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# 11 the mean rate of return on stock a is 10 and on

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11) The mean rate of return on stock A is 10% and on stock B is 20%. The standard deviation of the rate of return is 8% on stock A and 24% on stock B. The correlation coefficient, ρ , between stocks A and B is .4. What is the standard deviation of the return on the portfolio that has an expected return of 16%? Please read this background information. It should help you to interpret the regressions that follow. In the December 17, 1996 issue of PC Magazine , there are reviews of 18 new home personal computers. The speed of computers is measured using a Winstone score. This measures how fast a computer can complete a set of standard tasks using Windows programs. The higher the score, the faster the computer. In testing computers, PC Magazine measures the speed of several subsystems and assigns them scores. The Graphics score measures how fast images are drawn on the computer monitor. The

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graphics score depends on how fast the video card is, and also on how fast the CPU/memory subsystem is. The Disk score measures how fast the hard drive is. The CPU mark measures how fast the CPU/memory subsystem is. The CPU mark depends on how much memory is installed, on the raw speed of the CPU, and on the size of the secondary cache. More cache is better, and should improve the CPU mark. Typically, new computers have 16 megabytes of memory, but all the Pentium 200 systems reviewed had 32. There is also CD-ROM score that measures how fast the CD-ROM on the computer is. In each case, a higher score is better than a lower score. Below is a regression that explains the Winstone score with the scores of each of the subsystems. The regression equation is Winstone = 2.50 + 0.245 graphics + 0.0158 disk + 0.0423 cpu mark - 0.00434 cdRom Predictor Coef Stdev t-ratio p Constant 2.504 2.479 1.01 0.331 graphics 0.24481 0.04999 4.90 0.000 disk 0.015835 0.003209 4.93 0.000 cpu mark 0.042295 0.007963 5.31 0.000 cdRom -0.004341 0.002171 -2.00 0.067 s = 1.117 R-sq = 97.8% R-sq(adj) = 97.1% Analysis of Variance SOURCE DF SS MS F p Regression 4 716.06 179.01 143.49 0.000 Error 13 16.22 1.25 Total 17 732.28 Question 12 a) Does this regression do a good job of explaining the Winstone score? Explain . b) Carefully interpret the coefficient of the graphics score. c) Compute a 95% Confidence Interval for the coefficient of the graphics score. d) Let’s call the population coefficient for the cdRom score 4 β . Use the information to compute the p-value for the following hypothesis: 04 4 :0 A H H > . Do you accept or reject the null hypothesis? Would you want to leave the cdRom score in the regression or not? Explain . 13) There were four different video card manufacturers whose products appeared in these computers: ATI, Virge, Matrox, and Diamond. To try to determine which of these manufacturers has the best product, three dummy variables were introduced, to represent the ATI, Virge, and Matrox cards respectively. Then the following regression was run to explain the speed of the graphics subsystem. MTB > regress c3 4 c5 c7-c9
The regression equation is graphics = 23.7 + 0.0726 cpu mark - 17.9 ati - 13.8 virge - 4.71 matrox Predictor Coef Stdev t-ratio p Constant 23.652 4.554 5.19 0.000 cpu mark 0.07257 0.01129 6.43 0.000 ati -17.934 2.243 -7.99 0.000 virge -13.808 2.225 -6.21 0.000 matrox -4.709 2.763 -1.70 0.112 s = 2.685 R-sq = 94.3% R-sq(adj) = 92.5% Analysis of Variance SOURCE DF SS MS F p Regression 4 1548.79 387.20 53.72 0.000 Error 13 93.69 7.21 Total 17 1642.48

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