Help on using R^2 and phrasing why I used it?

Question

I've got some data where I'm plotted two variables, J(V). I also have a model for J(V).

Specifically I want a value related to dJ/dV at V=0. So to get that, I've taken the data around V=0 and used excel's linear regression to get a gradient, which I will report along with the associated error. I also expect that at this point it will be of the form J=mV + c

In order to show that my range of V is valid, can I use R^2?

I've plotted the graphs and got values of R^2 all exceeding 0.997. Is it fair to state that the linear model explains 99.7% of the variance in that range and therefore it's fine to use? (paraphrased from a friend - I don't have access to my paper copies of stats info right now).

Is this the right thing to do and if so, how do I phrase it?

Merlyn · Accepted Answer

You are correct in the interpretation "linear model explains 99.7% of the variance in that range" but that is it.  If you want to complete that note you would have said the "linear model explains 99.7% of the variance in that range", assuming that a linear model is valid to use.

R², the coefficient of determination is the measure of the variability in the responses explained by the variablity in the predictors, assuming the model is correct.  A good example of this is a cubic function, near the inflection point, can be modeled with a line very well, and in random data sets, you'll have a very good R² but we know that the line is not correct.

If you want to justify using the line, then use residual plots to check assumptions of independent and identically distributed error terms.  If there is not evidence of a violation of the model assumptions then you can say that based on the residual plots.

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Help on using R^2 and phrasing why I used it?

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