Need Stats help quick...

[BigToque]

I have a problem and I have no Idea why I'm getting the wrong answer...

(This should be a table but I cant make a real table here so bare with me)

X: Age (months) = (36, 48, 51, 54, 57, 60)
Y: Height (cm) = (86, 90, 91, 93, 94, 95)
From this, I know:

(Mean)
X-mean = 51
Y-mean = 91.5

(Standard Deviation)
SD(X) = 8.49
SD(Y) = 3.27

-----------------------------------------------------------------------

I need to find the correlation between these two variables. Using my Stats program, I get a positive correlation or .9944

Unfortunately, when I do it by hand I get a correlation of 0

The formula I need to use looks like this:

r = 1 / (n-1) Summation sign (Xi - X-mean) / SD(X) x (Yi - Y-mean) / SD(Y)

Example


Someone please help me find out how to plug everything in. The (Xi - X-mean) is confusing me.

My assignment is due tomorrow and this is the last question I need to finish.

 

[Geforcekj]

wow just learnt this in my stats class bear with me I'll do it up...

 

[Geforcekj]

Using Sum of Least Squares formula which is the most accurate way of determining corelation per the Gauss-Markov Therom (ok so now that I SOUND smart)

Exiyi = 28137
Ex^2 = 15966
Ey^2 = 50287

* E = Epsilon (sum of) * * sqrt = Square Root *

r = (Exiyi -n(x-mean)(y-mean)) / (sqrt((Exi^2-n(x-mean^2)(Eyi-n(y-mean^2))

r = (28137 - 6(91.5)(51)) / (sqrt(15966 - 6(51^2))(50287 - 6(91.5^2)))

r = (28137 - 27999) / (sqrt((15966 - 15606)(50287 - 50233.5)))

r = 138 / (sqrt(360)(53.5)))

r = 138 / (sqrt19260)

r = 138 / 138.7804

r = 0.9943767127

Which shows they are VERY correlated...do you need to prove that to a significance level or is that it?

 

[Geforcekj]

So anyone wanna verify that I am right...I just learned this stuff...

 

[Vincent]

You need to square



<< (Xi - X-mean) >>



and



<< (Yi - Y-mean) >>



If you don't square them, it's straightforward to show that you'll always get zero.

 

[BigToque]

Geforcekj,

Your answer seems right, but I cant use that for this question.

Vincent,

If I square (Xi - X-mean) and (Yi - Y-mean), then I get 360 and 53.5 respectively.

If I then Divide each of these by their Standard Deviation
(Xi - X-mean) / SD(X) and
(Yi - Y-mean) / SD(Y)

Then Multiply them together, I get an answer of 693.7465556

------------------------------------------

This leaves me with this as an equation:

r = 1 / n-1 Summation 693.7465556


What do I do at this point?

If I Divide 693.7465556 by 5 (n-1), then I get:

r = 138.749311

which is a far cry from the .9944 I'm looking for. obviously I'm not understanding exactly what is supposed to be happening here.

 

[Geforcekj]

.9944 is that not what my answer is?....hmmm...just a sec...

 

[Geforcekj]

formula should be

r / ((sqrt(1-r)/(n-2)))

so we get...

0.9944 / (sqrt((0.0056)/(4))

0.9944 / (sqrt(0.0014)

0.9944 / 0.3741

= 26.564579

 

[BigToque]

Geforcekj,

Your answer is correct.

I dont know WTF is going on here.

Here is the exact question:



<< Use a calculator to find the value of the correlation coefficient r. Give an interpretation of this value with regard to the strength and direction of the linear association >>

 

[Geforcekj]

<< Geforcekj,

Your answer is correct.

I dont know WTF is going on here.

Here is the exact question:



<< Use a calculator to find the value of the correlation coefficient r. Give an interpretation of this value with regard to the strength and direction of the linear association >>

>>



I edited it...dont this r in 1-r is suposed to be squared

 

[Geforcekj]

no just checked it's not ...so I think the above is correct...

 

[Geforcekj]

<<

<< Use a calculator to find the value of the correlation coefficient r. Give an interpretation of this value with regard to the strength and direction of the linear association >>

>>



so then a correlation coefficiant r of 0.9944 is VERY close to 1 so it is safe to say they are possitively correlated...

 

[BigToque]

HERE is the official assignment sheet.

Check Question #5.

The data is:

X: Age (months) = (36, 48, 51, 54, 57, 60)
Y: Height (cm) = (86, 90, 91, 93, 94, 95)

I have no fscking idea whats going on and its pissing me off!!

 

[BigToque]

<< so then a correlation coefficiant r of 0.9944 is VERY close to 1 so it is safe to say they are possitively correlated... >>



Yes I know that, but I dont know how to get to .9944 as an answer, using the equations I've been given.

 

[Geforcekj]

you got some time?

hehe jsut a sec...I'll give it a shot...

 

[Geforcekj]

<<

<< so then a correlation coefficiant r of 0.9944 is VERY close to 1 so it is safe to say they are possitively correlated... >>



Yes I know that, but I dont know how to get to .9944 as an answer, using the equations I've been given. >>



cant help you there that is the equation i was given

 

[Geforcekj]

E)

b = 0.9944

a = (y-mean) - b(x-mean)

a = 91.5 - (0.9944)(51)

a = 91.5 - 50.7144

a = 40.7856

(y-hat ) = a + bxi

(y-hat) = 40.7856 + 0.9944(xi)

so your line has a slope of 0.9944 with a y intercept of 40.7856

 

[Geforcekj]

F)

(y-hat) = predicted value per formula

(y-hat) = 40.7856 + 0.9944(xi)

40months
(y-hat) = 40.7856 + 0.9944(40)

(y-hat) = 40.7856 + 39.776

(y-hat) = 80.5616 inches

60months
= 40.7856 + 59.664

= 100.4496 inches

 

[Geforcekj]

anyway...way past my bedtime...hope it helped good luck

 

[Vincent]

You're right that my suggestion was wrong. Sorry but I don't have time to figure out the problem.

 

[BigToque]

Alright, my problem, I found out this morning, was I forgot how to multiply :|

Anyway, 5c is out of the way.

r = .9944

5d asks to find the coefficient of determination r^2

Am I just supposed to square r? We have not talked about the coefficient of determination in class and our text makes no mention of it. looking at examples on the net has me stumped.

 

[BigToque]

ack... please help... this is due in 50 minutes!

 

[Geforcekj]

yes I think so....