# The Best Fitting Curve

The great thing about using a spreadsheet is that we can change one value and all the other calculaitons will be done for you.

Refer to the population data set again. If we could find the square mean errors for all the possible curves that pass through the mean data point, we would find one that has the least mean square error. Recall that we only guessed another point to find one curve. We can do this in the spreadsheet by cahnging our value of b.

Look at this plot. This is a plot of square mean errors for various b's. This plot is that of a parabola. No matter what your analysis is, the plot of square mean errors versus b will always be a parabola. There will always be a minimum value of the square mean error and two arms that branch upwards.

In the spreadsheet change the value of b in cell E11 to find the value that gives the least square mean error.
Hint: The coefficient of the exponential is sensitive to small changes. Try changing b by 0.01 and work your way up or down to find the best fiting curve.

This is the b for the best-fitting curve. What do you think? ## Exercises

1.) Use your best-fitting equation to the population data to find the population of the U.S. in the year 1996.

2.)Click here to find the true population of the U.S. at this exact moment. How well does this equation predict the real population? (remember to click on Back in Netscape to return to this page.)

3.) For the polonium spreadsheet, find the best-fitting curve.

4.) The half-life of an element is the number of days it takes the amount of an element to divide in half. Using the equation you found in 3), find the half-life of Polonium.