Question

Refer to the table below. Consider the relationship between the number of houses sold (Y) and the mortgage rate (X). The values of X and Y for twelve (12) months are shown in the table below. M-Rates 8 9.5 7.5 11 8.5 10 10.5 7 7.5 11 9 8 Houses sold 188 145 181 137 157 148 140 203 188 144 150 166 Based on that, a. Calculate the coefficient of correlation between the number of houses sold and the mortgage rate. b. What does the correlation coefficient tell you about the relationship between the level of house sales and mortgage rates based on the calculation?

Answer 1

a.

X Values
∑ = 107.5
Mean = 8.958
∑(X - M_x)² = SS_x = 22.229

Y Values
∑ = 1947
Mean = 162.25
∑(Y - M_y)² = SS_y = 5496.25

X and Y Combined
N = 12
∑(X - M_x)(Y - M_y) = -318.375

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

r = -318.375 / √((22.229)(5496.25)) = -0.9108

b. As r is negative and it is near 1, so there is strong negative correlation between the level of house sales and mortgage rates based on the calculation.