For the problem you are describing (value of property as a function of location and time), there is no "governing equation" as such. (Or at least, if there is one, it would involve VASTLY more parameters than you have defined - interest rates, inflation, wage growth, stock exchange indices, natural disasters, transport infrastructure, fuel costs, political climate and government policy, etc would all be factors.)
The best you can hope to do is to do a "curve fit" or "look-up" approach to an acceptable fit, and using a format that is useful for the intended application - e.g. does your data set have any unusual discontinuities (such as high-priced suburbs in very close proximity to low-priced suburbs); will you be using your generated function to only interpolate between existing data points, or will you also use it to extrapolate beyond the data set; and how will it work across discontinuous or rapidly varying parts of the data-set?
As a trivial example - suppose you have a set of 20 (x,y) data points, which visually approximate to a straight line when plotted in Excel. You apply a linear trend-line, and look at the resulting Equation (which is your first estimate of the "governing equation") and r
2 value (which tells you how well the trend-line fits the data set). Now change the trend-line to a 2
nd order polynomial (i.e. a parabola) - chances are, the r
2 term will be slightly higher than you got for the linear fit.
Hmmm ... that's interesting - what happens if I go to higher and higher order polynomials? As you increase the order of the polynomial, r
2 gets bigger and bigger (Excel will let you go up to 6
th order), but the resulting trend-line gets more and more wiggly - is that actually a better fit to your data?
More importantly - look at the function expressions that are generated for your linear fit and the 6
th order polynomial fit, and calculate what would happen if you try to extrapolate a y-value for an x-value which lies just outside the bounds of your data set. The linear fit will generate predictable values when you extrapolate in either direction, but your 6
th order polynomial is likely to veer off dramatically at one or both ends when you go beyond the bounds of your input data.
Other statistical analysis packages will allow other function fitting approaches - e.g. using cubic splines will allow your interpolated data to fit smoothly and exactly to EVERY point in your data set - but is that actually a "better" fit than a linear trend-line?
Only you can decide which of these approximations to the "governing equation" are actually useful.
