i need help with discussing "errors" in data.

[gonenuclear]

I have a problem in which I was given some data to plot on a graph. Then i use a linear curve fit to display a line and get an equation and correlation coefficient (R). How do I discuss error in terms of accuracy, precision, random errors, systematic errors, trend line R^2 value, and uncertainty. I'm not sure where I begin with this problem. My equation is y = 13.2x - 24.11 with an R^2 value of 0.94. Any help with this issue would be greatly appreciated. Thanks.

 

[btrueblood]

Well, start by defining your terms, i.e. look up

http://en.wikipedia.org/wiki/Accuracy_and_precision

http://en.wikipedia.org/wiki/Least_squares

http://en.wikipedia.org/wiki/Regression_analysis

http://en.wikipedia.org/wiki/Squared_deviations

IMO, forget the trend line R^2 value, it's pretty much meaningless unless you are comparing fits before/after adjusting data sets. Better is to compute the errors for each experimental data point, and plot the errors vs. the independent variable(s), or perform other analyses (Student's t-test, ANOVA...) as you see fit. Bad pun there, sorry.

 

[IRstuff]

Did you ask your instructor?

TTFN

FAQ731-376

 

[gonenuclear]

So for the accuracy I should plug each data point into my equation and see how far the answer for the y value is compared to my true y-values?

 

[btrueblood]

"So for the accuracy I should plug each data point into my equation and see how far the answer for the y value is compared to my true y-values? "

Um, well, that would tell you the "accuracy" of the curve fit. The standard deviation of the errors about a least squares linear fit might also tell you something about the "precision" of the measurements. As to the "accuracy" of the measurements, you would need to have measurements taken of a known standard...

 

[SWComposites]

The book, "Applied Regression Analysis" by Draper and Smith, is a very good text. Suggest you get a copy. You probably need a lot more background info that people can/will post here.