Nov 3 2009 ECON 240A 1 Midterm L Phillips Answer All Five Questions 1 15 min This is data about some characteristics of American football players at all player positions 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 players Stems Leaves 17 0 18 19 0 20 0 21 00 22 000000 23 000 24 0000000 25 00055 26 000000555555555 27 000055 28 55555 29 04566 30 00000 31 000055 32 000005 33 0000008 34 0000 35 00025555 36 0 37 055555 38 0005 39 40 00001 41 42 001 43 44 0 Nov 3 2009 ECON 240A 2 Midterm L Phillips a 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 variables Nov 3 2009 ECON 240A 3 Midterm L Phillips Figure 2 2 A View of Weight Versus Height with the Bench Axis Coming Towards the Viewer Figure 2 3 A View Of Bench Versus Weight with the Height Axis Coming Towards the Viewer Nov 3 2009 ECON 240A 4 Midterm L Phillips a 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 patterns b Is weight independent of height Explain your answer No from second panel they are ositively correlated c Is the weight a player can bench press negatively correlated with player weight Explain your answer No from third panel they are positively correlated d 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 variables e 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 jointly 3 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 correlated b 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 proportionately c 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 45 Nov 3 2009 ECON 240A 5 Midterm L Phillips d 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 height e What other explanatory variable do you think might affect the weight a player can bench press Explain your answer Player height 4 15 Last Wednesday s Nexus featured an article on the research of Professor Michael Gurven in the Anthropology Department who studies the Tsuname Indians in Bolivia 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 or high cholesterol are shown in the following table Cholesterol High OK Blood Pressure High 0 11 0 16 OK 0 21 0 52 a What is the probability that an adult American male has both high blood pressure and high cholesterol 0 11 b What is the probability that an adult American male has high blood pressure 0 27 c What is the probability that an adult American male has high cholesterol 0 32 d 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 41 e 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 34 5 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 Midterm L Phillips Nov 3 2009 ECON 240A 7 Midterm L Phillips A 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 Time SUMMARY OUTPUT Regression Statistics Multiple R 0 98915603 R Square 0 97842966 Adjusted R Square 0 97798027 Standard Error 945 404323 Observations 50 ANOVA df Regression Residual Total Intercept Year 1 48 49 SS 1946027287 42901888 1 1988929175 Coefficient s 13204 1075 432 311666 Standard Error 263 439012 9 26488593 MS 1 946E 09 893789 33 F 2177 2774 Significance F 1 19171E 41 t Stat 50 122066 46 661305 P value 4 113E 43 1 192E 41 Lower 95 12674 42786 413 683365 Upper 95 13733 78711 450 9399677 Nov 3 2009 ECON 240A 8 Midterm L Phillips a 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 R2 c Is the F statistic statistically significant for the linear time trend regression Explain Yes large F with very small probability so reject null of no correlation d What is the estimated slope in the …
View Full Document
Unlocking...