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TABLE 15-9
Many Factors Determine the Attendance at Major League

Question 33

Multiple Choice

TABLE 15-9
Many factors determine the attendance at Major League Baseball games. These factors can include when the game is played, the weather, the opponent, whether or not the team is having a good season, and whether or not a marketing promotion is held. Data from 80 games of the Kansas City Royals for the following variables are collected.
ATTENDANCE = Paid attendance for the game
TEMP = High temperature for the day
WIN% = Team's winning percentage at the time of the game
OPWIN% = Opponent team's winning percentage at the time of the game WEEKEND - 1 if game played on Friday, Saturday or Sunday; 0 otherwise PROMOTION - 1 = if a promotion was held; 0 = if no promotion was held
The regression results using attendance as the dependent variable and the remaining five variables as the independent variables are presented below.
 Regression Statistics  Multiple R 0.5487 R Square 0.3011 Adjusted R Square 0.2538 Standard Error 6442.4456 Observations 80\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.5487 \\\text { R Square } & 0.3011 \\\text { Adjusted R Square } & 0.2538 \\\text { Standard Error } & 6442.4456 \\\text { Observations } & 80 \\\hline\end{array}\end{array}

 ANOVA df SS  MS  F  Significance F Regression 51322911703.0671264582340.61346.37470.0001 Residual 743071377751.120441505104.7449 Total 794394289454.1875\begin{array}{l}\text { ANOVA }\\\begin{array} { l c c c c c } \hline & \mathrm { df } & \text { SS } & \text { MS } & \text { F } & \text { Significance } \mathrm { F } \\\hline \text { Regression } & 5 & 1322911703.0671 & 264582340.6134 & 6.3747 & 0.0001 \\\text { Residual } & 74 & 3071377751.1204 & 41505104.7449 & & \\\text { Total } & 79 & 4394289454.1875 & & & \\\hline\end{array}\end{array}

Coefficients Standard Error t Statp-valueIntercept−3862.48086180.9452−0.62490.5340 Temp 51.703162.94390.82140.4140 Win% 21.108516.23381.30030.1975 OpWin% 11.34536.46171.75580.0833 Weekend 367.53772786.26390.13190.8954 Promotion 6927.88202784.34422.48820.0151\begin{array}{lrrrr}\hline&\text{Coefficients}&\text{ Standard Error}&\text{ t Stat}&\text{p-value}\\\hline\text{Intercept}&-3862.4808&6180.9452&-0.6249&0.5340\\\text { Temp } & 51.7031 & 62.9439 & 0.8214 & 0.4140 \\\text { Win\% } & 21.1085 & 16.2338 & 1.3003 & 0.1975 \\\text { OpWin\% } & 11.3453 & 6.4617 & 1.7558 & 0.0833 \\\text { Weekend } & 367.5377 & 2786.2639 & 0.1319 & 0.8954 \\\text { Promotion } & 6927.8820 & 2784.3442 & 2.4882 & 0.0151 \\\hline\end{array}


TABLE 15-9 Many factors determine the attendance at Major League Baseball games. These factors can include when the game is played, the weather, the opponent, whether or not the team is having a good season, and whether or not a marketing promotion is held. Data from 80 games of the Kansas City Royals for the following variables are collected. ATTENDANCE = Paid attendance for the game TEMP = High temperature for the day WIN% = Team's winning percentage at the time of the game OPWIN% = Opponent team's winning percentage at the time of the game WEEKEND - 1 if game played on Friday, Saturday or Sunday; 0 otherwise PROMOTION - 1 = if a promotion was held; 0 = if no promotion was held The regression results using attendance as the dependent variable and the remaining five variables as the independent variables are presented below. \begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l r } \hline \text { Multiple R } & 0.5487 \\ \text { R Square } & 0.3011 \\ \text { Adjusted R Square } & 0.2538 \\ \text { Standard Error } & 6442.4456 \\ \text { Observations } & 80 \\ \hline \end{array} \end{array} \begin{array}{l} \text { ANOVA }\\ \begin{array} { l c c c c c } \hline & \mathrm { df } & \text { SS } & \text { MS } & \text { F } & \text { Significance } \mathrm { F } \\ \hline \text { Regression } & 5 & 1322911703.0671 & 264582340.6134 & 6.3747 & 0.0001 \\ \text { Residual } & 74 & 3071377751.1204 & 41505104.7449 & & \\ \text { Total } & 79 & 4394289454.1875 & & & \\ \hline \end{array} \end{array} \begin{array}{lrrrr} \hline&\text{Coefficients}&\text{ Standard Error}&\text{ t Stat}&\text{p-value}\\ \hline\text{Intercept}&-3862.4808&6180.9452&-0.6249&0.5340\\ \text { Temp } & 51.7031 & 62.9439 & 0.8214 & 0.4140 \\ \text { Win\% } & 21.1085 & 16.2338 & 1.3003 & 0.1975 \\ \text { OpWin\% } & 11.3453 & 6.4617 & 1.7558 & 0.0833 \\ \text { Weekend } & 367.5377 & 2786.2639 & 0.1319 & 0.8954 \\ \text { Promotion } & 6927.8820 & 2784.3442 & 2.4882 & 0.0151 \\ \hline \end{array} The coefficient of multiple determination ( R <sup>2</sup> <sub>j</sub> ) of each of the 5 predictors with all the other remaining predictors are, respectively, 0.2675, 0.3101, 0.1038, 0.7325, and 0.7308 -Referring to Table 15-9, which of the following assumptions is most likely violated based on the residual plot for TEMP? A) normality of errors B) equal variance C) linearity D) none of the above

