QuestionA sample of nine public universities and nine private universities was taken. The total cost for the year (including room and board) and the median SAT score (maximum total is 2400) at each school were recorded. It was felt that schools with higher median SAT scores would have a better reputation and would charge more tuition as a result of that. The data is in the table below. Use regression to help answer the following questions based on this sample data. Do schools with higher SAT scores charge more in tuition and fees? Are private schools more expensive than public schools when SAT scores are taken into consideration? Discuss how accurate you believe these results are using information related the regression models.
Category Total Cost Median SAT
Public 21,700 1990
Public 15,600 1620
Public 16,900 1810
Public 15,400 1540
Public 23,100 1540
Public 21,400 1600
Public 16,500 1560
Public 23,500 1890
Public 20,200 1620
Private 30,400 1630
Private 41,500 1840
Private 36,100 1980
Private 42,100 1930
Private 27,100 2130
Private 34,800 2010
Private 32,100 1590
Private 31,800 1720
Private 32,100 1770
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In 2008, the total payroll for the New York Yankees was $209.1 million, while the total payroll for the Tampa By Rays was about $43.8 million about 1/5th of that of the Yankees. The table below lists the payrolls in millions for all 14 MLB teams in the American league and the total victories for 2008
Team Payroll millions victories
NY Yankees 209.1 89
Detroit Tigers 138.7 74
Boston Red Sox 133.4 95
Chicago White sox 121.2 89
Cleveland Indians 79 81
Baltimore Orioles 67.2 68
Oakland Athletics 48 75
Los Angeles Angels 119.2 100
Seattle Mariners 118 61
Toronto Blue Jays 98.6 86
Minnesota Twins 62.2 88
Kansas City 58.2 75
Tampa Bay 43.8 97
Texas Rangers 68.2 79
Develop a regression model to predict total number of victories based on payroll of the team. Based on results discuss how accurate the model is. Use the model to predict the number of victories for a team with a payroll of $79million
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In 2009, the New York Yankees won 103 baseball games during the regular season. The table on the next page lists the number of victories (W), the earned-run- average (ERA), and the batting average (AVG) of each team in the American League. The ERA is one measure of the effectiveness of the pitching staff, and a lower number is ***** The batting average is one measure of effectiveness of the hitters, and a higher number is *****
TEAM W ERA AVG
New York Yankees 103 4.26 0.283
Los Angeles Angels 97 4.45 0.285
Boston Red Sox 95 4.35 0.27
Minnesota Twins 87 4.5 0.274
Texas Rangers 87 4.38 0.26
Detroit Tigers 86 4.29 0.26
Seaattle Mariners 85 3.87 0.258
Tampa Bay Rays 84 4.33 0.263
Chicago White Sox 79 4.14 0.258
Toronto Blue Jays 75 4.47 0.266
Oakland Athletics 75 4.26 0.262
Cleveland Indians 65 5.06 0.264
Kansas City Royals 65 4.83 0.259
Baltimore Orioles 64 5.15 0.268
A.Develop a regression model that could be used to predict the number of victories based on the ERA.
B.Develop a regression model that could be used to predict the number of victories based on the batting average.
C.Which of the two models is better for predicting the number of victories?
D.Develop a multiple regression model that includes both ERA and batting average. How does this compare to the previous models?
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-24. Sale of industrial vacuum cleaners at R. Lowenthal Supply Co. over
the past 13 months are as follows:
Sales (1,000) Month Sales
11 January
14 August
14 February
17 September
16 March
12 October
10 April
14 November
15 May
16 December
17 June
11 January
11 July
(a) Using a moving average with three periods, determine the demand for
vacuum cleaners for next February.
(b) Using a weighted moving average with three periods, determine the
demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights
of the most recent, second most recent, and third most recent periods,
respectively. For example, if you were forecasting the demand for
February, November would have a weight of 1, December would have a
weight of 2, and January would have a weight of 3.