Refer to the Baseball 2018 data, which report information on the 30 Major League Baseball teams for the 2018 season. Let the number of games won be the dependent variable and the following variables be independent variables: team batting average, team earned run average (ERA), number of home runs, and whether the team plays in the American or the National League.
2.8 3 Team Arizona Diamondbacks Atlanta Braves Baltimore Orioles Boston Red Sox Chicago Cubs Chicago White Sox Cincinnati Reds Cleveland Indians Colorado Rockies Detroit Tigers Houston Astros Kansas City Royals Los Angeles Angels Los Angeles Dodgers Miami Marlins Milwaukee Brewers Minnesota Twins New York Mets New York Yankees Oakland Athletics Philadelphia Phillies Pittsburgh Pirates San Diego Padres San Francisco Giants Seattle Mariners St. Louis Cardinals Tampa Bay Rays Texas Rangers Toronto Blue Jays Washington Nationals League National National American American National American National American National American American American American National National National American National American American National National National American National National American American American National Team Salary ($ mil) HR 143.32 130.6 127.63 227.4 194.26 71.84 100.31 142.8 143.97 130.96 163.52 129.94 173.78 199.58 91.82 108.98 115.51 150.19 179.6 80.32 104.3 91.03 101.34 205.67 160.99 163.78 68.81 140.63 150.95 181.38 Year Stadiun Attendance Net Worth BA Wins ERA Opened mil $ bil 250 0.287 100 3.45 1998 2.242695 1.21 175 0.257 90 3.75 2017 2.555781 1.625 188 0.239 47 5.18 1992 1.564192 1.2 208 0.268 108 3.75 1912 2.895575 167 0.258 95 3.65 1914 3.181089 2.9 182 0.241 62 4.84 1991 1.608817 1.5 172 0.254 67 4.63 2003 1.629356 1.01 216 0.259 91 3.77 1994 1.926701 1.045 210 0.256 91 4.33 1995 3.01588 1.1 135 0.241 64 4.58 2000 1.85697 1.225 205 0.255 103 3.11 2000 2.980549 1.65 155 0.245 58 4.94 1973 1.665107 1.015 214 0.242 80 4.15 1966 3.020216 1.8 235 0.25 92 3.38 1962 3.8575 128 0.237 63 4.76 2012 0.811104 1 218 0.252 96 3.73 2001 2.850875 1.03 166 0.25 4.5 2010 1.959197 1.15 170 0.234 77 4.07 2009 2.224995 2.1 267 0.249 100 3.78 2009 3.482855 227 0.252 97 3.81 1966 1.573616 1.02 186 0.234 80 4.14 2004 2.158124 1.7 157 0.254 82 4 2001 1.465316 1.26 162 0.235 66 4.4 2004 2.168536 1.27 176 0.254 89 4.13 2000 2.299489 2.85 133 0.239 73 3.95 1999 3.156185 1.45 205 0.249 88 3.85 2006 3.403587 1.9 150 0.258 90 3.74 1990 1.154973 0.9 194 0.24 67 4.92 1994 2.107107 1.6 217 0.244 73 4.85 1989 2.325281 1.35 191 0.254 82 4.04 2008 2.529604 1.675 78 4 Refer to the Baseball 2018 data, which report information on the 30 Major League Baseball teams for the 2018 season. Let the number of games won be the dependent variable and the following variables be independent variables: team batting average, team earned run average (ERA), number of home runs, and whether the team plays in the American or the National League. picture Click here for the Excel Data File a-1. Develop a correlation matrix. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.) Wins ERA BA HR Wins ERA BA HR 1 a-2. Which independent variables have strong or weak correlations with the dependent variable? There is a correlation between "Wins" and the independent variable "ERA". a-3. Do you see any problems with multicollinearity? O Yes O No a-4. Are you surprised that the correlation coefficient for ERA is negative? O Yes O No b-1. Use a statistical software package to determine the multiple regression equation. Write out the regression equation. (Round your answers to 4 decimal places.) Wins = ERA + BA + HR. b-2. What is the value of R. (Round your answer to 2 decimal places.) R2 % b-3. Is the number of wins affected by whether the team plays in the National or the American League? O Yes O No Conduct a global test on the set of independent variables. Interpret. C-1. State