What Is The Hypothetical Equation And R Value To This?
The Pearson correlation coefficient is a statistic that measures the linear correlation between two sets of data on the same interval or ratio scale. It is represented by the symbol r and ranges from -1 to +1. The formula for calculating r takes into account the standard deviations and covariance of the two variables. A value of -1 indicates a strong negative correlation, while a +1 indicates a strong positive correlation. To calculate r, the standard deviations and covariance between the two variables must be determined. Finally, the coefficient can be calculated using the given formula.
The hypothetical equation for Pearson's correlation coefficient (r) is as follows:
[ r = \frac{n(\sum{XY}) - (\sum{X})(\sum{Y})}{\sqrt{[n\sum{X^2} - (\sum{X})^2][n\sum{Y^2} - (\sum{Y})^2]}} ]
where:
- n is the number of paired scores
- X and Y are the two variables
- Σ denotes summation
The Pearson correlation coefficient (r) ranges from -1 to +1, where:
- r ≈ 1 indicates a strong positive linear relationship
- r ≈ -1 indicates a strong negative linear relationship
- r ≈ 0 indicates no linear relationship
This hypothetical equation and the resulting r value provide a quantitative measure of the strength and direction of the linear relationship between variables such as cholesterol and blood pressure.
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