Bell Curve Regression question

Is there any way to make this regression equation more accurate ? Is their anyway to weight it ?

I'm not enough of a statistician to know the ins and outs of "weighting" points in something like this. When I have done "weighted" regressions, I have recreated the regression matrix so that each point has as many copies as weights. In your case, that would amount to 6500 data points. Which is ok, assuming Excel's LINEST() function can handle that large of an input matrix. If that is what you mean by "weighting", I think that will be the only way to approach it using the LINEST() function -- "expand" the regression matrix so there are, for example, 282 copies of the age 18 entry.

If you are allowed to look beyond the LINEST() function, you can set the regression up using Solver. Select an objective function, guess at some parameters (you could conceivable use the unweighted regression as a starting point), compute your objective function, then call Solver and tell it to minimize/maximize your objective function by changing the regression parameters. Your spreadsheet currently has a column for "residuals" (column G). A simple sumproduct of the residuals with the weights (=SUMPRODUCT(G7:G29,B7:B29)) might make a suitable objective function. Put that somewhere, then call Solver and tell it to minimize this sumproduct() function by changing D31:D33.

I cannot readily think of anything. The data are so "noisy", especially towards the ends, that all three regressions look "equally good" to me. I might even suggest that a quadratic might be "overfitting" the data, and you could limit yourself to a straight line and get an equally good fit.

It looks like an interesting analysis.