TABLE 15-9 Many factors determine the attendance at Major League Baseball games. These factors can include when the game is played, the weather, the opponent, whether or not the team is having a good season, and whether or not a marketing promotion is held. Data from 80 games of the Kansas City Royals for the following variables are collected. ATTENDANCE = Paid attendance for the game TEMP = High temperature for the day WIN% = Team's winning percentage at the time of the game OPWIN% = Opponent team's winning percentage at the time of the game WEEKEND - 1 if game played on Friday, Saturday or Sunday; 0 otherwise PROMOTION - 1 = if a promotion was held; 0 = if no promotion was held The regression results using attendance as the dependent variable and the remaining five variables as the independent variables are presented below. \begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l r } \hline \text { Multiple R } & 0.5487 \\ \text { R Square } & 0.3011 \\ \text { Adjusted R Square } & 0.2538 \\ \text { Standard Error } & 6442.4456 \\ \text { Observations } & 80 \\ \hline \end{array} \end{array} \begin{array}{l} \text { ANOVA }\\ \begin{array} { l c c c c c } \hline & \mathrm { df } & \text { SS } & \text { MS } & \text { F } & \text { Significance } \mathrm { F } \\ \hline \text { Regression } & 5 & 1322911703.0671 & 264582340.6134 & 6.3747 & 0.0001 \\ \text { Residual } & 74 & 3071377751.1204 & 41505104.7449 & & \\ \text { Total } & 79 & 4394289454.1875 & & & \\ \hline \end{array} \end{array} \begin{array}{lrrrr} \hline&\text{Coefficients}&\text{ Standard Error}&\text{ t Stat}&\text{p-value}\\ \hline\text{Intercept}&-3862.4808&6180.9452&-0.6249&0.5340\\ \text { Temp } & 51.7031 & 62.9439 & 0.8214 & 0.4140 \\ \text { Win\% } & 21.1085 & 16.2338 & 1.3003 & 0.1975 \\ \text { OpWin\% } & 11.3453 & 6.4617 & 1.7558 & 0.0833 \\ \text { Weekend } & 367.5377 & 2786.2639 & 0.1319 & 0.8954 \\ \text { Promotion } & 6927.8820 & 2784.3442 & 2.4882 & 0.0151 \\ \hline \end{array} The coefficient of multiple determination ( R <sup>2</sup> <sub>j</sub> ) of each of the 5 predictors with all the other remaining predictors are, respectively, 0.2675, 0.3101, 0.1038, 0.7325, and 0.7308 -Referring to Table 15-9, which of the following assumptions is most likely violated based on the residual plot for TEMP? A) normality of errors B) equal variance C) linearity D) none of the above TABLE 15-9 Many factors determine the attendance at Major League Baseball games. These factors can include when the game is played, the weather, the opponent, whether or not the team is having a good season, and whether or not a marketing promotion is held. Data from 80 games of the Kansas City Royals for the following variables are collected. ATTENDANCE = Paid attendance for the game TEMP = High temperature for the day WIN% = Team's winning percentage at the time of the game OPWIN% = Opponent team's winning percentage at the time of the game WEEKEND - 1 if game played on Friday, Saturday or Sunday; 0 otherwise PROMOTION - 1 = if a promotion was held; 0 = if no promotion was held The regression results using attendance as the dependent variable and the remaining five variables as the independent variables are presented below. \begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l r } \hline \text { Multiple R } & 0.5487 \\ \text { R Square } & 0.3011 \\ \text { Adjusted R Square } & 0.2538 \\ \text { Standard Error } & 6442.4456 \\ \text { Observations } & 80 \\ \hline \end{array} \end{array} \begin{array}{l} \text { ANOVA }\\ \begin{array} { l c c c c c } \hline & \mathrm { df } & \text { SS } & \text { MS } & \text { F } & \text { Significance } \mathrm { F } \\ \hline \text { Regression } & 5 & 1322911703.0671 & 264582340.6134 & 6.3747 & 0.0001 \\ \text { Residual } & 74 & 3071377751.1204 & 41505104.7449 & & \\ \text { Total } & 79 & 4394289454.1875 & & & \\ \hline \end{array} \end{array} \begin{array}{lrrrr} \hline&\text{Coefficients}&\text{ Standard Error}&\text{ t Stat}&\text{p-value}\\ \hline\text{Intercept}&-3862.4808&6180.9452&-0.6249&0.5340\\ \text { Temp } & 51.7031 & 62.9439 & 0.8214 & 0.4140 \\ \text { Win\% } & 21.1085 & 16.2338 & 1.3003 & 0.1975 \\ \text { OpWin\% } & 11.3453 & 6.4617 & 1.7558 & 0.0833 \\ \text { Weekend } & 367.5377 & 2786.2639 & 0.1319 & 0.8954 \\ \text { Promotion } & 6927.8820 & 2784.3442 & 2.4882 & 0.0151 \\ \hline \end{array} The coefficient of multiple determination ( R <sup>2</sup> <sub>j</sub> ) of each of the 5 predictors with all the other remaining predictors are, respectively, 0.2675, 0.3101, 0.1038, 0.7325, and 0.7308 -Referring to Table 15-9, which of the following assumptions is most likely violated based on the residual plot for TEMP? A) normality of errors B) equal variance C) linearity D) none of the above

