The relationship between the number of games won by an NHL team (x)and the average attendance at their home games (y)is analyzed.The mean number of games won was 70 with a standard deviation of 16.The mean attendance was 6993 with a standard deviation of 1400.The correlation between the games won and attendance was 0.47.
A) $\hat{\text { attendance } }$ = 4114 + 41.125 wins
B) $\hat{\text { attendance } }$ = 2360 + 66.1 wins
C) $\hat{\text { attendance } }$ = 6990 + 0.00537 wins
D) $\hat{\text { attendance } }$ = 868 + 87.5 wins
E) $\hat{\text { attendance } }$ = -2890 + 141 wins

Question

Quizplus · Accepted Answer

The correct regression line equation can be found using the formula for the slope ($b$) of the regression line: $b = r(\frac{s_y}{s_x})$, where $r$ is the correlation coefficient, $s_y$ is the standard deviation of y, and $s_x$ is the standard deviation of x. Here, $b = 0.47 \times \frac{1400}{16} = 41.125$. The intercept ($a$) can be calculated using the formula $a = \bar{y} - b\bar{x}$, where $\bar{y}$ is the mean of y and $\bar{x}$ is the mean of x. Thus, $a = 6993 - 41.125 \times 70 = 4114$. Therefore, the correct equation is $\hat{\text { attendance } }$ = 4114 + 41.125 wins.

The Relationship Between the Number of Games Won by an NHL