Analysis of Tasks for SPSS - Essay Example

SPSS Problems for Grade SPSS Problems for Grade The following table shows assets and sales for 16 large travelcorporations. Solve the following questions by using assets as X variable (5 points). Require: a) Draw a regression plot of the X and Y values b) Calculate the least squares regression equation and explain the equation From the co-efficient table, a = 2.289 and b = 0.765. Therefore, lease squares regression equation is: Y = 2.289 + 0.765 X The b value of 0.765 means that for each increase in the number of assets the total sales increase by 0.765. The (a) value of 2.289 is the point where the equation crosses the Y-axis. c) Calculate the correlation coefficient (r and the coefficient of determination (r2), and explain what they are used for. r = 0.8769 r2 = 0.769 The coefficient of correlation r is 0.8769, almost to 1.00, which shows a very strong positive correlation between number of assets and sales. If number of assets increases the total sales will also increase. The Coefficient of determination r2 is 0.8769, which means that 87.69 % percent of the variation in the number of assets sold is explained, or accounted for, by the variation in the movement of assets prices. Obviously, in this case, cake price is almost the single factor that influences cake sales. Assets (in billions) Sales (in billions) 7.8 9.2 8.8 8.5 7.0 8.4 6.0 8.0 4.1 6.5 6.6 6.4 5.3 6.2 4.3 5.8 3.6 5.5 4.2 5.4 1.8 4.7 4.6 4.4 4.3 4.3 3.3 3.9 2.8 3.9 1.5 3.7 2. Use 2007 Baseball Team data, let the games won be the dependent variable and total team salary be the independent variable. Solve the following problems (4 points): Require: a) Draw a regression plot of the X and Y values b) Calculate the least squares regression equation and explain the equation. How many additional wins will an additional $5 million in salary bring? From the co-efficient table, a = 69.365 and b = 0.140. Therefore, lease squares regression equation is: Y = 69.365 + 0.140 X The b value of 0.140 means that for each increase in the number of assets the total sales increase by 0.140. The (a) value of 0.140 is the point where the equation crosses the Y-axis. For 5 million salary, Y= (69.365 + (0.14*5) = 70.065 It will be 70 wins c) Calculate the correlation coefficient (r) and the coefficient of determination (r2), and explain what they measure. r = 0.505 r2 = 0.255 The coefficient of correlation r is 0.505, which shows a moderate positive correlation between the total number of wins and the team salary. If number team salary increases the number of wins also increases. The Coefficient of determination r2 is 0.255, which means that 25.5 % percent of the variation in the number of wins is explained or accounted for, by the variation in the team salary. d) Test the hypothesis that the two variables, games won and team salary are independent of each other in the population at 5% significant level. H0:  = 0 (The correlation in the population is zero) H1:   0 (The correlation in the population is different from zero). Significant level  = .05 Reject H0 if p value <  From the table the p-value is 0.04 H0 is rejected because p-value = 0.04 and therefore is smaller than the 95 % significance level. Therefore, there is strong evidence that the true population correlation for these two variables is not zero. 3. Revisit the CEO pay and firm performance problem you did for SPSS 4. In SPSS Assignment 4, you did a scatter plot to examine the relationship between the compensations of CEOs in the tourism industry and their respective firms’ performance measured by revenues. In this exercise, you are asked to test if there is any significant relationship between CEO compensation and firm performance using simple regression analysis (4 points) CEO’s name Type of industry Annual Compensation Company revenue Mr. Lyle A. Berman LACO (Leisure) 683k 53.35 M Mr. James W. P. Reid-Anderson SIX (Leisure) 2.78M 1.15B Mr. Matthew A. Ouimet MGM (Leisure) 2.47M 1.14B Mr. Arnold W. Donald CCL (Leisure) 1.92 M 15.82B Mr. Bradley D. Tilden ALK (Airline) 1.30M 5.27B Mr. Gary C. Kelly LUV(Airline) 1.77M 18.40B Mr. David Barger JBLU (Airline) 1.03 M 5.74 B Require: a) Draw a regression plot of the X and Y values b) Calculate the least squares regression equation and explain the equation. Explain the functions of the intercept and the slope. From the co-efficient table, a = 1.697 and b = 0.442. Therefore, lease squares regression equation is: Y = 1.697 + 0.442 X The b value of 0.442 means that for each increase in the total revenue there is an increase of 0.442 in the annual salary of the C.E.O. The (a) value of 0.442 is the point where the equation crosses the Y-axis. c) Calculate the correlation coefficient (r) and the coefficient of determination (r2), and explain what they measure. r =4.877*10-3 r2 = 0.2379*10-4 The coefficient of correlation r is 0.004877, which shows a weak positive correlation between the total revenue and C.E.O’s annual salary. If total revenue increases the annual salary of the