Question

help please Find the value of r and determine if a correlation exists at the indicated level of significance.
x y
8 26
11 30
13 32
14 33
α = 0.01 A. r = 0.9710; Correlation exists. B. r = 0.9997; Correlation exists. C. r = 0.9710; Correlation does not exist. D. r = 0.9971; Correlation exists.

Answer 1

no one i asked understands this

Answer 2

I always have to go back to the definition. Do you know what the formula for r is?

Answer 3

no

Answer 4

Here is Pearson's r. Deos that sound right?
http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient

Answer 5

Where do you get these problems from?

Answer 6

online school

Answer 7

OK. Look at the definition. The basic idea is to take the difference between each value in a series and the mean and then sum them.

Answer 8

So in your series the mean for the x-values is 11.5
And the mean for y-values is 30.25.

Answer 9

did you add and divide to get that

Answer 10

So for the numerator we'll go the series in parallel. The first x,y is 8,26. The difference from the means is 3.5,4.25. What we need to do is multiply those together then add the resulting values for the whole series...

Answer 11

Yeah mean is the sum of the values divided by the number of values.

Answer 12

o

Answer 13

Say it another way we have (8-11.5) times (26-30.25) for the first pair. We generate these products for each of the four pairs and add them together. That's what the numerator of the definition means.

Answer 14

you are smart how old are you

Answer 15

I'm not so smart, but I'm a professor of microbiology to tell the truth. I just like math.

Answer 16

And I love helping motivated students.

Answer 17

cool

Answer 18

so after + all of them together divide then -the frist number

Answer 19

Let's think big picture. The idea here is that if for a given pair x is a lot less than the mean of x-values, and y is a lot less than the mean of y-values, then the product will be large and positive, and the same is true if x and y are both a lot larger than the respective means except the product will be positive.

Answer 20

Here's the formula for reference.

Answer 21

So again, for the numerator we go through the x,y values as pairs in series and do the difference from the respective means and multiply, then sum at the end. Does that make sense?

Answer 22

14.875

Answer 23

I don't calculate on the fly too well any more. I believe you. If I wanted to do it I'd use Python but that's another subject. Anyway, for the denominator we have the variance of X and Y. Do you know about variance?
http://en.wikipedia.org/wiki/Variance

Answer 24

?

Answer 25

Variance. We take the difference of each value from the mean and square it, then add them all together and take the square root. We do this separately for the x and y series and then multiply together. Do you see this when you look at the formula I put up for r?

Answer 26

did not understand any of the formula

Answer 27

Hmm.. Do you have to do this problem. You've posted a variety of problem types as I recall.

Answer 28

The thing is, you need someone to lead your carefully through all the steps, explain them as you go, and then give you problems to do. You are just parachuting down into a field of problems.. with no preparation.

Answer 29

yes

Answer 30

i am a drop out from the 8grade but i am geting my high school deplomu on line so i can be a marine

Answer 31

USMC

Answer 32

Yes

Answer 33

sorry about the spelling

Answer 34

No worries. I suggest you leave this problem for now.

Answer 35

well i got to do it to get the next one

Answer 36

My wife's son finished 5 years recently and my Dad was a Lt. on Iwo Jima. Semper Fi.

Answer 37

cool

Answer 38

i am joining as some as i get my HSD o and i am 21 droped out at 16

Answer 39

The mean (or average) of x-values was 11.5.
And the mean for y-values is 30.25.
The x-values are: 8, 11, 13, 14
The y-values are 26, 30, 32, 33
The differences from the mean for the x-values are: [-3.5, -0.5, 1.5, 2.5]
The differences from the mean for the y-values are: [-4.25, -0.25, 1.75, 2.75]

The product of the differences is [14.875, 0.125, 2.625, 6.875]
The sum of this is 24.5.
I think.
That's the numerator.

Answer 40

[-3.5, -0.5, 1.5, 2.5]
[-4.25, -0.25, 1.75, 2.75]
how did you get this

Answer 41

The squares of the differences from the mean for the x-values are:
[12.25, 0.25, 2.25, 6.25]
The squares of the differences from the mean for the y-values are:
[18.0625, 0.0625, 3.0625, 7.5625]

>>> sqrt(sum(Xv))
4.58257569495584
>>> sqrt(sum(Yv))
5.361902647381804
>>> sqrt(sum(Xv)) * sqrt(sum(Yv))
24.57132475061123

Last step is 24.5 / 24.571
>>> 24.5 / 24.571
0.9971104147165357

Answer 42

Back to your question, then we'll move on.

Answer 43

The first value -3.5 is 8 - 11.5. The first x-value minus the mean for all x-values.

Answer 44

Never mind. You see we've (I've) matched one of the possible answers. The other part of it is the alpha = 0.01 thing. This means they want the r > 0.99 to be considered "significant." HTH.

Answer 45

i am opening a new question

Answer 46

I hope it's easier. Good luck.