Is the number of games won by a major league baseball team in a season related to the team's batting average? Data from 14 teams were collected and the summary statistics yield: $\sum y=1,134, \sum x=3.642, \sum{y} 2=93,110, \quad \sum{x}^{2}=.948622, \text { and } \sum x y=295.54$
Find the least squares prediction equation for predicting the number of games won, y, using a straight-line relationship with the team's batting average, x.

Question

Is the number of games won by a major league baseball team in a season related to the team's batting average? Data from 14 teams were collected and the summary statistics yield: $\sum y=1,134, \sum x=3.642, \sum{y} 2=93,110, \quad \sum{x}^{2}=.948622, \text { and } \sum x y=295.54$
 Find the least squares prediction equation for predicting the number of games won, y, using a straight-line relationship with the team's batting average, x.

Quizplus · Accepted Answer

The Answer is

S S_{x x}=\sum{x^{2}}-\frac{\left(\sum{x}\right)^{2}}{n}=.948622-\frac{(3.642)^{2}}{14}=.00118171

S S _ { x y } = \sum { x y } - \frac { \sum { x } \sum { y } } { n } = 295.54 - \frac { ( 3.642 ) ( 1,134 ) } { 14 } = .538

\bar { y } = \frac { \sum { y } } { n } = \frac { 1,134 } { 14 } = 81

\bar { x } = \frac { \sum { x } } { n } = \frac { 3.642 } { 14 } = .26014

\hat { \beta } 1 = \frac { S S _ { x y } } { S S _ { x x } } = \frac { .538 } { .00118171 } = 455.27

\hat { \beta } _ { 0 } = \bar { y } - \hat { \beta } 1 \bar { x } = 81 - 455.27 ( .26014 ) = - 37.434

The least squares equation is

\hat { y } = - 37.434 + 455.27 x

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Is the Number of Games Won by a Major League ∑y=1,134,∑x=3.642,∑y2=93,110,∑x2=.948622, and ∑xy=295.54\sum y=1,134, \sum x=3.642, \sum{y} 2=93,110, \quad \sum{x}^{2}=.948622, \text { and } \sum x y=295.54∑y=1,134,∑x=3.642,∑y2=93,110,∑x2=.948622, and ∑xy=295.54

Is the Number of Games Won by a Major League $\sum y=1,134, \sum x=3.642, \sum{y} 2=93,110, \quad \sum{x}^{2}=.948622, \text { and } \sum x y=295.54$