Question

or Find the correlation coefficient, r, of the data described below. Pam has trouble getting her math homework done on time, and her mother suspects it is due to lack of sleep. For the next few nights, Pam's mother notes the number of hours she sleeps, x, and the number of minutes it takes her to do her math homework the following day, y. Hours sleptMinutes needed to finish math homework 4.493 4.495 5.362 5.794 6.366

Answer 1

The correlation coefficient, r, of the given data is approximately -1.556.

Step-by-step explanation:

To find the correlation coefficient, we will use the formula:

r = (nΣxy - ΣxΣy) / √((nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2))

We can calculate the necessary values and plug them into the formula to find the correlation coefficient, r.

Step 1: Calculate the values we need:

For x: Σx = 4.49 + 4.49 + 5.36 + 5.79 + 6.36 = 26.49

For y: Σy = 63 + 95 + 93 + 72 + 60 = 383

For xy: Σxy = 4.49*63 + 4.49*95 + 5.36*93 + 5.79*72 + 6.36*60 = 1247.62

For x^2: Σx^2 = (4.49)^2 + (4.49)^2 + (5.36)^2 + (5.79)^2 + (6.36)^2 = 132.4196 + 132.4196 + 28.7296 + 33.4941 + 40.5696 = 367.6325

For y^2: Σy^2 = 63^2 + 95^2 + 93^2 + 72^2 + 60^2 = 3969 + 9025 + 8649 + 5184 + 3600 = 30427

Step 2: Plug the values into the formula:

r = (5 * 1247.62 - 26.49 * 383) / √((5 * 367.6325 - (26.49)^2)(5 * 30427 - (383)^2))

Step 3: Calculate the result:

r = (6238.1 - 10115.47) / √((1838.1625 - 700.0401)(152135 - 146689))

r = -3877.37 / √((1138.1224)(5446))

r = -3877.37 / √(6205753.11)

Step 4: Calculate the square root:

r = -3877.37 / 2489.801

r ≈ -1.556

Therefore, the correlation coefficient, r, is approximately -1.556.