My current maths course, HL IB, has posed the following question which I have no idea how to solve 'properly'. The question involves being given data and then you must fit a line of best fit through the data mathematically. The only way to fit the data I know is a straight line using Least Squares Method. Thus I must find what order the data will fit in order to raise the y values to this power in order to get a straight line.

Using Excel I just kept raising the Y values by powers, and graphing X against Y^(whatever value), till I got a straightish line, which happened to be the value to the power of 4, which meant I was graphing X on x-axis, and Y^4 on y-axis.

I also just to see what would happen changed the x-axis to a logarithmic scale and it produced a line that looked also kind of straight.

These two methods produced straight lines but only graphically and done by eye. So my question is, is there a way mathematically (pretty much algebraically) to determine this exponent value or logarithmic value?

Cheers

Qwertyuiop23

This is the data table shown below:

Code:

**X | Y**
50 | 36
100 | 41
200 | 52
300 | 59
400 | 60
500 | 63
600 | 67
800 | 72
1000 | 75
1500 | 86
2000 | 92