X 1 2 3 Y 4 1 7 The average of the xs is 2 and the SD of the

X: 1, 2, 3

Y: 4, 1, 7

The average of the x\'s is 2 and the SD of the x\'s is sqrt(2/3)

The average of the y\'s is 4 and the SD of the y\'s is sqrt(6)

(a) Find r.

(b) Since the average of y is twice the average of x, a researcher suggests doubling each x value to predict the y values. For example, when x=2, the predicted value of y will be 4. What will the rms error for this method be?

Solution

(a):r=[cov(x,y)/(sd_x*sd_y)]=[(27/3)-(2*4)]/[((2/3)*6)]=(9-8)/2=1/2=0.5.

(b): x:1,2,3 & y:2,4,6 then r=(9.333-8)/[((2/3)*(8/3))]=0.9998. RMSE=[[1-(r)²]][sd_y]=[[1-(.9998)²]]*[[8/3]]=0.0327.