What is the correlation coefficient between the variables? round to three decimal places. enter your answer in the box. r≈ age score 14 360 25 293 19 315 35 212 20 315 12 331 5 404

There are two data sets x and y.

X includes = 14 25 19 35 20 12 5

Y includes = 360 293 315 212 315 331 404

 to solve for the correlation coefficient, we need to get the following values step by step

Step 1: Find the mean of each set.

The mean of X = 18.571

The mean of Y = 318.571

Step 2: Subtract the mean of X from every value X value (denote this with letter a). Do the same for y (denote this with letter b).

The mean of X subtracted from every X value (a):

14 - 18.571 = -4.571

25 - 18.571 = 6.429

19 - 18.571 = 0.429

35 - 18.571 = 16.429

20 - 18.571 = 1.429

12 - 18.571 = -6.571

5 - 18.571 = -13.571

The mean of Y subtracted from every value of Y (b):

360 - 318.571 = 41.429

293 - 318.571 = -25.571

315 - 318.571 = -3.571

212 = 318.571 = -106.571

315 - 318.571 = -3.571

331 - 318.571 = 12.429

404 - 318.571 = 85.429

Step 3: Calculate: a *  b, a^2 and b^2 of every value.

For a*b

-189.388

-164.388

-1.531

-1750.816

-5.102

-81.673

-1159.388

Sum: -3352.286

For a²

20.898

41.327

0.184

269.898

2.041

43.184

184.184

Sum: 561.714

For b²

1716.327

653.898

12.755

11357.469

12.755

154.469

7298.041

Sum: 21205.714

Step 4: Solve using this formula

r = ∑a * b / √((a²)(b²))

r = -3352.286 / √((561.714)(21205.714))

 = -0.9713

The correlation coefficient is -0.971

step-by-step explanation: