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.

Dolphin	Number of Treats	Number of Attempts
Diana	4	5
Frederick	2	8
Fatima	1	8
Marlin	3	7

You can use the preceding sample data to obtain the regression line, where is the predicted value of Y:

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bX+abX+a

One formula for the slope of the regression line is as follows:

bb

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SPSSxSPSSx

To calculate the slope, first calculate SP and SSxx:

SP = , and SSxx= .

(Hint: For SP use the computational formula and for SSxxuse the definitional formula.)

The slope of the regression line is , and the Y intercept of the regression line is .

The difference between Y and for a particular sample point (observation) is called a residual. Calculate the predicted Y () for each of the dolphins, and then calculate the residuals.

Dolphin	Number of Treats	Number of Attempts	Predicted Y ()	Residual
Diana	4	5
Frederick	2	8
Fatima	1	8
Marlin	3	7

On the following scatter diagram of the blue sample points (circle symbol), use the orange points (square symbol) to plot the regression line. Make sure that the orange line spans the entire graph (from left to right). A line segment will automatically connect the points.

Regression Line012345109876543210NUMBER OF ATTEMPTSNUMBER OF TREATS

Use the regression line to estimate the number of trials it would take to learn these tricks if a dolphin received five treats per trick. for X = 5 would be .

The head dolphin trainer is pressuring you to teach the dolphins many new tricks quickly. She has asked you to use the least-squares regression line to predict how fast the dolphins can learn tricks if you were to give them 8 treats. Which of the following is the most appropriate response?

Since the regression line predicts that the dolphins will need a negative number of attempts, you can assume the dolphins need 0 attempts if given 8 treats.

The regression line predicts that the dolphins will need 5.5 attempts to learn a trick if they are given 8 treats.

The regression line predicts that the dolphins will need 1.5 attempts to learn a trick if they are given 8 treats.

The regression line was estimated using 1 to 4 treats and should not be used to predict what would happen if the dolphins were given 8 treats.