Consider a data set consisting of values for three variables: X, Y, and Z. Their sample means, standard deviations, and correlations (with Y) are: Sample Mean x = 8.07 y = 48.17 z = 4.27 Sample Standard Deviation sx = 1.95 sy = 23.04 sz = 2.79 Sample Correlation (with Y) rxy = -0.16 ryy = 1 rzy = 0.91 Consider the least squares line y = b0 + b1x . The slope of this least squares line is , and the intercept is . The variation in the variable X explains of the variation in the variable Y. Consider the least squares line y = c0 + c1z . The slope of this least squares line is , and the intercept is . The variation in the variable Z explains of the variation in the variable Y. Scatter Diagram A Scatter Diagram B depicts the relationship between Y and X, and depicts the relationship between Y and Z