Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed lemon/crash data, where lemon imports are in metric tons and the fatality rates are per 100,000 people, find the best predicted crash fatality rate for a year in which there are 500 metric tons of lemon imports. Is the prediction worthwhile? Lemon Imports Crash Fatality Rate 16.1 226 265 539 O 365 15.7 476 15.5 16 15,1
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.
![## Regression Analysis of Lemon Imports and Crash Fatality Rates
### Problem Statement
The task is to find the regression equation, letting the first variable be the predictor (x) variable. Given the listed lemon/crash data, where lemon imports are in metric tons and the fatality rates are per 100,000 people, we need to determine the best-predicted crash fatality rate for a year in which there are 500 metric tons of lemon imports. Finally, we need to evaluate if the prediction is worthwhile.
### Data
| Lemon Imports (Metric Tons) | Crash Fatality Rate (per 100,000 people) |
|-----------------------------|------------------------------------------|
| 226 | 16.1 |
| 265 | 16.0 |
| 365 | 15.7 |
| 476 | 15.5 |
| 539 | 15.1 |
### Explanation
The table presents two sets of data:
1. **Lemon Imports**: This variable shows the amount of lemon imports in metric tons.
2. **Crash Fatality Rate**: This variable represents the number of crash fatalities per 100,000 people.
The objective is to use this data to develop a regression equation that can predict the crash fatality rate based on lemon imports. In this context, lemon imports will serve as the independent variable (x), and the crash fatality rate will be the dependent variable (y).
### Steps to Follow
1. **Determine the Regression Equation**:
- Calculate the means of both variables.
- Compute the slope (b) and the y-intercept (a) of the regression line using the least squares method.
- Formulate the regression equation of the form \( y = a + bx \).
2. **Prediction for 500 Metric Tons**:
- Use the regression equation to predict the crash fatality rate when lemon imports are 500 metric tons.
3. **Evaluation of the Prediction**:
- Assess the correlation and causation between lemon imports and crash fatality rates.
- Consider residuals and potential errors.
Developing a clear understanding of these steps will enable us to make informed predictions and recognize the potential limitations of such correlations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5534fc6-b142-4cfc-8ed1-53ce39208227%2F4e470b5e-31db-435d-bdeb-f1faf09fedab%2Fwtx456f_processed.png&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Step by step
Solved in 3 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)