the decision rule at 0.05 significance level. (Round your answer to 2 decimal places.) Reject Ho if F> c-2. Compute the value of the test statistic at 0.05 significance level. (Round your answer to 4 decimal places.) The F statistic is C-3. What is your decision regarding Ho at 0.05 significance level? Decision: C-4. Interpret the result at 0.05 significance level. We can conclude that of the variables has a significant relationship to winning. d-1. State the null and alternate hypotheses to test the significance of each of the independent variables. O O Ho: B;= 0, H1. Bi+0. Ho: B;= 0, H1: B;= 0. Ho: B;#0, H1 B;+0. Ho Bis 0, H1: B;> 0. O d-2. Compute the critical value for a 5% significance level. (Round your answers to 3 decimal places.) Critical value d-3. What is your decision regarding Ho at 5% significance level? Decision: e-1. Develop a histogram of the residuals from the final regression equation. Choose the correct histogram. Histogram of the residuals i Histogram of the residuals 2 Histogram of the residuals 3 Histogram Histogram Histogram 12 12 12 10 10 10 8 Frequency Frequency 6 Frequency 4 2 0 0 0 1 upto 5 5 upto 9 -12 upto - -7 upto -2 -2 upto 3 3 upto 8 8 upto 13 -11 upto - -7 upto -3 -3 upto 1 7 -12 upto - -7 upto -2 -2 upto 3 3 upto 8 8 upto 13 7 Bin Bin Bin O Histogram of the residuals 1 Histogram of the residuals 2 Histogram of the residuals 3 e-2. Is it reasonable to conclude that the normality assumption has been met? O Yes O No f-1. Plot the residuals against the fitted values from the final regression equation with the residuals on the vertical axis and the fitted values on the horizontal axis. Which plot is correct? Residuals vs Fits 1 Residuals Vs. Predicted Wins Residuals vs Fits 2 Residuals Vs. Predicted Wins Residuals vs Fits 3 Residuals Vs. Predicted Wins 10 10 10 8 8 8 . 6 6 6 4 4 4 2 2 2 0 0 0 0 20 40 60 100 120 0 20 40 60 100 120 0 20 40 60 80 100 120 -2 -2 -2 -4 -4 . . -6 -8 -8 -8 -10 -10 -10 -12 -12 -12 Residuals vs Fits 1 O Residuals vs Fits 2 O Residuals vs Fits 3 f-2. What regression assumption is supported? The assumption supported is 2.8 3 Team Arizona Diamondbacks Atlanta Braves Baltimore Orioles Boston Red Sox Chicago Cubs Chicago White Sox Cincinnati Reds Cleveland Indians Colorado Rockies Detroit Tigers Houston Astros Kansas City Royals Los Angeles Angels Los Angeles Dodgers Miami Marlins Milwaukee Brewers Minnesota Twins New York Mets New York Yankees Oakland Athletics Philadelphia Phillies Pittsburgh Pirates San Diego Padres San Francisco Giants Seattle Mariners St. Louis Cardinals Tampa Bay Rays Texas Rangers Toronto Blue Jays Washington Nationals League National National American American National American National American National American American American American National National National American National American American National National National American National National American American American National Team Salary ($ mil) HR 143.32 130.6 127.63 227.4 194.26 71.84 100.31 142.8 143.97 130.96 163.52 129.94 173.78 199.58 91.82 108.98 115.51 150.19 179.6 80.32 104.3 91.03 101.34 205.67 160.99 163.78 68.81 140.63 150.95 181.38 Year Stadiun Attendance Net Worth BA Wins ERA Opened mil $ bil 250 0.287 100 3.45 1998 2.242695 1.21 175 0.257 90 3.75 2017 2.555781 1.625 188 0.239 47 5.18 1992 1.564192 1.2 208 0.268 108 3.75 1912 2.895575 167 0.258 95 3.65 1914 3.181089 2.9 182 0.241 62 4.84 1991 1.608817 1.5 172 0.254 67 4.63 2003 1.629356 1.01 216 0.259 91 3.77 1994 1.926701 1.045 210 0.256 91 4.33 1995 3.01588 1.1 135 0.241 64 4.58 2000 1.85697 1.225 205 0.255 103 3.11 2000 2.980549 1.65 155 0.245 58 4.94 1973 1.665107 1.015 214 0.242 80 4.15 1966 3.020216 1.8 235 0.25 92 3.38 1962 3.8575 128 0.237 63 4.76 2012 0.811104 1 218 0.252 96 3.73 2001 2.850875 1.03 166 0.25 4.5 2010 1.959197 1.15 170 0.234 77 4.07 2009 2.224995 2.1 267 