Question

Problem#

calculate the sample correlation coefficient.

Use the accompanying data to answer a and b.

x	1	2	3	4	5
y	1	4	8	9	12

1. Determine the least-squares prediction equation.
2. Use the least-squares prediction equation to predict y when x=6

Answer 1

X Values
∑ = 15
Mean = 3
∑(X - M_x)² = SS_x = 10

Y Values
∑ = 34
Mean = 6.8
∑(Y - M_y)² = SS_y = 74.8

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = 27

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 27 / √((10)(74.8)) = 0.9872

a.

Sum of X = 15
Sum of Y = 34
Mean X = 3
Mean Y = 6.8
Sum of squares (SS_X) = 10
Sum of products (SP) = 27

Regression Equation = ŷ = bX + a

b = SP/SS_X = 27/10 = 2.7

a = M_Y - bM_X = 6.8 - (2.7*3) = -1.3

ŷ = 2.7X - 1.3

b. For x=6, ŷ = (2.7*6) - 1.3=14.9