The data below was collected from manufacturer advertisements of their vehicles horsepower and highway gas mileage (mpg.). Use this data to answer the following questions.| x | 158 | 250 | 340 | 350 | 390 | 190 | 220 ||----|-----|-----|-----|-----|-----|-----|-----|| y | 33 | 28 | 15 | 17 | 11 | 35 | 42 |1. **Find the p-value to determine if there is a linear correlation between horsepower and highway gas mileage (mpg). Record the p-value below. Round to four decimal places.** - p-value = [________]2. **Is there a linear correlation between horsepower and highway gas mileage (mpg)?** - [Yes/No]3. **If there is a linear correlation, write the correlation coefficient below. Otherwise, leave it blank. Round your final answer to four decimal places.** - r = [________]4. **If there is a linear correlation, write the regression equation below. Otherwise, leave it blank. Round all numbers to four decimal places.** - ŷ = [________]5. **Using the data shown above, predict the highway gas mileage (mpg) for a car that has a horsepower of 225. Round your final answer to two decimal places.** - [________]6. **If there is a linear correlation, what percentage of variation in highway gas mileage (mpg) can be explained by horsepower? If there is not a linear correlation, leave it blank. Round your final answer to two decimal places.** - [________]%**Explanation of the Table:**- The "x" row represents the horsepower values for different vehicles.- The "y" row represents the corresponding highway gas mileage (mpg) for those vehicles. The questions guide the process of determining the correlation and creating a linear regression model if applicable.

Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any specific subpart to be answered then please submit that subpart only or specify the subpart in your message. 1. Hypothesis: The null and alternate hypotheses are below: H0: ρ=0H1: ρ≠0 Step-by-step procedure to find the sample correlation coefficient using Excel: In Excel sheet, enter X in one column and enter Y in one column. In Data, select Data Analysis and choose Correlation. In Input Variable Range, select X and Y. Click Labels. Click Ok.Output obtained using Excel is given below: From the output, the correlation coefficient r is -0.9040. The test statistic is obtained as follows: t=r×n-21-r2=-0.9040×7-21--0.90402=-2.02140.4275=-4.7284 Thus, the test statistic is -4.7284 Degrees of freedom: df=n-2=7-2=5 P value: The test statistic is |–4.7284|=4.7284. The P-value is obtained Excel function “=TDIST(x, degrees of freedom, tails)”. Output obtained using Excel is as follows: From the output, the p value is 0.0052 Thus, the p value is 0.00522. Decision Rule: If p value less than significance value α, then reject null hypothesis. Otherwise fail to reject null hypothesis. Conclusion: The p value is 0.0052 and significance value is 0.05 Here p value less than significance value. Thus, the null hypothesis is rejected. Therefore, there is sufficient evidence to conclude that there is a linear correlation between horsepower and highway gas mileage. 3. Thus, the correlation coefficient r is -0.9040

Math

Statistics

The data below was collected from manufacturer advertisements of their vehicles horsepower and highway gas mileage (mpg.). Use this data to answer the following questions. 390 350 15 17 220 35 42 158 250 340 190 y 33 28 11 1. Find the p-value to determine if there is a linear correlation between horsepower and highway gas mileage (mpg). Record the p-value below. Round to four decimal places. p-value = 2. Is there a linear correlation between horsepower and highway gas mileage (mpg)? 3. If there is a linear correation, write the correlation coefficient below. Otherwise, leave it blank. Round your final answer to four decimal places.

The data below was collected from manufacturer advertisements of their vehicles horsepower and highway gas mileage (mpg.). Use this data to answer the following questions. 390 350 15 17 220 35 42 158 250 340 190 y 33 28 11 1. Find the p-value to determine if there is a linear correlation between horsepower and highway gas mileage (mpg). Record the p-value below. Round to four decimal places. p-value = 2. Is there a linear correlation between horsepower and highway gas mileage (mpg)? 3. If there is a linear correation, write the correlation coefficient below. Otherwise, leave it blank. Round your final answer to four decimal places.

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

The data below was collected from manufacturer advertisements of their vehicles horsepower and highway gas mileage (mpg.). Use this data to answer the following questions.

| x | 158 | 250 | 340 | 350 | 390 | 190 | 220 |
|----|-----|-----|-----|-----|-----|-----|-----|
| y | 33 | 28 | 15 | 17 | 11 | 35 | 42 |

1. **Find the p-value to determine if there is a linear correlation between horsepower and highway gas mileage (mpg). Record the p-value below. Round to four decimal places.**
- p-value = [________]

2. **Is there a linear correlation between horsepower and highway gas mileage (mpg)?**
- [Yes/No]

3. **If there is a linear correlation, write the correlation coefficient below. Otherwise, leave it blank. Round your final answer to four decimal places.**
- r = [________]

4. **If there is a linear correlation, write the regression equation below. Otherwise, leave it blank. Round all numbers to four decimal places.**
- ŷ = [________]

5. **Using the data shown above, predict the highway gas mileage (mpg) for a car that has a horsepower of 225. Round your final answer to two decimal places.**
- [________]

6. **If there is a linear correlation, what percentage of variation in highway gas mileage (mpg) can be explained by horsepower? If there is not a linear correlation, leave it blank. Round your final answer to two decimal places.**
- [________]%

**Explanation of the Table:**
- The "x" row represents the horsepower values for different vehicles.
- The "y" row represents the corresponding highway gas mileage (mpg) for those vehicles.

The questions guide the process of determining the correlation and creating a linear regression model if applicable.

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