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 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 = SPSSx 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. Dolphin Number of Treats Number of Attempts Predicted Y (Ŷ) Residual Diana 2 6 Frederick 4 5 Fatima 1 8 Marlin 3 5

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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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	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:

bX + a

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

SPSSx

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.

Dolphin	Number of Treats	Number of Attempts
Diana	2	6
Frederick	4	5
Fatima	1	8
Marlin	3	5

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