0.249 100 3.78 2009 3.482855 227 0.252 97 3.81 1966 1.573616 1.02 186 0.234 80 4.14 2004 2.158124 1.7 157 0.254 82 4 2001 1.465316 1.26 162 0.235 66 4.4 2004 2.168536 1.27 176 0.254 89 4.13 2000 2.299489 2.85 133 0.239 73 3.95 1999 3.156185 1.45 205 0.249 88 3.85 2006 3.403587 1.9 150 0.258 90 3.74 1990 1.154973 0.9 194 0.24 67 4.92 1994 2.107107 1.6 217 0.244 73 4.85 1989 2.325281 1.35 191 0.254 82 4.04 2008 2.529604 1.675 78 4 Refer to the Baseball 2018 data, which report information on the 30 Major League Baseball teams for the 2018 season. Let the number of games won be the dependent variable and the following variables be independent variables: team batting average, team earned run average (ERA), number of home runs, and whether the team plays in the American or the National League. picture Click here for the Excel Data File a-1. Develop a correlation matrix. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.) Wins ERA BA HR Wins ERA BA HR 1 a-2. Which independent variables have strong or weak correlations with the dependent variable? There is a correlation between "Wins" and the independent variable "ERA". a-3. Do you see any problems with multicollinearity? O Yes O No a-4. Are you surprised that the correlation coefficient for ERA is negative? O Yes O No b-1. Use a statistical software package to determine the multiple regression equation. Write out the regression equation. (Round your answers to 4 decimal places.) Wins = ERA + BA + HR. b-2. What is the value of R. (Round your answer to 2 decimal places.) R2 % b-3. Is the number of wins affected by whether the team plays in the National or the American League? O Yes O No Conduct a global test on the set of independent variables. Interpret. C-1. State the decision rule at 0.05 significance level. (Round your answer to 2 decimal places.) Reject Ho if F> c-2. Compute the value of the test statistic at 0.05 significance level. (Round your answer to 4 decimal places.) The F statistic is C-3. What is your decision regarding Ho at 0.05 significance level? Decision: C-4. Interpret the result at 0.05 significance level. We can conclude that of the variables has a significant relationship to winning. d-1. State the null and alternate hypotheses to test the significance of each of the independent variables. O O Ho: B;= 0, H1. Bi+0. Ho: B;= 0, H1: B;= 0. Ho: B;#0, H1 B;+0. Ho Bis 0, H1: B;> 0. O d-2. Compute the critical value for a 5% significance level. (Round your answers to 3 decimal places.) Critical value d-3. What is your decision regarding Ho at 5% significance level? Decision: e-1. Develop a histogram of the residuals from the final regression equation. Choose the correct histogram. Histogram of the residuals i Histogram of the residuals 2 Histogram of the residuals 3 Histogram Histogram Histogram 12 12 12 10 10 10 8 Frequency Frequency 6 Frequency 4 2 0 0 0 1 upto 5 5 upto 9 -12 upto - -7 upto -2 -2 upto 3 3 upto 8 8 upto 13 -11 upto - -7 upto -3 -3 upto 1 7 -12 upto - -7 upto -2 -2 upto 3 3 upto 8 8 upto 13 7 Bin Bin Bin O Histogram of the residuals 1 Histogram of the residuals 2 Histogram of the residuals 3 e-2. Is it reasonable to conclude that the normality assumption has been met? O Yes O No f-1. Plot the residuals against the fitted values from the final regression equation with the residuals on the vertical axis and the fitted values on the horizontal axis. Which plot is correct? Residuals vs Fits 1 Residuals Vs. Predicted Wins Residuals vs Fits 2 Residuals Vs. Predicted Wins Residuals vs Fits 3 Residuals Vs. Predicted Wins 10 10 10 8 8 8 . 6 6 6 4 4 4 2 2 2 0 0 0 0 20 40 60 100 120 0 20 40 60 100 120 0 20 40 60 80 100 120 -2 -2 -2 -4 -4 . . -6 -8 -8 -8 -10 -10 -10 -12 -12 -12 Residuals vs Fits 1 O Residuals vs Fits 2 O Residuals vs Fits 3 f-2. What regression assumption is supported? The assumption supported is
