**Examining the Correlation Between Lemon Imports and Crash Fatality Rates**The table below provides annual data from various years, presenting the weights (in metric tons) of imported lemons and the car crash fatality rates per 100,000 population. The primary goal of this analysis is to construct a scatterplot, calculate the linear correlation coefficient $ r $, and determine the P-value at the significance level $ \alpha = 0.05 $. The objective is to assess if there is sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates. We will also explore if the results suggest a causal relationship between imported lemons and car fatalities.| **Lemon Imports (metric tons)** | 229 | 265 | 358 | 481 | 534 ||---------------------------------|-----|-----|-----|-----|-----|| **Crash Fatality Rate** | 15.8| 15.7| 15.4| 15.3| 14.8|### Steps for Analysis1. **Scatterplot Construction**: - Plot the data points on a graph with lemon imports on the x-axis and crash fatality rates on the y-axis to visually inspect the relationship between the two variables.2. **Calculation of Linear Correlation Coefficient $ r $**: - Use the formula for the linear correlation coefficient to quantify the strength and direction of the linear relationship.3. **Hypothesis Testing**: - Formulate null and alternative hypotheses: - $ H_0 $: There is no linear correlation between lemon imports and crash fatality rates ($ \rho = 0 $). - $ H_1 $: There is a linear correlation between lemon imports and crash fatality rates ($ \rho \neq 0 $). - Calculate the P-value to test the significance of $ r $ at $ \alpha = 0.05 $.### Interpreting Results- **Scatterplot Inspection**: - Look for a pattern or trend in the scatterplot. A downward trend would indicate a negative correlation, while an upward trend would suggest a positive correlation.- **Value of $ r $**: - The coefficient $ r $ will range between -1 and 1. A value close to 1 or -1 indicates a strong linear relationship, while a value near 0 suggests a weak or no linear relationship.- **P-value

A correlation coefficient gives the association between two variables. If the correlation…

Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities? 229 265 15.7 358 534 Lemon Imports Crash Fatality Rate 481 15.8 15.4 15.3 14.8

Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities? 229 265 15.7 358 534 Lemon Imports Crash Fatality Rate 481 15.8 15.4 15.3 14.8

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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Concept explainers

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.

Question

**Examining the Correlation Between Lemon Imports and Crash Fatality Rates**

The table below provides annual data from various years, presenting the weights (in metric tons) of imported lemons and the car crash fatality rates per 100,000 population. The primary goal of this analysis is to construct a scatterplot, calculate the linear correlation coefficient $ r $, and determine the P-value at the significance level $ \alpha = 0.05 $. The objective is to assess if there is sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates. We will also explore if the results suggest a causal relationship between imported lemons and car fatalities.

| **Lemon Imports (metric tons)** | 229 | 265 | 358 | 481 | 534 |
|---------------------------------|-----|-----|-----|-----|-----|
| **Crash Fatality Rate** | 15.8| 15.7| 15.4| 15.3| 14.8|

### Steps for Analysis

1. **Scatterplot Construction**:
- Plot the data points on a graph with lemon imports on the x-axis and crash fatality rates on the y-axis to visually inspect the relationship between the two variables.

2. **Calculation of Linear Correlation Coefficient $ r $**:
- Use the formula for the linear correlation coefficient to quantify the strength and direction of the linear relationship.

3. **Hypothesis Testing**:
- Formulate null and alternative hypotheses:
- $ H_0 $: There is no linear correlation between lemon imports and crash fatality rates ($ \rho = 0 $).
- $ H_1 $: There is a linear correlation between lemon imports and crash fatality rates ($ \rho \neq 0 $).
- Calculate the P-value to test the significance of $ r $ at $ \alpha = 0.05 $.

### Interpreting Results

- **Scatterplot Inspection**:
- Look for a pattern or trend in the scatterplot. A downward trend would indicate a negative correlation, while an upward trend would suggest a positive correlation.

- **Value of $ r $**:
- The coefficient $ r $ will range between -1 and 1. A value close to 1 or -1 indicates a strong linear relationship, while a value near 0 suggests a weak or no linear relationship.

- **P-value

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