can a curve on a graph have more than 1 line of best fit?

Question

im drawing a calibration curve for my physics coursework. its quite a steep, straight graph at first and then it makes a gentle curve. i'm able to make 3 lines of best fit that would describe the gradient of the graph well. but am i allowed to make 3 lines of best fit and therefore, get 3 different gradients for the curve?

Answer 1

I believe that for the whole graph there can only be 1 line of best fit.

Answer 2

The way you're asking, it appears that you want to model one set of data, but it isn't linear? Then you can do some different things.

First, you may need to do a transformation to straighten it out. Depending on the shape, you might graph y v. x^2 or y v. 1/x or log(y) v. x or log(y) v. log(x), etc. If that straightens the graph out then you can do a line of best fit for the new data.

Otherwise you seem to be talking about defining the function piecewise. You could say 'the data are modeled by the line y = a + bx for values of x from 0 to 25, then the line y = c + dx for values of x greater than 25.' This is perfectly acceptable.

However, what do you know of the underlying science? Is there some reason that the model would change at some point? If not, you would not look for a piecewise definition. You would want one model to explain the entire relationship.

Answer 3

There are computer programs that will give you the best-fit curve, but you can eye-ball it unaided. Don't give the first and last points any more importance than any of the others. The curve doesn't have to pass through any of the points. Read Wikipedia on curve fitting.

Answer 4

You may only make one line of best fit... seeing as it is the "Best Fit". Not one of 3 that best fit... make sure your line is straight and does not curve as a line of best fit does not curve at all.

Answer 5

best can only be one