how can I find the correlation coefficient ?

Answer 1

Hi,
Well, this is a long formula that requires a lot of busy work if you’re going to do it by hand. I’ll first give you the formula and explain what a few things mean; then I’ll tell you how to save a lot of work by doing it with a TI-83 Plus or TI-84 graphing calculator just in case you have one.

Here’s the formula:
r =
n(∑xy)-(∑x)(∑y)
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√[n(∑x²)-(∑x²)]√[n(∑y²)-(∑y)²]

The part above the dashed line is the numerator and the part below the line is the denominator of the formula.
Where n is the number of data points, and the x and y items are your data pairs.

∑xy Means to multiply the xy terms and add them all up.
∑y means add up all of the y-terms.
∑x² means to square each x-term and add all of those squared terms.
This is quite a lot of arithmetic. You definitely need some type of calculator, at least to do the arithmetic.

Now, here’s how to do it with a TI calculator:
1) First press 2ND, CATALOG, then the letter “d” ; scroll down to DiagnosticOn and press ENTER.
2) Press STAT, ENTER and enter your x-data in list L1 and your y-data in L2.
3) Press 2ND QUIT, STAT, move the cursor to CALC and select the item based on whether you data is linear, QuadReg or whatever. Let’s assume it’s linear.
4) If the data appears to be linear, press 4 and LinReg (ax+b) will be displayed on the home screen. Press ENTER and the coefficients for the formula, the correlation coefficient, r, and r² will be displayed.

Hope this helps.
FE