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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![## Problem Set: Chapter 14 Correlation and Regression
### To calculate the slope, first calculate SP and SSx:
\[ SP = \_\_\_ \]
\[ SS_x = \_\_\_ \]
(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 \( \hat{Y} \) 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.
| Dolphin | Number of Treats | Number of Attempts | Predicted \( Y (\hat{Y}) \) | Residual |
|----------|------------------|--------------------|----------------------------|----------|
| Diana | 2 | 5 | | |
| Frederick| 4 | 4 | | |
| Fatima | 1 | 7 | | |
| Marlin | 3 | 4 | | |
### Graph Explanation
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.
- The x-axis represents Number of Treats.
- The y-axis represents Number of Attempts.
- Blue circles represent individual data points.
- The orange squares should be placed to create the regression line.
There is a visual graph beneath the table that appears blank with axes marked. This graph is intended for plotting the data points and drawing the regression line after calculating the predicted values and residuals.
### Steps:
1. Calculate the slope (b) and intercept (a) using the given data.
2. Use the regression equation \( \hat{Y} = a + bX \) to find predicted values \( \hat{Y} \).
3. Plot the predicted points on the graph with the regression line.
4. Determine the residuals by finding the difference between the actual Y values and the predicted \(\hat{Y}\) values for each dolphin.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2579f974-48a4-4696-a686-9cca22653cdc%2Fa6b1dab7-738c-4cd6-88cd-40a0ab9e17ed%2Fxcyxgxr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem Set: Chapter 14 Correlation and Regression
### To calculate the slope, first calculate SP and SSx:
\[ SP = \_\_\_ \]
\[ SS_x = \_\_\_ \]
(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 \( \hat{Y} \) 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.
| Dolphin | Number of Treats | Number of Attempts | Predicted \( Y (\hat{Y}) \) | Residual |
|----------|------------------|--------------------|----------------------------|----------|
| Diana | 2 | 5 | | |
| Frederick| 4 | 4 | | |
| Fatima | 1 | 7 | | |
| Marlin | 3 | 4 | | |
### Graph Explanation
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.
- The x-axis represents Number of Treats.
- The y-axis represents Number of Attempts.
- Blue circles represent individual data points.
- The orange squares should be placed to create the regression line.
There is a visual graph beneath the table that appears blank with axes marked. This graph is intended for plotting the data points and drawing the regression line after calculating the predicted values and residuals.
### Steps:
1. Calculate the slope (b) and intercept (a) using the given data.
2. Use the regression equation \( \hat{Y} = a + bX \) to find predicted values \( \hat{Y} \).
3. Plot the predicted points on the graph with the regression line.
4. Determine the residuals by finding the difference between the actual Y values and the predicted \(\hat{Y}\) values for each dolphin.
![**CENGAGE | MINDTAP**
## Problem Set: Chapter 14 Correlation and Regression
### 15. Computing the regression line and making predictions
**Problem Description:**
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 | 5 |
| Frederick | 4 | 4 |
| Fatima | 1 | 7 |
| Marlin | 3 | 4 |
**Instructions:**
You can use the preceding sample data to obtain the regression line, where \( \hat{Y} \) is the predicted value of Y:
\[
\hat{Y} = bX + a
\]
**Formulas and Calculations:**
One formula for the slope of the regression line is as follows:
\[
b = \frac{SP}{SS_X}
\]
To calculate the slope (\(b\)), first calculate \(SP\) and \(SS_X\):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2579f974-48a4-4696-a686-9cca22653cdc%2Fa6b1dab7-738c-4cd6-88cd-40a0ab9e17ed%2Fc9eswgl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**CENGAGE | MINDTAP**
## Problem Set: Chapter 14 Correlation and Regression
### 15. Computing the regression line and making predictions
**Problem Description:**
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 | 5 |
| Frederick | 4 | 4 |
| Fatima | 1 | 7 |
| Marlin | 3 | 4 |
**Instructions:**
You can use the preceding sample data to obtain the regression line, where \( \hat{Y} \) is the predicted value of Y:
\[
\hat{Y} = bX + a
\]
**Formulas and Calculations:**
One formula for the slope of the regression line is as follows:
\[
b = \frac{SP}{SS_X}
\]
To calculate the slope (\(b\)), first calculate \(SP\) and \(SS_X\):
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