The correct answer is C. The covariance between the variables.
Karl Pearson’s coefficient of correlation is a measure of the linear correlation between two variables. It is denoted by $\rho$ and ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.
The covariance between two variables is a measure of how much they vary together. It is calculated by taking the average of the product of the deviations of the two variables from their means.
The square root of the product of the regression coefficients is the standard deviation of the residuals. The residuals are the differences between the observed values of the dependent variable and the predicted values of the dependent variable.
The product of the standard deviations is not a measure of correlation. It is simply the product of the two standard deviations.
Therefore, the correct answer is C. The covariance between the variables.