Which formula represents the slope (m) in the least squares regression line?

The formula that represents the slope (m) in the least squares regression line is derived from the correlation coefficient (r) and the standard deviations of the variables involved. In the correct formula, the slope is given by the product of the correlation coefficient and the ratio of the standard deviation of the y-scores to the standard deviation of the x-scores.

This is significant because it not only takes into account the linear relationship between the two variables (as represented by the correlation coefficient) but also scales this relationship properly by the variability in each set of scores. Essentially, the slope indicates how much the dependent variable (y) will change for a unit change in the independent variable (x), after adjusting for their respective dispersions.

The other formulas do not represent the slope correctly. For example, attempting to calculate the slope as the mean of y divided by the mean of x ignores the relationship and variability in the dataset. Meanwhile, the formula involving y² and x² does not relate to the concept of slope at all, as it fails to incorporate the necessary adjustments for standard deviations and correlation. Thus, the choice that specifies the slope calculation in relation to both the correlation and the standard deviations accurately reflects the mathematical foundation required for defining the slope in the least