**Title: Analysis of Lemon Imports and Crash Fatality Rates**A researcher collects data on both lemon imports (x) and the crash fatality rate (y) in the USA. The seven observations are randomly selected cities across the country.### Graph Description:The scatter plot titled "Crash Fatality Rate" displays data points representing the relationship between lemon imports and crash fatality rates in various cities.### Summary Output:- **Multiple R:** 0.939894457- **R Square:** 0.88340159- **Adjusted R Square:** 0.860810197- **Standard Error:** 0.125395887- **Observations:** 7### ANOVA Table:| Source | df | SS | MS | F | Significance F ||--------------|----|-----------|----------|---------|-----------------|| Regression | 1 | 0.595665072 | 0.595665 | 37.88223 | 0.001646686 || Residual | 5 | 0.07826042 | 0.015724 | | || Total | 6 | 0.674285714 | | | |### Coefficients Table:| | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% ||----------------|---------------|----------------|---------|----------|-------------|-------------|| Intercept | 16.517343501 | 0.1831502 | 90.18528 | 3.18E-09 | 16.04663289 | 16.9882371 || Lemon Imports | -0.002918808 | 0.000471112 | -6.15485| 0.001647 | -0.00413683 | -0.00169935 |### Questions:**1. What is the regression equation?**- $ \hat{y} = 16.517 - 0.003x $**2. The best description of the correlation is to describe it as:**- Strong negative correlation. **Interpret the slope of the line.**- For a 1 unit increase in the crash fatality rate, lemon imports will, on average, increase by 16.517 units.- For a 1 unit increase in lemon imports, the crash fatality rate will, on average, increase by 0.003 units.- For a 1 unit increase in lemon imports, the crash fatality rate will, on average, increase by 16.517 units.- For a 1 unit increase in the crash fatality rate, lemon imports will, on average, increase by 0.003 units.- None of the above**Give a practical interpretation of the coefficient of determination.**- 88.34% of the sample variation in crash fatality rates can be explained by the least-squares regression line.- 88.34% of the differences in crash fatality rates are caused by differences in lemon imports.- We can predict the crash fatality rate correctly 88.34% of the time using lemon imports in a least-squares regression line.- 93.99% of the differences in crash fatality rates are caused by differences in lemon imports.- We can predict the crash fatality rate correctly 93.99% of the time using lemon imports in a least-squares regression line.- 93.99% of the sample variation in crash fatality rates can be explained by the least-squares regression line.**Is it reasonable to use the regression equation to make a prediction for lemon imports of 200? Justify your answer.**- No, $ r^2 $ does not indicate that there is a reasonable amount of correlation.- No, this prediction is far outside the scope of available data.- Yes, all of the criteria are met.- No, the regression line does not fit the points reasonably well.**What can we say about the relationship between lemon imports and crash fatality rate?**- There is no relationship between lemon imports and crash fatality rate.- While lemon imports and crash fatality rate and strongly related, this relationship is likely due to some third variable that affects them both.- Because of the strong relationship, lemon imports are a leading cause of crash fatality rate.

What is the regression equation? Oy = 16.517 – 0.003z Oŷ = 16.517 – 0.003z y = 16.517z – 0.003 Oŷ = 16.517z – 0.003 The best description of the correlation is to describe it as strong linear correlation. O strong negative correlation. O strong positive correlation. O None of the above

What is the regression equation? Oy = 16.517 – 0.003z Oŷ = 16.517 – 0.003z y = 16.517z – 0.003 Oŷ = 16.517z – 0.003 The best description of the correlation is to describe it as strong linear correlation. O strong negative correlation. O strong positive correlation. O None of the above

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

**Title: Analysis of Lemon Imports and Crash Fatality Rates**

A researcher collects data on both lemon imports (x) and the crash fatality rate (y) in the USA. The seven observations are randomly selected cities across the country.

### Graph Description:
The scatter plot titled "Crash Fatality Rate" displays data points representing the relationship between lemon imports and crash fatality rates in various cities.

### Summary Output:
- **Multiple R:** 0.939894457
- **R Square:** 0.88340159
- **Adjusted R Square:** 0.860810197
- **Standard Error:** 0.125395887
- **Observations:** 7

### ANOVA Table:
| Source | df | SS | MS | F | Significance F |
|--------------|----|-----------|----------|---------|-----------------|
| Regression | 1 | 0.595665072 | 0.595665 | 37.88223 | 0.001646686 |
| Residual | 5 | 0.07826042 | 0.015724 | | |
| Total | 6 | 0.674285714 | | | |

### Coefficients Table:
| | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% |
|----------------|---------------|----------------|---------|----------|-------------|-------------|
| Intercept | 16.517343501 | 0.1831502 | 90.18528 | 3.18E-09 | 16.04663289 | 16.9882371 |
| Lemon Imports | -0.002918808 | 0.000471112 | -6.15485| 0.001647 | -0.00413683 | -0.00169935 |

### Questions:

**1. What is the regression equation?**
- $ \hat{y} = 16.517 - 0.003x $

**2. The best description of the correlation is to describe it as:**
- Strong negative correlation.

**Interpret the slope of the line.**

- For a 1 unit increase in the crash fatality rate, lemon imports will, on average, increase by 16.517 units.
- For a 1 unit increase in lemon imports, the crash fatality rate will, on average, increase by 0.003 units.
- For a 1 unit increase in lemon imports, the crash fatality rate will, on average, increase by 16.517 units.
- For a 1 unit increase in the crash fatality rate, lemon imports will, on average, increase by 0.003 units.
- None of the above

**Give a practical interpretation of the coefficient of determination.**

- 88.34% of the sample variation in crash fatality rates can be explained by the least-squares regression line.
- 88.34% of the differences in crash fatality rates are caused by differences in lemon imports.
- We can predict the crash fatality rate correctly 88.34% of the time using lemon imports in a least-squares regression line.
- 93.99% of the differences in crash fatality rates are caused by differences in lemon imports.
- We can predict the crash fatality rate correctly 93.99% of the time using lemon imports in a least-squares regression line.
- 93.99% of the sample variation in crash fatality rates can be explained by the least-squares regression line.

**Is it reasonable to use the regression equation to make a prediction for lemon imports of 200? Justify your answer.**

- No, $ r^2 $ does not indicate that there is a reasonable amount of correlation.
- No, this prediction is far outside the scope of available data.
- Yes, all of the criteria are met.
- No, the regression line does not fit the points reasonably well.

**What can we say about the relationship between lemon imports and crash fatality rate?**

- There is no relationship between lemon imports and crash fatality rate.
- While lemon imports and crash fatality rate and strongly related, this relationship is likely due to some third variable that affects them both.
- Because of the strong relationship, lemon imports are a leading cause of crash fatality rate.

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