C.E.O’s also increases slightly. The Coefficient of determination r2 is 0.2379*10-4, which means 0.0024% of the variation of the C.E.O’s salary is accounted for by the total revenue. d) Test the hypothesis that the two variables, CEO salary and firm performance are independent of each other in the population at 5% significant level. H0:  = 0 (The correlation in the population is zero) H1:   0 (The correlation in the population is different from zero). Significant level  = .05 Reject H0 if p value <  From the table the p-value is 0.974 H0 is not rejected because p-value (0.974) is greater than 0.05 and therefore there is strong evidence to show that the true population correlation for the population is zero. 4. Exercise.com (7 points) The U.S. Senate passed S. 1023, the "Travel Promotion Act of 2009" (TPA) in September, 2009. TPA calls for the establishment of the Corporation for Travel Promotion as an independent nonprofit corporation to promote leisure, business and scholarly visits to the U.S. In October, the U.S. House of Representatives passed the Travel Promotion Act (H.R. 1035), sending this bill back to the Senate for one last vote. The U.S. Senate finally passed this Bill (78 to 10) on February 25, 2010 and President Obama signed the Travel Promotion Act of 2009 into law on March 4, 2010. This Act calls for the creation of the Corporation for Travel Promotion (now Brand USA) which will allocate financial resources to promote the U.S. as an international destination. The promotion is funded through a matching program featuring up to $100 million in private sector contributions and a $10 fee on foreign travelers who do not pay $131 for a visa to enter the United States. The fee will be collected once every two years in conjunction with the Department of Homeland Security’s Electronic System for Travel Authorization. No money is provided by U.S. taxpayers. It is estimated that international promotion will generate 1.6 million addition international visitors to the U.S. and create $1.6 billion in visitor spending annually. Japan is targeted as one of the major countries for aggressive promotion by the Tourism Industries Office in the Department of Commerce and Brand USA (the newly created public and private partnership responsible for marketing USA implemented by the Travel Promotion Act). As a tourism market analyst specialized in Japan inbound travel to the U.S., you are very interested in studying the movement of currency exchange rates between U.S. dollar and Japanese yen and its impact on Japanese travel to the U.S. So you want to research the impact, if any, of currency exchange rate fluctuation on Japanese inbound arrivals to the U.S. To perform this study, you need to obtain data from two sources. Year Visitors Exch. Rate 1985 1,496,202 201.05 1986 1,681,071 160.1 1987 2,128,481 122 1988 2,542,140 125.9 1989 3,080,396 143.4 1990 3,231,495 135.05 1991 3,319,934 125.12 1992 3,652,828 124.7 1993 3,542,546 111.72 1994 3,804,551 99.7 1995 4,598,354 103.35 1996 5182555 116.1 1997 5367578 130.15 1998 4885369 113.6 1999 4826077 102.13 2000 5061377 114.39 2001 4082661 131.11 2002 3627264 118.51 2003 3169682 107.05 2004 3748000 103.05 2005 3,884,000 117.84 2006 3673000 119.01 2007 3531000 112.25 2008 3250000 90.36 2009 2918000 92.23 2010 3386000 81.54 2011 3250000 77.4 2012 3698000 85.88 Require: a) Draw a regression plot of the X and Y values b) Calculate the least squares regression equation and explain the equation. From the co-efficient table, a = 5444427.790 and b = - 15874.529 Therefore, lease squares regression equation is: Y = 5444427.790 - 15874.529 X The b value of - 15874.529 means that for each decrease in the exchange rate there is increase in the total number of visitors from Japan by 15875 c) Calculate the correlation coefficient (r) and the coefficient of determination (r2), and explain what they measure. r = -0.4099 r2 = 0.168 The coefficient of correlation r is 0.004877, which shows a moderate negative correlation between the exchange rates and the number of Japanese visitors’. It therefore means that if the exchange rate decreases the number of Japanese visitors’ increases moderately. The Coefficient of determination r2 is 0.168 which means 16.8 % of the variation of the number of visitors is accounted for by the exchange rate. d) Write a brief report to the Director of Tourism Industries Office to explain if foreign exchange rate between $ and ¥ is an important factor in influencing Japanese travel to the U.S. in the last 28 years. H0:  = 0 (The correlation in the population is zero) H1:   0 (The correlation in the population is different from zero). Significant level  = .05 Reject H0 if p value <  From the table the p-value is 0.03 H0 is rejected because p-value (0.03) is less than 95% confidence level and therefore there is strong evidence to show that the true population correlation for the population is not zero. Conclusion: Therefore, a decrease of exchange rates is an important factor in influencing Japanese travel to the US. Read More