------------------------------------------------------------------------------------------------------------------------Table 3: Data for Pooled Sample, Appel Buy Plus Chart Buy, and Data for No BuyBuy No BuySample Mean 1.153 0.812Figure 1: Sample Mean +/- One Standard Deviation of the Mean 0.0000.2000.4000.6000.8001.0001.2001.4001.600Appel Buy Chart Buy No Buy% ChangeDec. 11, 2000 ECON 240A-4 L. PhillipsFinalSample Variance 0.4388 0.4868# of Observations 16 84-----------------------------------------------------------------------------------------------------------Table 4: Anova: Single FactorSUMMARYGroups Count Sum Average VarianceAppel 7 7.92 1.131429 0.481614Chart 9 10.53 1.17 0.4608No 84 68.17 0.811548 0.48677ANOVASource of Variation SS df MS F P-value F critBetween Groups 1.573971 2 0.786986 1.624966 0.202233 3.090193Within Groups 46.97798 97 0.484309Total 48.55196 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 -0.038571 0.350712 -0.109980 0.9127NOBUY -0.358452 0.244085 -1.468553 0.1452C 1.170000 0.231974 5.043660 0.0000R-squared 0.032418 Mean 0.866200Adjusted R-squared 0.012468 S.D. 0.700303S.E. of regression 0.695923 Akaike 2.142386Sum squared resid 46.97798 Schwarz 2.220541Log likelihood -104.1193 F-statistic 1.624966Durbin-Watson stat 2.068029 Prob(F- 0.202233------------------------------------------------------------------------------------2-1012-1012310 20 30 40 50 60 70 80 90 100Residual Actual FittedFigure 2: Actual Fitted, and Residuals from Regression of Pct. Change In NYSE on Constant and Dummies For Appel Buy and No BuyDec. 11, 2000 ECON 240A-5 L. PhillipsFinal--------------------------------------------------------------------------------------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
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