Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with 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 4 1 3 Frederick Fatima Marlin You can use the preceding sample data to obtain the regression line, where Ŷ is the predicted va of Y: Y = bX + a One formula for the slope of the regression line is as follows: b = SP = To calculate the slope, first calculate SP and SSx: 8587 and SSx = Y. (Hint: For SP use the computational formula and for SSx use the definitional formula.) The slope of the regression line is I Frederick Fatima Marlin 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. Dolphin Number of Treats Number of Attempts Predicted Y (Ŷ) Residual Diana 2 8 4 5 1 8 3 7 On the following scatter diagram of the blue sample points (circle symbol), use the orange point (square symbol) to plot the regression line. Make sure that the orange line spans the entire grap (from left to right). A line segment will automatically connect the points.
Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with 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 4 1 3 Frederick Fatima Marlin You can use the preceding sample data to obtain the regression line, where Ŷ is the predicted va of Y: Y = bX + a One formula for the slope of the regression line is as follows: b = SP = To calculate the slope, first calculate SP and SSx: 8587 and SSx = Y. (Hint: For SP use the computational formula and for SSx use the definitional formula.) The slope of the regression line is I Frederick Fatima Marlin 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. Dolphin Number of Treats Number of Attempts Predicted Y (Ŷ) Residual Diana 2 8 4 5 1 8 3 7 On the following scatter diagram of the blue sample points (circle symbol), use the orange point (square symbol) to plot the regression line. Make sure that the orange line spans the entire grap (from left to right). A line segment will automatically connect the points.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:### Understanding Regression Line for Dolphin Training
#### Graph Analysis
The graph displays the relationship between the number of treats given to dolphins (X-axis) and the number of attempts required for the dolphins to learn tricks (Y-axis). The plotted points represent data collected from trials with 1 to 4 treats. A regression line is shown to provide a predictive model for the data.
#### Regression Line Estimation
To predict the number of trials needed for a dolphin to learn tricks if given five treats:
- Use the regression line equation to estimate \( \hat{Y} \) for \( X = 5 \).
- Input the estimated value in the provided blank space.
#### Response to Head Trainer's Request
When asked to predict learning with 8 treats, choose the appropriate response based on regression analysis considerations:
- The regression line should only be used within the data range (1 to 4 treats). Making predictions for 8 treats requires caution as it may not accurately reflect reality.
- **Correct response:**
- 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.
This ensures a clear understanding of data limitations and appropriate use of the regression model.
![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 | 8 |
| Frederick | 4 | 5 |
| Fatima | 1 | 8 |
| Marlin | 3 | 7 |
You can use the preceding sample data to obtain the regression line, where Ŷ 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 SSₓ:
\[ SP = \underline{\hspace{3cm}}, \text{ and } SS_x = \underline{\hspace{3cm}}. \]
*(Hint: For SP use the computational formula and for SSₓ use the definitional formula.)*
The slope of the regression line is \(\underline{\hspace{1cm}}\), and the Y intercept of the regression line is \(\underline{\hspace{1cm}}\).
The difference between Y and Ŷ for a particular sample point (observation) is called a residual. Calculate the predicted Ŷ for each of the dolphins, and then calculate the residuals.
| Dolphin | Number of Treats | Number of Attempts | Predicted Ŷ | Residual |
|-----------|-----------------|-------------------|-------------|----------|
| Diana | 2 | 8 | | |
| Frederick | 4 | 5 | | |
| Fatima | 1 | 8 | | |
| Marlin | 3 | 7 | | |
**Explanation of Graph:**
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd71a2400-639a-427f-823f-f7a795926fd4%2Fea9e3a74-8aae-41e0-9811-6f5146e03254%2Fyueb61f_processed.png&w=3840&q=75)
Transcribed Image Text: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 | 8 |
| Frederick | 4 | 5 |
| Fatima | 1 | 8 |
| Marlin | 3 | 7 |
You can use the preceding sample data to obtain the regression line, where Ŷ 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 SSₓ:
\[ SP = \underline{\hspace{3cm}}, \text{ and } SS_x = \underline{\hspace{3cm}}. \]
*(Hint: For SP use the computational formula and for SSₓ use the definitional formula.)*
The slope of the regression line is \(\underline{\hspace{1cm}}\), and the Y intercept of the regression line is \(\underline{\hspace{1cm}}\).
The difference between Y and Ŷ for a particular sample point (observation) is called a residual. Calculate the predicted Ŷ for each of the dolphins, and then calculate the residuals.
| Dolphin | Number of Treats | Number of Attempts | Predicted Ŷ | Residual |
|-----------|-----------------|-------------------|-------------|----------|
| Diana | 2 | 8 | | |
| Frederick | 4 | 5 | | |
| Fatima | 1 | 8 | | |
| Marlin | 3 | 7 | | |
**Explanation of Graph:**
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 22 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman