Please answer last 2 questions. Questions read: What is the interpretation of the slope? What is the predicted temperature in degrees F when 17 chirps per second is measured? Thanks
Please answer last 2 questions. Questions read: What is the interpretation of the slope? What is the predicted temperature in degrees F when 17 chirps per second is measured? Thanks
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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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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Please answer last 2 questions.
Questions read:
What is the interpretation of the slope?
What is the predicted temperature in degrees F when 17 chirps per second is measured?
Thanks
 to download the spreadsheet for use in this activity.
---
### Educational Content
#### Linear Regression Using Cricket Chirps
According to the Farmer’s Almanac, the frequency of cricket chirps varies with the ambient temperature. By counting the number of chirps and dividing by the time period, the temperature can be predicted using a linear equation. The dataset in the second sheet of the spreadsheet linked above provides 15 observations of the number of cricket chirps per second and the corresponding temperature in degrees Fahrenheit (°F).
##### Linear Regression Equation:
The equation for the least squares regression line is:
\[ \hat{y} = 3.291x + 25.232 \]
##### Definitions:
- **Predictor Variable:** This is the variable used to predict another variable. In this context, it is the **Number of chirps**.
- **Response Variable:** This is the variable that is being predicted. In this context, it is the **Temperature**.
##### Interpretation:
- **Slope:** To understand the slope of the line, select the appropriate interpretation from the dropdown options.
- **Intercept:** To understand the intercept of the line, select the appropriate interpretation from the dropdown options.
Choose the correct interpretation for the slope and intercept:
- **Slope:** Indicates how much the temperature changes for a one-unit increase in the number of chirps.
- **Intercept:** Indicates the temperature when the number of chirps is zero.
---
##### Quick Quiz:
1. **What is the predictor variable?**
- [x] Number of chirps
- [ ] Temperature
2. **What is the response variable?**
- [ ] Number of chirps
- [x] Temperature
3. **What is the interpretation of the slope?**
- [ ] Number of chirps when the temperature is 0 degrees F
- [ ] Rate at which the number of chirps changes as temperature increases
- [x] Rate at which the temperature changes as the number of chirps increases
- [ ] Temperature when the number of chirps is 0
4. **What is the interpretation of the intercept?**
- [ ] Number of chirps when the temperature is 0 degrees F
- [ ] Rate at which the number of chirps changes as temperature increases
- [](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52bd3cfe-3c9b-40ce-8732-3b0b81ba9280%2F78ea18e8-3228-404b-8163-f7f5d905479d%2F8o3t94r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### 2.3.2: Excel: Linear Regression
#### Challenge Activity
##### Instructions:
Click [this link](#) to download the spreadsheet for use in this activity.
---
### Educational Content
#### Linear Regression Using Cricket Chirps
According to the Farmer’s Almanac, the frequency of cricket chirps varies with the ambient temperature. By counting the number of chirps and dividing by the time period, the temperature can be predicted using a linear equation. The dataset in the second sheet of the spreadsheet linked above provides 15 observations of the number of cricket chirps per second and the corresponding temperature in degrees Fahrenheit (°F).
##### Linear Regression Equation:
The equation for the least squares regression line is:
\[ \hat{y} = 3.291x + 25.232 \]
##### Definitions:
- **Predictor Variable:** This is the variable used to predict another variable. In this context, it is the **Number of chirps**.
- **Response Variable:** This is the variable that is being predicted. In this context, it is the **Temperature**.
##### Interpretation:
- **Slope:** To understand the slope of the line, select the appropriate interpretation from the dropdown options.
- **Intercept:** To understand the intercept of the line, select the appropriate interpretation from the dropdown options.
Choose the correct interpretation for the slope and intercept:
- **Slope:** Indicates how much the temperature changes for a one-unit increase in the number of chirps.
- **Intercept:** Indicates the temperature when the number of chirps is zero.
---
##### Quick Quiz:
1. **What is the predictor variable?**
- [x] Number of chirps
- [ ] Temperature
2. **What is the response variable?**
- [ ] Number of chirps
- [x] Temperature
3. **What is the interpretation of the slope?**
- [ ] Number of chirps when the temperature is 0 degrees F
- [ ] Rate at which the number of chirps changes as temperature increases
- [x] Rate at which the temperature changes as the number of chirps increases
- [ ] Temperature when the number of chirps is 0
4. **What is the interpretation of the intercept?**
- [ ] Number of chirps when the temperature is 0 degrees F
- [ ] Rate at which the number of chirps changes as temperature increases
- [
Transcribed Image Text:## Cricket Chirps and Temperature Correlation
### Data Table
This table presents data on cricket chirps (chirps per second) and the corresponding temperature in degrees Fahrenheit (°F).
| Cricket Chirps (chirps/sec) | Temperature (degrees F) |
|-----------------------------|-------------------------|
| 20.0 | 88.6 |
| 16.0 | 71.6 |
| 19.8 | 93.3 |
| 18.4 | 84.3 |
| 17.1 | 80.6 |
| 15.5 | 75.2 |
| 14.7 | 69.7 |
| 17.1 | 82.0 |
| 15.4 | 69.4 |
| 16.2 | 83.3 |
| 15.0 | 79.6 |
| 17.2 | 82.6 |
| 16.0 | 80.6 |
| 17.0 | 83.5 |
| 14.4 | 76.3 |
### Analysis
The right side of the image contains a graph and a short analysis statement. The statement indicates:
- **Field:** Cricket chirps (chirps/sec) and **Field:** Temperature (degrees F) appear highly correlated.
#### Graph Description
The graph is a scatter plot that shows cricket chirps (chirps/sec) on the X-axis and temperature (degrees F) on the Y-axis.
- **X-axis (Horizontal):** Represents the rate of cricket chirps per second, ranging from 0.0 to 25.0 chirps/sec.
- **Y-axis (Vertical):** Represents the temperature in degrees Fahrenheit, ranging from approximately 60.0 to 100.0 °F.
**Observations:**
- The data points are plotted as orange dots.
- There appears to be a positive correlation, suggesting that as the number of cricket chirps per second increases, the temperature also increases.
This correlation implies that cricket chirps can be used as an indicator of temperature changes, typically chirping more frequently at higher temperatures.
For further learning, you can explore the mathematical concept of correlation and how such natural phenomena have been historically used in traditional methods of weather prediction.
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