Frequency Domain Variant of Pearson's Sample Correlation Coefficient?

1. What is Pearson's sample correlation coefficient?
2. How do you find the variance of a Pearson correlation?
3. Is the Pearson correlation scale invariant?
4. Can you use any type of variables for Pearson's correlation coefficient?

What is Pearson's sample correlation coefficient?

Revised on December 5, 2022. The Pearson correlation coefficient (r) is the most common way of measuring a linear correlation. It is a number between –1 and 1 that measures the strength and direction of the relationship between two variables. When one variable changes, the other variable changes in the same direction.

How do you find the variance of a Pearson correlation?

The strength of the relationship between X and Y is sometimes expressed by squaring the correlation coefficient and multiplying by 100. The resulting statistic is known as variance explained (or R²). Example: a correlation of 0.5 means 0.5²x100 = 25% of the variance in Y is "explained" or predicted by the X variable.

Is the Pearson correlation scale invariant?

The Pearson correlation coefficient is symmetric: corr(X,Y) = corr(Y,X). A key mathematical property of the Pearson correlation coefficient is that it is invariant (up to a sign) to separate changes in location and scale in the two variables.

Can you use any type of variables for Pearson's correlation coefficient?

Can you use any type of variable for Pearson's correlation coefficient? No, the two variables have to be measured on either an interval or ratio scale.