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15. Computing the regression line and making predictions Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to each, and the average number of attempts necessary for each to learn to perform the tricks. Number of Number of Dolphin Treats Attempts Diana 2 6 Frederick 4 5 Fatima 1 8 Marlin 3 5 You can use the preceding sample data to obtain the regression line, where $\hat{Y}$ is the predicted value of Y: $\hat{Y}$ = bX + a One formula for the slope of the regression line is as follows: b = $\frac{SP}{SS_x}$ To calculate the slope, first calculate SP and $SS_x$: SP = _____, and $SS_x$ = _____. (Hint: For SP use the computational formula and for $SS_x$ use the definitional formula.) The slope of the regression line is _, and the Y intercept of the regression line is _. The difference between Y and $\hat{Y}$ for a particular sample point (observation) is called a residual. Calculate the predicted Y ($\hat{Y}$) for each of the dolphins, and then calculate the residuals.

          15. Computing the regression line and making predictions
Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each
successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to
each, and the average number of attempts necessary for each to learn to perform the tricks.
Number of Number of
Dolphin
Treats
Attempts
Diana
2
6
Frederick
4
5
Fatima
1
8
Marlin
3
5
You can use the preceding sample data to obtain the regression line, where $\hat{Y}$ is the predicted value of Y:
$\hat{Y}$ = bX + a
One formula for the slope of the regression line is as follows:
b = $\frac{SP}{SS_x}$ 
To calculate the slope, first calculate SP and $SS_x$:
SP = _____, and $SS_x$ = _____.
(Hint: For SP use the computational formula and for $SS_x$ use the definitional formula.)
The slope of the regression line is _____, and the Y intercept of the regression line is _____.
The difference between Y and $\hat{Y}$ for a particular sample point (observation) is called a residual. Calculate the
predicted Y ($\hat{Y}$) for each of the dolphins, and then calculate the residuals.

15. Computing the regression line and making predictions
Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each
successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to
each, and the average number of attempts necessary for each to learn to perform the tricks.
Number of Number of
Dolphin
Treats
Attempts
Diana
2
6
Frederick
4
5
Fatima
1
8
Marlin
3
5
You can use the preceding sample data to obtain the regression line, where Ŷ is the predicted value of Y:
Ŷ = bX + a
One formula for the slope of the regression line is as follows:
b = (SP)/(SSx)
To calculate the slope, first calculate SP and SSx:
SP = , and SSx = .
(Hint: For SP use the computational formula and for SSx use the definitional formula.)
The slope of the regression line is , and the Y intercept of the regression line is .
The difference between Y and Ŷ for a particular sample point (observation) is called a residual. Calculate the
predicted Y (Ŷ) for each of the dolphins, and then calculate the residuals.

Added by Jessica P.

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