Question

which of the following statements about the slope of the least - squares regression line is true? it has the same sign as the correlation coefficient r. the square of the slope equals the proportion of the variation in the response variable that is explained by the explanatory variable. it is unitless. when the x - variable is 0, this is what the y - variable is predicted to be.

Explanation:

The slope of the least - squares regression line has the same sign as the correlation coefficient r. When r is positive, the slope of the regression line is positive, indicating a positive linear relationship between the variables. When r is negative, the slope of the regression line is negative, indicating a negative linear relationship. The other statements are incorrect: The square of the slope does not equal the proportion of the variation in the response variable explained by the explanatory variable. The slope is not unitless. And the statement about predicting the y - variable when the x - variable is 0 is not a general property of the slope of the least - squares regression line.

Answer:

It has the same sign as the correlation coefficient r.