Problem 1: A team must score more than their opponents to win a game, and so they must ultimately score runs, since they cannot win with a score of zero. Are runs correlated with wins; i. e., does a team that scores more runs win more games? Conduct a correlation analysis to determine if there is a correlation between Runs and Wins. Use a .05 significance level. Answer the following questions: a. State your conclusion. Base this on the p-value.
b. Find the correlation coefficient and the coefficient of determination.
c. What is the best fit regression equation that can predict the Wins from the Runs?
d. How many games would you expect a team to win if they scored 800 runs in a season?
Problem 2: Let us look at a popular argument that it takes money to win. Kansas City had one of the lowest payrolls and won it all, Houston had the second lowest payroll and made it far in the playoffs, and seven of the top ten payrolls did not even qualify for the playoffs. The evidence will show that money is not a predicting factor, but we are going to make it official. Perform a correlation analysis to determine if there is a correlation between Payroll and Wins. Use a .05 significance level. Answer the following questions:
a. Is the p-value statistically significant?
b. What is the correlation coefficient and the coefficient of determination?
c. If the results are not statistically significant, you would normally stop at this point?
d. What is the regression equation, even if the results are not statistically significant?
Problem 3: In order to obtain an even better model for predicting Wins, we are going to look at multiple variables. Create a multiple regression equation predicting the Wins using Runs, Hits, Home Runs, Average, Strikeouts, Stolen Bases and ERA. Use the Stepwise procedure to eliminate non-significant variables until the final equation has only significant variables. After you create your regression equation, predict the Wins for a team that has 700 runs, 1500 hits, 200 homeruns, a .260 average, 1000 strikeouts, 100 stolen bases and a 3.00 ERA