Measure how strongly two lists are related

Find the correlation coefficient r, which runs from -1 (perfect downhill) to +1 (perfect uphill).

The correlation coefficient r tells you how closely points follow a straight line. Near +1 the points climb, near -1 they fall, and near 0 there is no straight-line pattern.

The example has x = 1 to 5 and y = 9, 7, 6, 3, 2. The points fall steadily, so r is about -0.9879.

Classic Graphing 84

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

Type x into L1 and y into L2.
stat11enter2enter3enter4enter5enter▶9enter7enter6enter3enter2enter
Run LinReg(ax+b) from STAT, CALC, option 4. Move down to Calculate and press enter.
stat▶4▼▼▼▼enter

You should seer is about -0.988, and r² (the share of the pattern explained by the line) is about 0.976.

Classic Graphing 84 key reference

Classic Scientific 30

Start on the main screen: Press 2nd then mode (QUIT) to leave any menu or screen and return to the calculation screen.

Type x into L1 and y into L2.
data1enter2enter3enter4enter5enter▶▲▲▲▲▲9enter7enter6enter3enter2enter
Open the STAT menu (2nd then data) and choose LinReg ax+b. Accept the lists with enter.
2ndstatdata3enterenterenter
Press the down arrow a few times to scroll to r.
▼▼▼▼

You should see4:r=-0.9878783399

Classic Scientific 30 key reference

Natural Scientific 991

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

Open Statistics, choose y=a+bx and type the x column.
MENU621=2=3=4=5=
Go back to the top, one column right, and type the y column.
▶▲▲▲▲▲9=7=6=3=2=AC
Press OPTN and choose Regression Calc. The last line is r.
OPTN3

You should seer=-0.9878783399

Natural Scientific 991 key reference

RPN Scientific 15

Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.

Clear the statistics memory first, so old data cannot sneak into the answer.
fCLR ΣGSB
For each pair, key in y, press ENTER, key in x, then press Σ+.
9ENTER1Σ+7ENTER2Σ+6ENTER3Σ+3ENTER4Σ+2ENTER5Σ+
Key in any x, here 6, and press f then the decimal point (ŷ,r). The correlation r lands one level up the stack.
6fŷ,r.

You should see-0.9879

RPN Scientific 15 key reference

RPN Advanced 42

Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.

For each pair, key in y, press ENTER, key in x, then press the Σ+ key.
9ENTER1Σ+7ENTER2Σ+6ENTER3Σ+3ENTER4Σ+2ENTER5Σ+
Open the STAT menu, then FIT, and press the last key (r).
⇧STAT÷XEQLN

You should seex: -0.9879

RPN Advanced 42 key reference

Tips

A strong correlation does not prove that one thing causes the other.
r only measures straight-line patterns. A perfect curve can still give an r near 0.