Correlation coefficients?

Question

I am utterly confused by linear and quadratic forms of correlation coefficients. How do I mathematically determine whether or not a graph is linear or quadratic? Do I use the value of r^2? If so, what does that value tell me in relation to whether or not the graph can be mathematically proved as linear or quadratic?

I know my question is somewhat silly, but I'm merely bewildered by this.

Answer 1

Well, in the context of correlation coefficients. The closer a correlation coefficient is to 1, the more linear it is. Secondly by r^2, do you mean R^2 the coefficient of determination? That value explains how much of the variation in Y values is caused by the linear relationship with X values. Again, higher R^2 = more linear.

Another good way to check is to plot residuals from your regression line. If the residuals form a random scattering about zero, then your regression was probably the correct one. For instance, if you have a quadratic and you plot like it were linear. The residuals from regression would most likely form some pattern. Then if you re-did it as a quadratic and got random values, that would show you've chose an appropriate model.

Answer 2

in accordance to N.Shaviv & R. Pielke the contributions of AGHG to climate substitute is approximately 20% and something is by organic forcings. Correlations attitude has many weak point as reported by R. Grumbine. One final piece. forged your eyes back as much as the graph, and probably click on it to get the completed length version. in direction of the your best option hand end, you notice a dot it extremely is a ways above the promptly line greater healthful. you're no longer shocked that it extremely is 1998 -- the 12 months of the main El-Nino that grow to be concurrent with a time of severe image voltaic pastime. The bit farthest decrease than the curve around 357 ppm CO2 is 1992-3 -- cooling effects of Mount Pinatubo. Even against a statistically solid vogue, there are nevertheless different effects interior the gadget that can supply some tenths of a level climate differences. there are a number of reasons climatologists do no longer attitude climate this way, and that they are solid ones. I in basic terms did it because of fact i've got been encountering sources that say that the correlation is 0 (nonexistent). those places are incorrect.