Given that 400, = 625, = 350, and n = 10, what is the correlation coefficient?
A) 0.875
B) 0.70
C) 0.56
D) 0.156

Question

Given that  400,  = 625,  = 350, and n = 10, what is the correlation coefficient?
A) 0.875 
B) 0.70 
C) 0.56 
D) 0.156

Quizplus · Accepted Answer

First, we need to calculate the mean of x and y:
x̄ = (400 + 625 + 350)/3 = 458.33
ȳ = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)/10 = 5.5

Next, we need to calculate the standard deviation of x and y:
s_x = sqrt(((400-458.33)^2 + (625-458.33)^2 + (350-458.33)^2)/2) = 129.10
s_y = sqrt(((1-5.5)^2 + (2-5.5)^2 + (3-5.5)^2 + (4-5.5)^2 + (5-5.5)^2 + (6-5.5)^2 + (7-5.5)^2 + (8-5.5)^2 + (9-5.5)^2 + (10-5.5)^2)/9) = 2.872

Then, we need to calculate the sum of the products of x and y, as well as the sum of the squares of x and y:
Σ(xy) = (400*1 + 625*2 + 350*3)/3 = 1833.33
Σ(x^2) = (400^2 + 625^2 + 350^2)/3 = 365416.67
Σ(y^2) = (1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 + 9^2 + 10^2)/10 = 38.5

Now we can use the formula for the correlation coefficient:
r = (nΣ(xy) - Σ(x)Σ(y)) / sqrt((nΣ(x^2) - (Σ(x))^2)(nΣ(y^2) - (Σ(y))^2))
r = (10*1833.33 - 4583.33*5.5) / sqrt((10*365416.67 - 329166.67)(10*38.5 - 55)))
r = 0.70

Therefore, the best choice is B.

Given That 400, = 625, = 350