Nov. 3, 2009 ECON 240A-1 L. PhillipsMidtermAnswer All Five Questions.1. (15 min.) This is data about some characteristics of American football players at all playerpositions, obtained from a JMP data file. The first figure is a stem and leaf diagram of bench press weight in pounds for the 115 players who reported this variable out of 130 total players. Bench pressing is a form of weight lifting where you lie prone on your back on a bench and lift, i.e. press, weights.Figure 1.1:Stem & Leaf Display, Bench press weight in pounds for 115 football playersStems Leaves17 ->01819 ->020 ->021 ->0022 ->00000023 ->00024 ->000000025 ->0005526 ->00000055555555527 ->00005528 ->5555529 ->0456630 ->0000031 ->00005532 ->00000533 ->000000834 ->000035 ->0002555536 ->037 ->05555538 ->00053940 ->000014142 ->0014344 ->0Nov. 3, 2009 ECON 240A-2 L. PhillipsMidterma. What is the minimum weight pressed? _170_pounds_____(It was a wide receiver)b. What is the maximum weight pressed? _440 pounds__________ (it was a defensive lineman)c. What is the range? __270 pounds, i.e 170-440_________d. What is the median? Middle observation is 57th,_296 pounds__________e. What is the most likely or modal bench press weight reported? 265 pounds_______2. (15 min) Three views of three variables from the JMP football player data set are presented in the spinning plot format. Height is player height in inches, weight is player weight in pounds, and bench is the weight in pounds the player can bench press..Figure 2.1: A three dimensional view of the three variablesNov. 3, 2009 ECON 240A-3 L. PhillipsMidtermFigure 2.2:A View of Weight Versus Height with the Bench Axis Coming Towards theViewerFigure 2.3: A View Of Bench Versus Weight with the Height Axis Coming Towards the ViewerNov. 3, 2009 ECON 240A-4 L. PhillipsMidterma. Are these three player characteristic variables distributed jointly normally and independent of one another? Explain your answer. No they are not distributed spherically about the origin but in patternsb. Is weight independent of height? Explain your answer No, from second panel they are positively correlatedc. Is the weight a player can bench press negatively correlated with player weight? Explain your answer. No, from third panel they are positively correlatedd. In general what is the purpose of examining a three dimensional plot of the data? To see if there are visible patterns and relationships amongst the three variablese. Why is exploratory graphical data analysis necessary since a normal distribution can be completely described with two parameters, a mean and a variance? Variables may not be normally distributed, individually and/or jointly3. (15 points) Figure 3-1 is an Excel plot of the weight a player can bench press regressed against the weight of the player, for the 105 players that reported both measures.a. In terms of the exploratory data analysis that we conducted in Question 2 above, what does this regression result confirm? Explain. Bench press weight and player weight are positively correlatedb. How does the weight a player can bench press in pounds increase with the weight of the player in pounds? 1.088 pounds per pound or approximately proportionatelyc. What fraction of the variation across players in their strength, as measured by bench press weight, is explained by the size of the player, as measured by the weight of the player? R2 = 0.45Nov. 3, 2009 ECON 240A-5 L. PhillipsMidtermd. If the intercept were shown to be significantly different from zero, do you think that makes any sense? No, e.g. a newborn can not bench press, so this may reflect the influence of the third variable, player heighte. What other explanatory variable do you think might affect the weight a player can bench press? Explain your answer. Player height4. (15) Last Wednesday’s Nexus featured an article on the research of Professor Michael Gurven in the Anthropology Department who studies the Tsuname Indians inBolivia. He found that in this tribe, inflammation of the heart did not cause heart attacks in contrast with experience in the developed world. There are many causes of heart attacks. Heart attack is the number one killer of men and women all over the world. Both high blood pressure and high “bad’ cholesterol contribute to the risk of heart attacks.The joint probabilities that an adult American male has high blood pressure and/orhigh cholesterol are shown in the following table.Blood PressureCholesterol High OKHigh 0.11 0.21OK 0.16 0.52a. What is the probability that an adult American male has both high blood pressure and high cholesterol? 0.11b. What is the probability that an adult American male has high blood pressure? 0.27c. What is the probability that an adult American male has high cholesterol? 0.32d. If an adult American male has high blood pressure what is the probability that he has high cholesterol? P(HC/HBP) = P(HC^HBP)/P(HBP) = 0.11/0.27) = 0.41e. If an adult American male has high cholesterol, what is the probability he has high blood pressure? P(HBP/HC) = P(HBP^HC)/P(HC) = 0.11/0.32 = 0.345. (15) Personal income per capita in California, CAYPC, corrected for inflation, i.e. in year 2000 dollars is available at the California Department of Finance Web Site for the years 1959-2008. A plot of this time series follows in Figure 5-1.Nov. 3, 2009 ECON 240A-6 L. PhillipsMidtermNov. 3, 2009 ECON 240A-7 L. PhillipsMidtermA linear regression was also investigated regressing CAYPC against a time index which was zero in 1959, 1 in 1960, etc. ending at 49 in 2008. This regression is reported in Table 5-1.Table 5-1; Linear Regression of California Income Per capita in 2000 Dollars Against TimeSUMMARY OUTPUTRegression StatisticsMultiple R 0.98915603R Square 0.97842966Adjusted R Square 0.97798027Standard Error 945.404323Observations 50ANOVA df SS MS FSignificanceFRegression 1 1946027287 1.946E+09 2177.2774 1.19171E-41Residual 48 42901888.1 893789.33Total 49 1988929175 CoefficientsStandardError t Stat P-value Lower 95% Upper 95%Intercept 13204.1075 263.439012 50.122066 4.113E-43 12674.42786 13733.78711Year 432.311666 9.26488593 46.661305 1.192E-41 413.683365 450.9399677Nov. 3, 2009 ECON 240A-8 L. PhillipsMidterma. What is the estimated percentage rate of growth of real California Personal Income Per capita? 1.9%b. Which regression appears to fit the best, an exponential trend or a linear trend? Explain. Linear regression has a slightly higher R2c. Is the F-statistic statistically
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