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

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

Lainelle Albeza · Accepted Answer

Final Answer : A, Explanation :   The correct regression line equation can be found using the formula for the slope (  b b b  ) of the regression line:   b = r ( s y s x ) b = r(\frac{s_y}{s_x}) b = r ( s x ​ s y ​ ​ )  , where   r r r   is the correlation coefficient,   s y s_y s y ​   is the standard deviation of y, and   s x s_x s x ​   is the standard deviation of x. Here,   b = 0.47 × 1400 16 = 41.125 b = 0.47 	imes \frac{1400}{16} = 41.125 b = 0.47 × 16 1400 ​ = 41.125  . The intercept (  a a a  ) can be calculated using the formula   a = y ˉ − b x ˉ a = \bar{y} - b\bar{x} a = y ˉ ​ − b x ˉ  , where   y ˉ \bar{y} y ˉ ​   is the mean of y and   x ˉ \bar{x} x ˉ   is the mean of x. Thus,   a = 6993 − 41.125 × 70 = 4114 a = 6993 - 41.125 	imes 70 = 4114 a = 6993 − 41.125 × 70 = 4114  . Therefore, the correct equation is    attendance  ^ \hat{	ext { attendance } }  attendance  ^   = 4114 + 41.125 wins.

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