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

Question 24

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 OPWIN%? A) equal variance B) linearity C) normality of errors 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 OPWIN%? A) equal variance B) linearity C) normality of errors 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 OPWIN%? A) equal variance B) linearity C) normality of errors 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 OPWIN%? A) equal variance B) linearity C) normality of errors 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 OPWIN%?


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

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