The correlation coefficient r between the values assumed by

The correlation coefficient r between the values assumed by two variables, X
and Y is .75, the standard deviations of X and Y are Sx=1.88 and Sy=2.45
respectively, and the point (13, 9) is on the line of best fit.

A. Find the slope of the line of best fit to the raw-score scatterplot.

B. Find the equation of the line of best fit.
C. Find y given that . x = 12

Solution

b = r Sy/Sx
b = (0.75) (2.45)/(1.88) = 0.9774

B)
y = a + bx
y = a + 0.9774x

substitute x=13 and y=9
9 = a + (0.9774)(13)
a = 9- (0.9774)(13)
a=-3.706

y = -3.706 + 0.9774 x

c)
substitute x=12 into the line of best fit
y-hat = -3.706 + (0.9774)(12) = 8.0228