Can someone please show me how to solve this step by step. I'm trying to understand the whole concept but I'm getting confused...
Find the sample linear correlation coefficient between x and y:
x: 5, 2, 2
y: 7, 4, 7
x^2: 25, 4, 4
y^2: 49, 16, 49
xy: 35, 18, 14
I know how to find the correlation coefficient (r), it's SS(xy) / sqr root of SS(x)SS(y)
But when I solve that I get 9....I know r has to be between 0 and 1 so that can't be right at all... Help!
Nevermind!
I had SS(x) = 6, and SS(y) = 6, but I kept thinking SS(xy) = 54...I wasn't solving completely. SS(xy) = 3,...so r = .5
sum(x) = 9
Sum(y) = 18
sum(x^2) = 33
sum(y^2) = 114
sum( xy) = 57
n = 3
r = 3(57)-(9)(18)/sqrt(3(33)-9^2)sqrt(3(114)-18^2)
r = (171-162)/sqrt(99-81)sqrt(342-324)
r = 9/sqrt(18)sqrt(18)
r = 9/18 = .5
To find the sample linear correlation coefficient (r), we can follow these steps:
Step 1: Calculate the sum of x, y, x^2, y^2, and xy.
∑x = 5 + 2 + 2 = 9
∑y = 7 + 4 + 7 = 18
∑x^2 = 25 + 4 + 4 = 33
∑y^2 = 49 + 16 + 49 = 114
∑xy = 35 + 18 + 14 = 67
Step 2: Calculate the sum of squares for x (SS(x)) and y (SS(y)).
SS(x) = ∑x^2 - ((∑x)^2 / n)
= 33 - ((9)^2 / 3)
= 33 - (81 / 3)
= 33 - 27
= 6
SS(y) = ∑y^2 - ((∑y)^2 / n)
= 114 - ((18)^2 / 3)
= 114 - (324 / 3)
= 114 - 108
= 6
Step 3: Calculate the sum of products of x and y (SS(xy)).
SS(xy) = ∑xy - ((∑x * ∑y) / n)
= 67 - ((9 * 18) / 3)
= 67 - (162 / 3)
= 67 - 54
= 13
Step 4: Calculate the sample linear correlation coefficient (r).
r = SS(xy) / √(SS(x) * SS(y))
= 13 / √(6 * 6)
= 13 / √36
= 13 / 6
≈ 0.722
The sample linear correlation coefficient (r) is approximately 0.722, which indicates a moderate positive correlation between the variables x and y.
When you calculated SS(xy) / √(SS(x) * SS(y)), it seems there was an error in your calculations. Double-check your calculations to ensure accurate results.