Here is a bivariate data set. y 52.8 36.9 51.5 34.6 48.4 35.7 22.2 54.6 60.5 17 49 39 66.1 24 56.1 37.6 54.2 48.5 50.2 29.9 61.1 41.1 Find the correlation coefficient and report it accurate to three decimal places. What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. R2 =

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Topic Video
Question
### Bivariate Data Set and Analysis

Here is a bivariate data set:

|   x   |   y   |
|-------|-------|
| 52.8  | 36.9  |
| 51.5  | 34.6  |
| 48.4  | 35.7  |
| 22.2  | 54.6  |
| 60.5  |  17   |
|  49   |  39   |
| 66.1  |  24   |
| 56.1  | 37.6  |
| 54.2  | 48.5  |
| 50.2  | 29.9  |
| 61.1  | 41.1  |

**Instructions:**

1. **Find the Correlation Coefficient**
   - Calculate the correlation coefficient (r) for the given data set and report it accurate to three decimal places.
   - \( r = \_\_\_\_\_ \)

2. **Proportion of Variation Explained**
   - Determine what proportion of the variation in \( y \) can be explained by the variation in the values of \( x \). Report the answer as a percentage accurate to one decimal place.
   - \( R^2 = \_\_\_\_\_ \% \)

### Guidance

- **Correlation Coefficient (r):**
  The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values close to 1 or -1 indicate a strong linear relationship, and values close to 0 indicate a weak linear relationship.
  
- **Proportion of Variation Explained (R²):**
  \( R^2 \) is the coefficient of determination that indicates the proportion of the variance in the dependent variable (\( y \)) that is predictable from the independent variable (\( x \)). It is expressed as a percentage.

Make sure to perform the necessary calculations accurately for precise results.
Transcribed Image Text:### Bivariate Data Set and Analysis Here is a bivariate data set: | x | y | |-------|-------| | 52.8 | 36.9 | | 51.5 | 34.6 | | 48.4 | 35.7 | | 22.2 | 54.6 | | 60.5 | 17 | | 49 | 39 | | 66.1 | 24 | | 56.1 | 37.6 | | 54.2 | 48.5 | | 50.2 | 29.9 | | 61.1 | 41.1 | **Instructions:** 1. **Find the Correlation Coefficient** - Calculate the correlation coefficient (r) for the given data set and report it accurate to three decimal places. - \( r = \_\_\_\_\_ \) 2. **Proportion of Variation Explained** - Determine what proportion of the variation in \( y \) can be explained by the variation in the values of \( x \). Report the answer as a percentage accurate to one decimal place. - \( R^2 = \_\_\_\_\_ \% \) ### Guidance - **Correlation Coefficient (r):** The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values close to 1 or -1 indicate a strong linear relationship, and values close to 0 indicate a weak linear relationship. - **Proportion of Variation Explained (R²):** \( R^2 \) is the coefficient of determination that indicates the proportion of the variance in the dependent variable (\( y \)) that is predictable from the independent variable (\( x \)). It is expressed as a percentage. Make sure to perform the necessary calculations accurately for precise results.
Expert Solution
steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Knowledge Booster
Centre, Spread, and Shape of a Distribution
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman