I made two graphs and found the correlation coefficients r^2. Help me with this question please?

Question

anonymous · Answer

Is the difference in the two R2-values calculated in the two problems above significant? What do the two R2-values say about your cubic and quartic polynomial models?



R^2 = 0.994408 for the first
R^2 = 0.996725 for the second

anonymous · Answer

@mathmale

mathmale · Answer

Morning!  
You know me by now.  I'd like for you to explain in your own words what "R^2" means in practical terms, what its name is and how it's related to the correlation coefficient, r.

anonymous · Answer

Okay, I am all up for that.

mathmale · Answer

I'm feeling a little bad for having dumped such a big load of questions in your lap, but knowing what you know about r^2 will help me respond to your question.

anonymous · Answer

So far I just no that "r" is the correlation coefficient

mathmale · Answer

Right.  We've talked about that a couple of times.  Any clue at all what r^2 means?

anonymous · Answer

I would say that it is the correl. coeff. squared

mathmale · Answer

Certainly is.  I'm curious:  when in a situation in which you're not certain what something such as r^2 means, what do you typically do to investigate it?  Have you tried any of those actions yet?

anonymous · Answer

No I have not tried anything of that sort. And sorry that it has been taking a while to reply. My mom and dad are both at work and both of my siblings have friends over, so I am the adult of the house today.

mathmale · Answer

Lot of responsibility for you, not to mention your having to learn these principles of statistics.

r:  correlation coefficient

r^2:  coefficient of determination.  Have you heard or read anything about that?

anonymous · Answer

Not really, just correlation coefficient

mathmale · Answer

Even though I can explain the coefficient of determination, I'm always hoping that you'll look up such terms in whatever resources you have available:  book, syllabus, Internet, etc.

the coeff. of det., r^2, tells us what percentage of the variation in the dependent variable (usually y) is explained by the independent variable (usually x).

mathmale · Answer

You have in front of you two r^2 values.

Both are very, very close to 1, aren't they?

What this tells you is that your two different models  very closely and accurately model the actual relationship between x and y in each case.

If, however, r^2 were .6 (for example), only 60% of the variation in y would be explained by the model you've developed, meaning that the other 40% would be explained by factors other than x.

mathmale · Answer

Is the difference in the two R2-values calculated in the two problems above significant? What do the two R2-values say about your cubic and quartic polynomial models?


R^2 = 0.994408 for the first
R^2 = 0.996725 for the second

Answering a question that has to do with how much one variable influences another quantity is at best an approximation, so I would respond to the first question, above, by saying something like, "No, the difference in the two r^2 values are not particularly significant.  One rounds off to 0.99, the other to 1.00, a difference of only 1%.  

2nd question:  "These two r^2 values, rounding off as they do to 1.00 and 0.99 respectively, both indicate that the cubic and quartic models are excellent representations of the data on which they are founded:  Just about 100% of the variation in y with x, in each case, is explained by the associated model."

I don't expect you to come up with such fancy language, but would certainly hope that you could give a fairly accurate explanation, in your own words, of what r^2 stands for, how it's obtained and what it means.

mathmale · Answer

guess you're tied up with other responsibilities.  Just respond when you're back.  I'll be away from my computer for a while.  MM