Consider the following table and use the formulas that are given for computing the correlation coefficient. (Give your answer correct to two decimal places.)
x 1 1 0 0 0
y 7 3 5 6 6
r =
n
xy
−
x
y
n
x2
−
x
2
n
y2
−
y
2
(1)
r =
SS(xy)
SS(x) · SS(y)
(2)
This is what I done (2)(27)/5 =10.8 for ss(xy) then 2^/5=.8 for SS(x), ten (27^)/5=145.8 for SS(y), then I put 10.8 over sqrt.8 X 145.8 = 1.00
To calculate the correlation coefficient, we can use the given formulas:
Formula (1):
r = (n * Σxy - Σx * Σy) / √[(n * Σx^2 - (Σx)^2) * (n * Σy^2 - (Σy)^2)]
Given table:
x: 1 1 0 0 0
y: 7 3 5 6 6
Let's calculate the necessary components step by step:
1. Calculate Σxy:
Σxy = (1 * 7) + (1 * 3) + (0 * 5) + (0 * 6) + (0 * 6) = 10
2. Calculate Σx:
Σx = 1 + 1 + 0 + 0 + 0 = 2
3. Calculate Σy:
Σy = 7 + 3 + 5 + 6 + 6 = 27
4. Calculate Σx^2:
Σx^2 = (1^2) + (1^2) + (0^2) + (0^2) + (0^2) = 2
5. Calculate Σy^2:
Σy^2 = (7^2) + (3^2) + (5^2) + (6^2) + (6^2) = 149
6. Calculate n (the number of data points):
n = 5 (since there are 5 values of x and y)
Now, we can substitute these values into Formula (1) to find the correlation coefficient (r):
r = (n * Σxy - Σx * Σy) / √[(n * Σx^2 - (Σx)^2) * (n * Σy^2 - (Σy)^2)]
= (5 * 10 - 2 * 27) / √[(5 * 2 - 2^2) * (5 * 149 - 27^2)]
= (50 - 54) / √[(10 - 4) * (745 - 729)]
= -4 / √[6 * 16]
= -4 / √96
= -4 / 9.8 (rounded to two decimal places)
≈ -0.41 (rounded to two decimal places)
Therefore, the correlation coefficient (r) is approximately -0.41.