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 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, there is enough evidence to conclude that PROMOTION makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance.

Question

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 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, there is enough evidence to conclude that PROMOTION makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance.

Quizplus · Accepted Answer

The question states that "there is enough evidence to conclude that PROMOTION makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance." This means that the p-value for PROMOTION is less than 0.05, which indicates that there is a statistically significant relationship between PROMOTION and the dependent variable.

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

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