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i need help with discussing "errors" in data.

thread962-261269

i need help with discussing "errors" in data.

i need help with discussing "errors" in data.

(OP)
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.   

RE: i need help with discussing "errors" in data.

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.

RE: i need help with discussing "errors" in data.

(OP)
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?

RE: i need help with discussing "errors" in data.

"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...

RE: i need help with discussing "errors" in data.

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.

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