Question

Calculate the correlation coefficient, r, for the pair data

provided below.
x 1 4 5 8 10
y 5 12 13 13 16
Round your answer to three decimal places.

Answer 1

To calculate the correlation coefficient, r, for the given pair of data, use the formula r = (nΣ(xy) - ΣxΣy) / sqrt((nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)). Substituting the values from the provided data into the formula, the correlation coefficient is approximately 0.453.

Step-by-step explanation:

To calculate the correlation coefficient, r, for the given pair of data, we can use the following formula:

r = (nΣ(xy) - ΣxΣy) / sqrt((nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2))

Substituting the values from the provided data into the formula:

r = ((5*5)+(4*12)+(5*13)+(8*13)+(10*16) - (1+4+5+8+10)(5+12+13+13+16)) / sqrt(((5^2)+(4^2)+(5^2)+(8^2)+(10^2) - ((1+4+5+8+10)^2))((5^2)+(12^2)+(13^2)+(13^2)+(16^2) - ((5+12+13+13+16)^2)))

r = 0.4526

Therefore, the correlation coefficient, r, for the given data is approximately 0.453.