Here is a bivariate data set. y 69 73.4 69.1 64.9 67.9 69.3 81.3 65.1 66.1 71.1 65.5 70.3 51.9 85.9 35 70.8 53.2 66.6 Find the correlation coefficient and report it accurate to three decimal places. r = 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
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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### Bivariate Data Analysis

#### Here is a bivariate data set:

| x   | y    |
|-----|------|
| 69  | 73.4 |
| 69  | 64.9 |
| 67.9| 69.3 |
| 81.3| 65.1 |
| 66.1| 71.1 |
| 66.1| 71.1 |
| 65.5| 70.3 |
| 51.9| 85.9 |
| 35  | 70.8 |
| 53.2| 66.6 |

#### Tasks:
1. **Find the correlation coefficient and report it accurate to three decimal places.**
   
   $$ r = \_\_\_\_\_ $$

2. **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.**
   
   $$ R^2 = \_\_\_\_% $$

### Instructions
- Calculate the correlation coefficient, which measures the strength and direction of the linear relationship between the two variables x and y.
- Use the \( R^2 \) value, also known as the coefficient of determination, to indicate the proportion of the variance in the dependent variable (y) that is predictable from the independent variable (x).

### Note:
This information helps in understanding the degree of association between the two variables and the effectiveness of the variable x in predicting the variable y.
Transcribed Image Text:### Bivariate Data Analysis #### Here is a bivariate data set: | x | y | |-----|------| | 69 | 73.4 | | 69 | 64.9 | | 67.9| 69.3 | | 81.3| 65.1 | | 66.1| 71.1 | | 66.1| 71.1 | | 65.5| 70.3 | | 51.9| 85.9 | | 35 | 70.8 | | 53.2| 66.6 | #### Tasks: 1. **Find the correlation coefficient and report it accurate to three decimal places.** $$ r = \_\_\_\_\_ $$ 2. **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.** $$ R^2 = \_\_\_\_% $$ ### Instructions - Calculate the correlation coefficient, which measures the strength and direction of the linear relationship between the two variables x and y. - Use the \( R^2 \) value, also known as the coefficient of determination, to indicate the proportion of the variance in the dependent variable (y) that is predictable from the independent variable (x). ### Note: This information helps in understanding the degree of association between the two variables and the effectiveness of the variable x in predicting the variable y.
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