Applying a quadratic regression, I got:
R^2 is 1, so it's about as accurate as it gets.
With this x=4 results in 2804.076
Title pretty much says it all. I have three points: (1, 4.077), (2, 11.667), and (3, 945). I need to come up with an equation that explains a relationship between these three points and should predict what the y value with be at x=4. Also, the equation should always be increasing. Much thanks to anyone who can help me out with this.
if you're not afraid of a little tedious calculations, you can do it by hand.
assume that a quadratic passes through all three points. let this quadratic be of the form
since we pass though the point (1,4.077) we know that f(1) = 4.077
similarly, we know that f(2) = 11.667 and f(3) = 945
thus we can construct a system of three equations:
.....................(1)
................(2)
.....................(3)
now solve for a,b, and c and you will have your curve
Let me teach you how to do it with the program "Graph 4.3".
1)Click FUNCTION.
2)INSERT POINT SERIES.
3)Label the points and click OK.
4)Right-click on the left hand side which is the point series.
5)Select INSERT TREDLINE.
6)Select the least-squares approximation you want.
7)You can also gaze upon the "r^2" value which tells you how good approximation is, if r^2=1, then it is perfect.