Pearson correlation • A correlation is a statistical method used to measure and describe the relationship between two variables. • A relationship exists when changes in one variable tend to be accompanied by consistent and predictable changes in the other variable. • The magnitude of the Pearson correlation ranges from 0 (indicating no linear relationship between X and ) to 1.00 (indicating a perfect straight-line relationship between X and Y). • The correlation can be either positive or negative depending on the direction of the relationship. Formulas for Pearson correlation: ; where r – is a correlation coefficient calculated for the sample; Coefficient of det ermination (effect size forr) R =r²; where r is a coefficient correlation calculated for the sample You have two variables X and Y. Calculate the Pearson correlation r-test and the coefficient of determination R2. 4. x = 4 y = 6 SS, = 40; SS, = 54 2 1. 8 10 E(Ti – x) (yi – y) = 40 6 9. N=5 4 6. Paragrani
Pearson correlation • A correlation is a statistical method used to measure and describe the relationship between two variables. • A relationship exists when changes in one variable tend to be accompanied by consistent and predictable changes in the other variable. • The magnitude of the Pearson correlation ranges from 0 (indicating no linear relationship between X and ) to 1.00 (indicating a perfect straight-line relationship between X and Y). • The correlation can be either positive or negative depending on the direction of the relationship. Formulas for Pearson correlation: ; where r – is a correlation coefficient calculated for the sample; Coefficient of det ermination (effect size forr) R =r²; where r is a coefficient correlation calculated for the sample You have two variables X and Y. Calculate the Pearson correlation r-test and the coefficient of determination R2. 4. x = 4 y = 6 SS, = 40; SS, = 54 2 1. 8 10 E(Ti – x) (yi – y) = 40 6 9. N=5 4 6. Paragrani
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2. you have two variables x and y. calculate the pearson correlation r test and the coefficient of determination R^2
![**Pearson Correlation**
A correlation is a statistical method used to measure and describe the relationship between two variables. A relationship exists when changes in one variable tend to be accompanied by consistent and predictable changes in the other variable.
The magnitude of the Pearson correlation ranges from 0 (indicating no linear relationship between X and Y) to 1.00 (indicating a perfect straight-line relationship between X and Y). The correlation can be either positive or negative depending on the direction of the relationship.
**Formulas for Pearson Correlation:**
\[ r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}} = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{SS_x \cdot SS_y}} \]
Where \( r \) is a correlation coefficient calculated for the sample; Coefficient of determination (effect size for \( r \)) \( R^2 = r^2 \), where \( r \) is a coefficient correlation calculated for the sample.
You have two variables, X and Y. Calculate the Pearson correlation r-test and the coefficient of determination \( R^2 \).
| X | Y |
|----|----|
| 0 | 4 |
| 2 | 1 |
| 8 | 10 |
| 9 | 6 |
| 6 | 9 |
- \( \bar{x} = 5 \), \( \bar{y} = 6 \)
- \( SS_x = 40 \), \( SS_y = 54 \)
- \( \sum (x_i - \bar{x})(y_i - \bar{y}) = 40 \)
- \( N = 5 \)
(Note: The table provides the data values for variables X and Y and also includes other statistical calculations necessary for computing Pearson's correlation and the coefficient of determination.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2c28418-a35a-446b-a108-7c356c7aba50%2F7d535c92-f307-422e-80c7-46973c7bf19e%2Fgbeilrc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Pearson Correlation**
A correlation is a statistical method used to measure and describe the relationship between two variables. A relationship exists when changes in one variable tend to be accompanied by consistent and predictable changes in the other variable.
The magnitude of the Pearson correlation ranges from 0 (indicating no linear relationship between X and Y) to 1.00 (indicating a perfect straight-line relationship between X and Y). The correlation can be either positive or negative depending on the direction of the relationship.
**Formulas for Pearson Correlation:**
\[ r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}} = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{SS_x \cdot SS_y}} \]
Where \( r \) is a correlation coefficient calculated for the sample; Coefficient of determination (effect size for \( r \)) \( R^2 = r^2 \), where \( r \) is a coefficient correlation calculated for the sample.
You have two variables, X and Y. Calculate the Pearson correlation r-test and the coefficient of determination \( R^2 \).
| X | Y |
|----|----|
| 0 | 4 |
| 2 | 1 |
| 8 | 10 |
| 9 | 6 |
| 6 | 9 |
- \( \bar{x} = 5 \), \( \bar{y} = 6 \)
- \( SS_x = 40 \), \( SS_y = 54 \)
- \( \sum (x_i - \bar{x})(y_i - \bar{y}) = 40 \)
- \( N = 5 \)
(Note: The table provides the data values for variables X and Y and also includes other statistical calculations necessary for computing Pearson's correlation and the coefficient of determination.)
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