baseball Team Payroll Wins Arizona Diamondbacks 73,571,667 70 Atlanta Braves 96,726,167 86 Baltimore Orioles 67,101,667 64 Boston Red Sox 122,696,000 95 Chicago Cubs 135,050,000 83 Chicago White Sox 96,068,500 79 Cincinnati Reds 70,968,500 78 Cleveland Indians 81,625,567 65 Colorado Rockies 75,201,000 92 Detroit Tigers 115,085,145 86 Florida Marlins 36,814,000 87 Houston Astros 102,996,415 74 70,908,333 65 Kansas City Royals Los Angeles Angels 113,709,000 97 Los Angeles Dodgers 100,458,101 95 Milwaukee Brewers 79,857,502 80 Minnesota Twins 65,299,267 87 New York Mets 135,773,988 70 New York Yankees 201,449,289 103 Oakland Athletics 62,310,000 75 Philadelphia Phillies 113,004,048 93 Pittsburgh Pirates 48,743,000 62 San Diego Padres 42,796,700 75 San Francisco Giants 82,161,450 88 Seattle Mariners 98,904,167 85 St. Louis Cardinals 88,528,411 91 Tampa Bay Devil Rays 63,313,035 84 Texas Rangers 68,646,023 87 Toronto Blue Jays 80,993,657 75 Washington Nationals 59,328,000 59 In baseball, as in the rest of the business world, it is generally believed that salary reflects ability. We would, therefore, expect baseball teams with a higher payroll to win more games. Refer to the CSV file in the link below which contains data from the 2009 baseball season. Data (CSV): 5 Note: the file is Tab separated. Some versions of R may not automatically identify it, in which case you need to tell R by choosing Tab in the drop down list of Separator. Indicate the sample mean payroll price in millions. Round your result to the nearest million. (e.g. for 1.2 million, write 1.2 not 1,200,000) Indicate the corresponding standard deviation. Round your result to the nearest million. Your next step is to do descriptive statistics on the variables that you will be using: number of wins and payroll in millions of dollars. Based on the summary statistics, what is the average number of wins? What is the maximum payroll measured in million dollars? To get a quick feel for the data you decide to check the correlation between the number of wins and payroll in millions. Using two decimal places what is the correlation between these two variables? The group of investors believes that having a higher payroll would result in more wins and asks you to run a regression to examine this hypothesis. Pick "wins" as the dependent/response variable and "Payroll.millions" as the explanatory variable. Which of the values below best matches your by or slope parameter result? 0.06 65.76 0.17 0.25 The estimated coefficient for the explanatory variable in the regression model you just ran tells us that for every additional [ Select ] in [Select] we expect wins to [ Select ] by [Select] [ Select ] Say that our null hypothesis is that the effect of payroll on number of wins is equal to zero and that the alternative hypothesis is that it is not equal to zero. Using a significance level of 5% we [ Select] v the null hypothesis because the p-value for the Payroll.million coefficient is | [ Select ] [ Select] What is the predicted number of wins if the group of investors can achieve a payroll of 88 million dollars? Round to the closest integer (no decimal points). Easiest is to use your calculator for this one, but you can also use the R command "coef": coef(modelName)["coefficientName"] Note that the names R uses for the coefficients are what is printed by the summary. This prediction is very close to the [Select ] in the descriptive statistics above because a regression line always runs through the [Select ] v of the variables. One of the investors in the group is very ambitious. She wants to raise enough funds to break the Yankees' hold on the largest payroll. Her plan is to raise enough funds to make the payroll 225 million dollars. What would your model predict that the number of wins would be for a team with a $225 million payroll? Use nearest integer again. In addition to the predicted number of wins with $225 million in payroll you just found for the investor, what should you also tell her about this prediction and its reliability? that the prediction is problematic because it is for a payroll number above those used to estimate the model. that the prediction is problematic because it is for a payroll number below those used to estimate the model. that you have a high confidence in the number because the coefficient on payroll is significant. The R-squared for your regression model is [Select] ? This means that variation in [Select ] explains [ Select ] [ Select ] of the variation in [ Select ]