I have a dataset composed of 7 or 8 data points. I think the relationship between Y and X should be Y=AX+B+C (where A and B are constants and C is a random number), and at least Y should increase with the increase of X from (0, +infinity(or a number big enough for me). while I was still open to other probabilities (for example, whether it is Y=AX^1.01+B+C or Y=AX^0.99+B+C or Y=AX^2+DX+B+C, with D being another constant), I am confused on how can I determine which of the possibilities are true, or at least possible. You are really kind if you can answer my question...
Matlab provides an easy tool to help you : the Curve Fitting Toolbox (cftool command to start)
You specify x and y data from the workspace (also z if necessary), and you choose a model in a provided list : linear, power, gaussian, exponential, etc. You can also define your own model (custom equation).
Matlab will compute the parameters of your model (for example a and b coefficients if you are using a linear model y = ax+b) as well as the goodness of the fit.
Expressing the equation as Y+C1 = A(X+C2)+B might clarify. C1 and C2 being the noise in Y and X measurements, respectively
If you have a reason to expect the relationship to be a straight line, just calculate the errors in X and Y measurements, draw the resulting rectangle for each data point and see if a straight line can be found that intersects all of them. With only 7 or 8 points it should be no big job.
If such a straight line does not exist, the equation is not a straight line and your physics needs to be re-examined or your measurements have additional problems.
You can use a Lagrance interpolation polynom. If there is a function f such that y=f(x) for your 7 or 8 points, you can approximate f by a polynomial.
@Ron Larham
1. What do you want to do with the relationship when you have found it?
I am trying to find the correlation between score (something from computer) and the IC50 of the compounds that my group have synthesized. I want to use the equation to predict the IC50 of virtually designed compounds.
2. Do you have a theoretical reason for preferring one form of relation over another?
I am doing docking, a computer-aided way of estimating the binding energy (ΔG) between molecules and proteins. Theoretically, the ΔG should positively related to (-log(Km)) in enzyme kinetics in a linear way, and (-log(Km)) should have a linear relation with IC50 of a reversible inhibitor.
3. How were the data collected?
The estimation of ΔG (i.e., the score) is from running computer simulations, and the IC50 is from inhibition assays.
4. Plot a scatter diagram, does this suggest anything?
Well... if I include a specific spot into the graph it seems as if the correlation should be Y=AX^2+BX+C, but if I do not include this spot, I would rather consider them as more linear than including that spot.
Finally without knowing what you are trying to do, or seeing your data we will only be able to give very general advice.
Here, I have attached the result. The spot which is a little different (with which the correlation would be more bent towards AX^2) has been labeled red.
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