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)) (my answer was 100.9)
Incorrect: Your answer is incorrect. . (SS(y)) (my answer was 720)
Incorrect: Your answer is incorrect. . (SS(xy)) (My answer was 1396)
I have got several answers and none of them have been correct.
(b) Find r. (Give your answer correct to three decimal places.) (my answer was 7.04) and it was wrong, could some one work this out so I can see how I missed it.
Incorrect: Your answer is incorrect. .
What happen if you got a D on your finials but you have good grade in that class can you still pass
This does not explain how to come up with the right answer for me. I have worked it out several times and come up with the same answers, which I posted above. Can someone work this out so I can see what I have done wrong and can learn from my mistakes...
shame
To complete the preliminary calculations, we need to calculate the sums of squares (SS) for x, y, and xy.
To calculate SS(x), follow these steps:
1. Find the mean of x by adding up all the values of x and dividing by the total number of values (in this case, 5):
Mean of 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
So, SS(x) = 4.8
To calculate SS(y), follow similar steps:
1. Find the mean of y:
Mean of 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
So, SS(y) = 280
To calculate SS(xy), follow these steps:
1. Multiply each value of x by its corresponding y value:
(7 * 95) + (7 * 90) + (5 * 75) + (5 * 85) + (7 * 95)
= 665 + 630 + 375 + 425 + 665 = 2760
2. Find the mean of xy by dividing the sum from step 1 by the total number of values (in this case, 5):
Mean of xy = 2760 / 5 = 552
3. Subtract the mean of xy from each value of xy and square the result:
(665 - 552)^2 + (630 - 552)^2 + (375 - 552)^2 + (425 - 552)^2 + (665 - 552)^2
= 131769 + 69729 + 222784 + 34969 + 131769 = 589020
So, SS(xy) = 589020
Now, to find r (the correlation coefficient), we can use the following formula:
r = SS(xy) / sqrt(SS(x) * SS(y))
Substituting the values we calculated:
r = 589020 / sqrt(4.8 * 280) = 589020 / sqrt(1344) ≈ 589020 / 36.657 ≈ 16.050 (rounded to three decimal places)
Therefore, the correct answer for r is 16.050.