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????
I do not know if we use the same terminology.
Is SS(x) sum of squares of x?
If it is, I get 197.
Would it be S(xy) instead of SS(xy), meaning just the sum of the products?
Does r mean coefficient of correlation, which has a range of -1 to 1.
If you get 7.04, perhaps you are calculating something else.
No it is written in book as (SS(x), so I have not ideal what to do on this one It ask for three answers in first question and 1 answer in the second part and I have missed all of it and I keep coming up with the same answers so I am not sure what I am doing on this one
I was questioning SS(xy) only.
We need Sum of xy for calculating other parameters, but not sum of squares of xy.
How did you get your answers? I got 197 for SS(x). All of your answers seem to come up a little more than half of mine.
197-(31)squared divided by 10 197-961 over 10 = 96.1 then 197-96.1=100.9
I did the same thing that Gayle done on this for x and then y which was both wrong answers.
I think you have the right formulas, but the wrong N.
N equals 5 (count either number of x values or number of y values).
So
SSx=197-31²/5=4.8
SSy=39000-440²/5=280
Sxy=2760-31*440/5=32
r=Sxy/sqrt(SSx*SSy)=0.87287
To find the preliminary calculations (SS(x), SS(y), and SS(xy)), you need to calculate the sum of squares for each variable.
(a) Calculating SS(x):
- First, calculate the mean of x by summing all the values of x and dividing by the total number of values (n). In this case, there are 5 values, so the mean of x is (7 + 7 + 5 + 5 + 7) / 5 = 6.
- Next, subtract the mean (6) from each value of x and square the result.
- Compute the sum of the squared differences.
Using the given values of x: 7, 7, 5, 5, 7
- (7 - 6)^2 = 1
- (7 - 6)^2 = 1
- (5 - 6)^2 = 1
- (5 - 6)^2 = 1
- (7 - 6)^2 = 1
The sum of the squared differences (SS(x)) is 1 + 1 + 1 + 1 + 1 = 5. Therefore, SS(x) = 5.
(b) Calculating SS(y):
- Follow a similar process as in SS(x). Calculate the mean of y, which is (95 + 90 + 75 + 85 + 95) / 5 = 88.
- Subtract the mean (88) from each value of y and square the result.
- Compute the sum of the squared differences.
Using the given values of y: 95, 90, 75, 85, 95
- (95 - 88)^2 = 49
- (90 - 88)^2 = 4
- (75 - 88)^2 = 169
- (85 - 88)^2 = 9
- (95 - 88)^2 = 49
The sum of the squared differences (SS(y)) is 49 + 4 + 169 + 9 + 49 = 280. Therefore, SS(y) = 280.
(c) Calculating SS(xy):
- Multiply the differences between each x value and the mean of x by the differences between each corresponding y value and the mean of y.
- Compute the sum of the products.
Using the given values of x and y:
- (7 - 6)(95 - 88) = 49
- (7 - 6)(90 - 88) = 2
- (5 - 6)(75 - 88) = -143
- (5 - 6)(85 - 88) = -9
- (7 - 6)(95 - 88) = 49
The sum of the products (SS(xy)) is 49 + 2 - 143 - 9 + 49 = -52. Therefore, SS(xy) = -52.
Now, to find the correlation coefficient (r):
- Use the formula: r = SS(xy) / sqrt(SS(x) * SS(y))
- Plug in the values you obtained:
r = -52 / sqrt(5 * 280) ≈ -0.524
Therefore, the correlation coefficient (r) is approximately -0.524, rounded to three decimal places.