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 425 metric tons of lemon imports. Is the prediction worthwhile? 226 268 Lemon Imports Crash Fatality Rate 16.1 16 360 15.8 492 15.6 518 O 15.1 Find the equation of the regression line. (Round the constant three decimal places as needed. Round the coefficient to six decimal places as needed.)
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.
![**Understanding Regression Analysis with Lemon Imports and Crash Fatality Rate**
This exercise focuses on finding the regression equation, using the first variable as the predictor (x variable). The data provided gives us lemon imports in metric tons and the crash fatality rates per 100,000 people. Our task is to predict the crash fatality rate for a scenario where 425 metric tons of lemons are imported. We will evaluate the viability of this prediction.
**Data Table:**
- **Lemon Imports (in metric tons):** 226, 268, 360, 492, 518
- **Crash Fatality Rate (per 100,000 people):** 16.1, 16, 15.8, 15.6, 15.1
**Objective:**
1. Determine the equation of the regression line.
2. Predict the crash fatality rate for an import value of 425 metric tons.
3. Assess whether this prediction is worthwhile.
**Equation of the Regression Line:**
The regression line is represented by the formula:
\[
\hat{y} = a + bx
\]
where \( \hat{y} \) is the predicted value, \( a \) is the intercept, \( b \) is the slope of the line, and \( x \) is the independent variable (lemon imports in this case).
- **Instructions for Calculation:**
- Round the constant \( a \) to three decimal places.
- Round the coefficient \( b \) to six decimal places.
**Graph/Diagram Explanation:**
The graph would typically display lemon imports on the x-axis and the crash fatality rate on the y-axis. The regression line will show the relationship between these two variables, indicating whether more lemon imports seem to correlate with changes in the crash fatality rate.
This educational exploration not only helps in understanding the relationship between the selected factors but also provides insight into predictive modeling, which plays a crucial role in statistical and data analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f6319fd-3db3-4131-945e-33c3df9bac4f%2F5d06835c-41d4-49c6-980a-eafbd7207840%2F8ylwj2k_processed.jpeg&w=3840&q=75)
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