# How to plot a polynomial curve?

I have used Calc to perform a polynomial regression on a two-dimensional dataset (x,y) by

- charting the two-dimensional dataset as a scatterplot (Chart Type: Line, Points Only),
- fitting a polynomial curve with 4 degrees (Insert Trend Line), and
- displaying the coefficient of determination of a linear regression and the equation of the polynomial curve (Insert R² and and Trend Line Equation).

The coefficient of determination is very good (0.984) and the trend line fits the data.

I have then applied the equation of the polynomial curve to calculate values of y given x, but the results do not fit the data, the error/divergency increases with x.

The “Trend Line Equation” is: f(x) = - 0 x^4 + 0.0029 x^3 - 0.1063 x^2 + 0.8729 x + 1.7942

I have applied the following function:
=-(0*A2^4)+(0.0029*A2^3)-(0.1063*A2^2)+(0.8729*A2)+1.7942

My questions are

- Can the coefficient of determination of a linear regression (R²) provide valid information about the fit of a polynomial curve?
- What is/are the alternative/s?
- How do I calculate y given x using the “Trend Line Equation”?

*EDIT*

Always (except for very rare cases) attach or make available "the real thing", here the

.ods.I will see to get enough "karma" for you to be able to attach directly to your question (by editing it).

Did you already try a polynomial approximation using LINEST()? (Do you know how?)

355^4 is about 1.6*10^10. The predefined format of the topmost coefficient surely suppresses significant digits. Factually you got your second table based on a fake approximation of third order therefore.

Thanks for the hint, I did not know I could attach (.ods) files to my post! I find that my charts get dislocated everytime I close and open my .ods file (I have tried to Anchor To Page and Anchor To Cell) and I thought the screenshots to be most easily readable. I have now attached my files to my post.