TABLE 15-9 Many factors determine the attendance at Major League Baseball games. These factors can include when the game is played, the weather, the opponent, whether or not the team is having a good season, and whether or not a marketing promotion is held. Data from 80 games of the Kansas City Royals for the following variables are collected. ATTENDANCE = Paid attendance for the game TEMP = High temperature for the day WIN% = Team's winning percentage at the time of the game OPWIN% = Opponent team's winning percentage at the time of the game WEEKEND - 1 if game played on Friday, Saturday or Sunday; 0 otherwise PROMOTION - 1 = if a promotion was held; 0 = if no promotion was held The regression results using attendance as the dependent variable and the remaining five variables as the independent variables are presented below. \begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l r } \hline \text { Multiple R } & 0.5487 \\ \text { R Square } & 0.3011 \\ \text { Adjusted R Square } & 0.2538 \\ \text { Standard Error } & 6442.4456 \\ \text { Observations } & 80 \\ \hline \end{array} \end{array} \begin{array}{l} \text { ANOVA }\\ \begin{array} { l c c c c c } \hline & \mathrm { df } & \text { SS } & \text { MS } & \text { F } & \text { Significance } \mathrm { F } \\ \hline \text { Regression } & 5 & 1322911703.0671 & 264582340.6134 & 6.3747 & 0.0001 \\ \text { Residual } & 74 & 3071377751.1204 & 41505104.7449 & & \\ \text { Total } & 79 & 4394289454.1875 & & & \\ \hline \end{array} \end{array} \begin{array}{lrrrr} \hline&\text{Coefficients}&\text{ Standard Error}&\text{ t Stat}&\text{p-value}\\ \hline\text{Intercept}&-3862.4808&6180.9452&-0.6249&0.5340\\ \text { Temp } & 51.7031 & 62.9439 & 0.8214 & 0.4140 \\ \text { Win\% } & 21.1085 & 16.2338 & 1.3003 & 0.1975 \\ \text { OpWin\% } & 11.3453 & 6.4617 & 1.7558 & 0.0833 \\ \text { Weekend } & 367.5377 & 2786.2639 & 0.1319 & 0.8954 \\ \text { Promotion } & 6927.8820 & 2784.3442 & 2.4882 & 0.0151 \\ \hline \end{array} The coefficient of multiple determination ( R <sup>2</sup> <sub>j</sub> ) of each of the 5 predictors with all the other remaining predictors are, respectively, 0.2675, 0.3101, 0.1038, 0.7325, and 0.7308 -Referring to Table 15-9, which of the following assumptions is most likely violated based on the residual plot for TEMP? A) normality of errors B) equal variance C) linearity D) none of the above

The coefficient of multiple determination ( R 2 j ) of each of the 5 predictors with all the other remaining predictors are,
respectively, 0.2675, 0.3101, 0.1038, 0.7325, and 0.7308
-Referring to Table 15-9, which of the following assumptions is most likely violated based on the residual plot for TEMP?


A) normality of errors
B) equal variance
C) linearity
D) none of the above

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