1.Thirteen students entered the undergraduate business program at Rollins College 2 years ago. The following table indicates what their grade-point averages (GPAs) were after being in the program for 2 years and what each student scored on the SAT exam (maximum 2400) when he or she was in high school. Is there a meaningful relationship between grades and SAT scores? If a student scores a 1200 on the SAT, what do you think his or her GPA will be? What about a student who scores 2400?
2.Tim Cooper plans to invest money in a mutual fund that is tied to one of the major market indices, either the S&P 500 or the Dow Jones Industrial Average. To obtain even more diversification, Tim has thought about investing in both of these. To determine whether investing in two funds would help, Tim decided to take 20 weeks of data and compare the two markets. The closing price for each index is shown in the table below:
Develop a regression model that would predict the DJIA based on the S&P 500 index. Based on this model, what would you expect the DJIA to be when the S&P is 1,100? What is the correlation coefficient (r) between the two markets?
3.In 2008, the total payroll for the New York Yankees was $209.1 million, while the total payroll for the Tampa Bay Rays was about $43.8 million, or about one-fifth that of the Yankees. Many people have suggested that some teams are able to buy winning seasons and championships by spending a lot of money on the most talented players available. The table below lists the payrolls (in millions of dollars) for all 14 Major League Baseball teams in the American League as well as the total number of victories for each in the 2008 season:
Develop a regression model to predict the total number of victories based on the payroll of a team. Based on the results of the computer output, discuss how accurate this model is. Use the model to predict the number of victories for a team with a payroll of $79 million.