First, we need to calculate the correlation coefficient, r, using the formula:
r = Σ((x - x̄)(y - ȳ)) / √(Σ(x - x̄)^2 * Σ(y - ȳ)^2)
Where x̄ is the mean of the x values, ȳ is the mean of the y values, and Σ means the sum of.
First, we need to calculate the mean of x and y:
x̄ = (41 + 66 + 70 + 72 + 95) / 5 = 68.8
ȳ = (3 + 10 + 3 + 4 + 9) / 5 = 5.8
Next, we calculate the sum of the products of the differences between x and y and their means:
Σ((x - x̄)(y - ȳ)) = (41 - 68.8)(3 - 5.8) + (66 - 68.8)(10 - 5.8) + (70 - 68.8)(3 - 5.8) + (72 - 68.8)(4 - 5.8) + (95 - 68.8)(9 - 5.8) = -79.4
Then, we calculate the sum of the squares of the differences between x and its mean, and between y and its mean:
Σ(x - x̄)^2 = (41 - 68.8)^2 + (66 - 68.8)^2 + (70 - 68.8)^2 + (72 - 68.8)^2 + (95 - 68.8)^2 = 1023.6
Σ(y - ȳ)^2 = (3 - 5.8)^2 + (10 - 5.8)^2 + (3 - 5.8)^2 + (4 - 5.8)^2 + (9 - 5.8)^2 = 19.6
Now, we can plug these values into the correlation coefficient formula:
r = -79.4 / √(1023.6 * 19.6) ≈ -0.308
Therefore, the correlation coefficient, r, is approximately -0.308.
or
Find the correlation coefficient, r, of the data described below.
Piquant Candy Company is testing a new additive designed to make its hard caramel candies dissolve more slowly. Company scientists gave several taste testers pieces of candy with varying amounts of the additive.
The scientists recorded the amount of additive in each piece (in milligrams), x, and how long the taste tester said it took to dissolve completely (in minutes), y.
Milligrams Minutes
41 3
66 10
70 3
72 4
95 9
Round your answer to the nearest thousandth.
r=
1 answer