Question;A 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 SATPublic 21,700 1990Public 15,600 1620Public 16,900 1810Public 15,400 1540Public 23,100 1540Public 21,400 1600Public 16,500 1560Public 23,500 1890Public 20,200 1620Private 30,400 1630Private 41,500 1840Private 36,100 1980Private 42,100 1930Private 27,100 2130Private 34,800 2010Private 32,100 1590Private 31,800 1720Private 32,100 1770# *****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 2008Team Payroll millions victoriesNY Yankees 209.1 89Detroit Tigers 138.7 74Boston Red Sox 133.4 95Chicago White sox 121.2 89Cleveland Indians 79 81Baltimore Orioles 67.2 68Oakland Athletics 48 75Los Angeles Angels 119.2 100Seattle Mariners 118 61Toronto Blue Jays 98.6 86Minnesota Twins 62.2 88Kansas City 58.2 75Tampa Bay 43.8 97Texas Rangers 68.2 79Develop 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#32In 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 AVGNew York Yankees 103 4.26 0.283Los Angeles Angels 97 4.45 0.285Boston Red Sox 95 4.35 0.27Minnesota Twins 87 4.5 0.274Texas Rangers 87 4.38 0.26Detroit Tigers 86 4.29 0.26Seaattle Mariners 85 3.87 0.258Tampa Bay Rays 84 4.33 0.263Chicago White Sox 79 4.14 0.258Toronto Blue Jays 75 4.47 0.266Oakland Athletics 75 4.26 0.262Cleveland Indians 65 5.06 0.264Kansas City Royals 65 4.83 0.259Baltimore Orioles 64 5.15 0.268A.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?# *****-24. Sale of industrial vacuum cleaners at R. Lowenthal Supply Co. overthe past 13 months are as follows:Sales (1,000) Month Sales11 January14 August14 February17 September16 March12 October10 April14 November15 May16 December17 June11 January11 July(a) Using a moving average with three periods, determine the demand forvacuum cleaners for next February.(b) Using a weighted moving average with three periods, determine thedemand for vacuum cleaners for February. Use 3, 2, and 1 for the weightsof the most recent, second most recent, and third most recent periods,respectively. For example, if you were forecasting the demand forFebruary, November would have a weight of 1, December would have aweight of 2, and January would have a weight of 3.
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