The linear correlation coefficient is r= (Round to three decimal places as needed.) Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evider two variables. Choose the correct answer below. A. There is insufficient evidence to support the claim of a nonlinear correlation between the two variable: B. There is insufficient evidence to support the claim of a linear correlation between the two variables. C. There is sufficient evidence to support the claim of a linear correlation between the two variables. O D. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scat A. The scatterplot reveals a distinct pattern that is a straight-line pattern with positive slope. B. The scatterplot reveals a distinct pattern that is a straight-line pattern with negative slope. C. The scatterplot does not reveal a distinct pattern. D. The scatterplot reveals a distinct pattern that is not a straight-line pattern.

The linear correlation coefficient is r= (Round to three decimal places as needed.) Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evider two variables. Choose the correct answer below. A. There is insufficient evidence to support the claim of a nonlinear correlation between the two variable: B. There is insufficient evidence to support the claim of a linear correlation between the two variables. C. There is sufficient evidence to support the claim of a linear correlation between the two variables. O D. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scat A. The scatterplot reveals a distinct pattern that is a straight-line pattern with positive slope. B. The scatterplot reveals a distinct pattern that is a straight-line pattern with negative slope. C. The scatterplot does not reveal a distinct pattern. D. The scatterplot reveals a distinct pattern that is not a straight-line pattern.

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

### Linear Correlation Analysis

#### Data Set
Use the given data set to complete parts (a) through (c) below. (Use α = 0.05.)

| x | 10 | 8 | 13 | 9 | 11 | 14 | 6 | 4 | 12 | 7 | 5 |
|----|----|----|----|----|----|----|----|----|----|----|----|
| y | 9.14 | 8.15 | 8.75 | 8.77 | 9.26 | 8.10 | 6.13 | 3.10 | 9.14 | 7.26 | 4.73 |

#### Graphical Representations
Three scatterplots are shown to visualize potential correlations:
1. **Scatterplot 1**: Displays a dataset with a linear pattern that appears to have a positive correlation.
2. **Scatterplot 2**: Displays a dataset with a linear pattern that appears to have a negative correlation.
3. **Scatterplot 3**: Displays a dataset showing a nonlinear pattern.

#### Analysis
**b. Calculate the Linear Correlation Coefficient**

- Find the linear correlation coefficient, $ r $, using the given data and determine if there is sufficient evidence to support a linear correlation between the variables. (Round to three decimal places as needed.)

**Choose the correct interpretation based on the correlation coefficient:**

- A. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables.
- B. There is insufficient evidence to support the claim of a linear correlation between the two variables.
- C. There is sufficient evidence to support the claim of a linear correlation between the two variables.
- D. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables.

**c. Identify Missing Features Without a Scatterplot**

- Determine the characteristic that might be missed if visual analysis is not performed:
- A. The scatterplot reveals a distinct pattern that is a straight-line pattern with a positive slope.
- B. The scatterplot reveals a distinct pattern that is a straight-line pattern with a negative slope.
- C. The scatterplot does not reveal a distinct pattern.
- D. The scatterplot reveals a distinct pattern that is not a straight-line pattern.

Click to select the answer(s).

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