This is a Multiple Regression Analysis Project – There Are 3 X variables and 1 Y variable: X1: # of Players Who Were “All-Stars” During A Given Year On The Detriot Pistons X2: Points Per Game (In Regular Season) Each Season X3: (Dummy Variable) Whether The Detroit Pistons Made The Playoffs The Previous Season (Dummy Variable Because It Is Either A Yes Or No Statistic.) Y: Regular Season Winning Percentage – The goal is to analyze the regression model, prepare a write-up to explain the idea and the results. THE GOAL: Create a Multiple Regression Model to help a Company, Government, or in our case, a Sports Organization understand somthing more about their data. As Seen In The Table Below: The DETROIT PISTONS (A National Basketball Association Team/Organization) STATISTICS FOR THE GIVEN VARIABLES FOR EACH SEASON FROM 1984 – 2016: Year All Stars (X1) Points Per Game (X2) Playoffs Previous Season (X3) Win Percentage (Y) 2016 1 102 0 0.537 2015 0 98.5 0 0.39 2014 0 101 0 0.345 2013 0 94.9 0 0.345 2012 0 73.1 0 0.379 2011 0 97 0 0.366 2010 0 94 1 0.329 2009 1 94.2 1 0.476 2008 3 97.5 1 0.72 2007 2 96 1 0.646 2006 4 96.8 1 0.78 2005 1 93.3 1 0.659 2004 1 90.1 1 0.659 2003 1 91.4 1 0.61 2002 0 94.3 0 0.61 2001 1 95.6 1 0.39 2000 2 103.5 1 0.512 1999 0 55.1 0 0.58 1998 1 94.2 1 0.451 1997 2 94.2 1 0.659 1996 1 95.4 0 0.561 1995 2 98.2 0 0.341 1994 0 96.9 0 0.244 1993 2 100.6 1 0.488 1992 3 98.9 1 0.585 1991 2 100.1 1 0.61 1990 2 104.3 1 0.72 1989 1 106.6 1 0.768 1988 1 109.2 1 0.659 1987 2 111.2 1 0.634 1986 1 114.2 1 0.561 1985 2 116 1 0.561 With The Given Table Filled With Statistics of The Last 30-32 Seasons Of The Detroit Pistons, Answer The Following: 1) Include the three tables from the Excel regression including adjusted R2, R2, standard error for the model, ANOVA results, as well as the variable names, estimated intercept, estimated coefficients, t-test statistics, p-values, and 95% confidence intervals. (No more than four decimal places should be displayed.)
2) Write out the regression model using the variable names. Y = 0.5633 + 0.0602 * X1 – 0.0017 * X2 + 0.1035 * X3 Win Percentage = 0.5633 + 0.0602 * All Stars – 0.0017 * Points Per Game + 0.1035 * Playoffs Previous Season 3) Create a scatter diagram for each independent variable (except the dummy variable) and the dependent variable. In other words, plot X1 with Y on a scatter diagram. On a second graph, plot X2 with Y. If you have more independent variables, also plot them individually with Y. Write about what you observe in these scatter plots. Both scatter plots show that the points are randomly distributed. This may indicate a low degree of correlation between X1 and Y, and X2 and Y. 4) Comment on the strength of the model using adjusted R2 and F-test (use the p-value approach) to assess the fit. Show how you would calculate R2 and F if they weren’t provided in the tables.
