When using the $\mathrm{CORREL}$ function in spreadsheet software, what does the function calculate between two variables?

• A. The mean of the two variables $\frac{x+y}{2}$
• B. The slope of the regression line between two variables $y=\mathrm{mx}+b$
• C. The Pearson correlation coefficient, which measures the linear relationship between two variables $r=\frac{\sum (x-\mu )(y-\nu )}{\sqrt{\sum (x-\mu )2^{}}\sqrt{\sum (y-\nu )2^{}}}$
• D. The standard deviation of the differences between two variables $\sqrt{\frac{\sum (x-y)2^{}}{n}}$

Answer: (C)

Verified step by step guidance

1. Understand that the CORREL function in spreadsheet software is designed to measure the strength and direction of a linear relationship between two variables.
2. Recall that the Pearson correlation coefficient, denoted as \(r\), quantifies how closely two variables move together linearly, ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation).
3. Recognize that the CORREL function does not calculate the mean of the variables, the slope of a regression line, or the standard deviation of differences, but specifically computes the Pearson correlation coefficient.
4. The formula for the Pearson correlation coefficient between variables \(X\) and \(Y\) is given by: \[r = \frac{\sum (X_i - \bar{X})(Y_i - \bar{Y})}{\sqrt{\sum (X_i - \bar{X})^2 \sum (Y_i - \bar{Y})^2}}\] where \(\bar{X}\) and \(\bar{Y}\) are the means of \(X\) and \(Y\) respectively.
5. Therefore, when you use the CORREL function, it calculates this \(r\) value, providing a measure of the linear association between the two input variables.