I'm trying ti find the correlation coefficient for the following:
The scores of 10 students on their midterm exam (x) and on their final (y) yielded the following data.
Σx = 638 Σx2 = 43,572
Σy = 690 Σy2 = 49,014
Σxy = 44,636
Is the answer 0.547? HELP!!!
To find the correlation coefficient for the given data, you can follow these steps:
Step 1: Calculate the mean (average) of x and y.
Mean of x (x̅) = Σx/n = 638/10 = 63.8
Mean of y (y̅) = Σy/n = 690/10 = 69
Step 2: Calculate the sum of the squared differences from the mean for x and y.
Σ(x - x̅)² = Σx² - (Σx)²/n = 43,572 - (638)²/10 = 4,357.2 - 40,694/10 = 4,357.2 - 4,069.4 = 287.8
Σ(y - y̅)² = Σy² - (Σy)²/n = 49,014 - (690)²/10 = 4,901.4 - 47,610/10 = 4,901.4 - 4,761 = 1401.4
Step 3: Calculate the sum of the products.
Σxy = 44,636
Step 4: Calculate the correlation coefficient using the formula:
r = Σxy / √(Σ(x - x̅)² * Σ(y - y̅)²)
Substituting the values into the formula:
r = 44,636 / √(287.8 * 1401.4)
Calculating the denominator:
√(287.8 * 1401.4) ≈ √403,105.72 ≈ 635.1
Now, divide the numerator by the denominator:
r ≈ 44,636 / 635.1 ≈ 70.33
Therefore, the correlation coefficient for the given data is approximately 0.70, not 0.547.
So, the answer you have mentioned, 0.547, is incorrect. The correct correlation coefficient is around 0.70.