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.
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.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter3: Straight Lines And Linear Functions
Section3.CR: Chapter Review Exercises
Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...
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Transcribed Image Text:Problem Set: Chapter 14 Correlation and Regression
To calculate the slope, first calculate SP and SSx:
SP =
V and SS =
(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 (Y) for each of the dolphins,
and then calculate the residuals.
Number of Treats
Number of Attempts
Residual
Predicted Y (Y)
Dolphin
Diana
2
5
Frederick
4
4
Fatima
1
7
Marlin
3
4
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.
10
9
Regression Line
8
Transcribed Image Text:K
CENGAGE MINDTAP
Problem Set: Chapter 14 Correlation and Regression
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.
Dolphin Number of Treats
Number of Attempts
Diana
2
Frederick
4
4
Fatima
1
7
Marlin
3
4
You can use the preceding sample data to obtain the regression line, where Ŷ is the predicted value of Y:
Y = bx + a
One formula for the slope of the regression line is as follows:
b = SP₁
To calculate the slope, first calculate SP and SSx:
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