Does studying for an exam pay off? The number of hours studied, x, is compared with the exam grade received, y.
x 7 7 5 5 7
y 95 90 75 85 95
(a) Complete the preliminary calculations: SS(x), SS(y), and SS(xy).
Incorrect: Your answer is incorrect. . (SS(x))
Incorrect: Your answer is incorrect. . (SS(y))
Incorrect: Your answer is incorrect. . (SS(xy))
(b) Find r. (Give your answer correct to three decimal places.)
My answers were (a) 100.9, 19640 and 1396. (B) 7.04 But wrong can someone help????
Sorry, did not realize that I had done it twice was working on different problems...thought I had posted another question.
To answer this question, we need to calculate the sums of squares (SS) for the variables x and y, as well as the sum of products (SS(xy)). Here's how you can calculate them:
(a) Calculating SS(x):
1. Calculate the mean (average) of x by summing up all the values of x and dividing by the total number of observations (in this case, 5):
mean(x) = (7 + 7 + 5 + 5 + 7) / 5 = 31 / 5 = 6.2
2. Subtract the mean from each value of x and square the result:
(7 - 6.2)^2 + (7 - 6.2)^2 + (5 - 6.2)^2 + (5 - 6.2)^2 + (7 - 6.2)^2
= 0.64 + 0.64 + 1.44 + 1.44 + 0.64 = 4.8
Therefore, SS(x) = 4.8.
(b) Calculating SS(y):
1. Calculate the mean of y:
mean(y) = (95 + 90 + 75 + 85 + 95) / 5 = 440 / 5 = 88
2. Subtract the mean from each value of y and square the result:
(95 - 88)^2 + (90 - 88)^2 + (75 - 88)^2 + (85 - 88)^2 + (95 - 88)^2
= 49 + 4 + 169 + 9 + 49 = 280
Therefore, SS(y) = 280.
(c) Calculating SS(xy):
1. Subtract the respective means of x and y from each value of x and y, respectively, and sum the products:
(7 - 6.2)(95 - 88) + (7 - 6.2)(90 - 88) + (5 - 6.2)(75 - 88) + (5 - 6.2)(85 - 88) + (7 - 6.2)(95 - 88)
= 6(7) + 0.8(2) + (-1.2)(-13) + (-1.2)(-3) + 6(7)
= 42 + 1.6 + 15.6 + 3.6 + 42
= 105.6
Therefore, SS(xy) = 105.6.
(b) Calculating the Pearson correlation coefficient (r):
The formula to calculate r is given by:
r = SS(xy) / √(SS(x) * SS(y))
Substituting the calculated values, we have:
r = 105.6 / √(4.8 * 280)
r = 105.6 / √(1344)
r ≈ 105.6 / 36.65
r ≈ 2.879
Rounding the answer to three decimal places, we get r ≈ 2.879.
Therefore, the correct answers are:
(a) SS(x) = 4.8, SS(y) = 280, and SS(xy) = 105.6.
(b) r ≈ 2.879.