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 =

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
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### 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.
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