I'm making a graph of force vs stretch for springs. I have 7 data trials with the k (F = kx) ranging from 28 to 31, average is 29.6.

Question

Now I need to find the slope and write an equation for the graph. If I use the first two points to get the slope, I get a slope of 29.4. If I use the first point and the last point, I get a slope of 28. I understand the larger interval would give the best value, but using the first two points to compute it gives a slope closer to my "k" value. I know the slope is my spring constand or k value so they should be close.

Question is: which interval should I use: first and second points or first and last points to compute the slope.

Answer 1

You should use all three and minimize the square error when fitting a straight line through the origin.

It's called a linear regression best fit.

This will also give you an error estimate.

Answer 2

So my slope doesn't have to be so exact to the k value?

When I use the equation to predict the stretch, I get a value of .085 using the first two points and a value of .089 when using the first and last points. The given data table lists the actual stretch at 0.085.

So in showing my work, which 2 points should I use?

Answer 3

You should use all seven of your data points, and a linear regression curve-fitting technique. There are tools online at places like
http://people.hofstra.edu/Stefan_Waner/RealWorld/newgraph/regressionframes.html