Question

Introductory statistics: If the correlation between age and physical flexibility is -.68, what does this mean? How would this correlation look on a scatter diagram? What general shape would it have?

Answer 1

Correlation means how two characteristics are related.

If an increase in age of one year caused an increase in flexibility of "1" (whatever that means), then correlation would be "1".... they vary directly.

A negative correlation means that as one characteristic increases, the other decreases.

A correlation of less than one (positive or negative) means that as one characteristic increases (or decreases), the other changes... but it changes proportionally less than the first characteristic. For example, in this case, a correlation of 0.5 would mean a change in age of 1 year would cause an increase in flexibility of 0.5. If correlation was -0.5, then an increase in age of 1 year would cause a DECREASE in flexibility of 0.5.

So a -0.68 correlation between age and flexibility indicates that as you get older, you get less flexible... and the -0.68 gives you a proportion of how MUCH less flexible you get for every year you get older.

Answer 2

Thank you for the explanation. How would I go about making a scatter diagram for this?

Answer 3

Well, you could set up 2 axis (axes? I never know...) with age on the x axis and flexibility on the y.

A normal population of people will not perfectly follow this guideline... it's just sort of like an average... so a scatter plot would have points above and below the "rule" that says age is correlated with flexibility by -0.68.

If you notice, you don't have to plot a perfect scatter plot... you have to describe it and it's general shape. So, thinking back to earlier math, if I told you "y" varied with "x", and y changed -0.68 for every change of +1 in x, you could describe that as a line, right? something like y = -0.68x + b

In this case, flexibility is the "function" of age, making it the "y" term... age is the x term.

So flexibility = -0.68(age) + b

That's a diagonal line facing toward the top left... negative slope.

Scatter plot would have a bunch of points all around, above and below but generally near, that line.

Answer 4

P.S. don't worry about the y intercept, "b" :)

Answer 5

Got it! Thank you SO much for a thoroughly explained response! I became a fan! :)

Answer 6

Hey thanks! Can I ask you a minor and self serving favor?

Answer 7

Sure...

Answer 8

Uh, maybe never mind... but do you know how to add a fan testimonial? I think it appears on a person that you have added as your fan?

I've helped a bunch of people and have a pitiful "2" testimonials. It affects your score, apparently, and although I primarily do this because I enjoy helping (and it helps me stay sharp on math), it wouldn't hurt to bump my score up a little.

Your call, completely, but if you thought the discussion was helpful, you could give me a little "bonus" with a testimonial (if you can figure it out... I'm still working through how this site works)

Thanks again, no pressure.. enjoyed the discussion :)

Answer 9

Sure thing! Thanks again. :)