Ask for constructing function from coordinate(x,y) points

[bundit]

Hello,

I'm new in this forum. I would like to know how to calculate to obtain the function expression of some given coordinate points(x,y). For example, if I have 6 coordinate points which are

(x,y)
(0.23, 4.5)
(0.25, 6.5)
(0.35, 8.8)
(0.43, 15)
(0.45, 17)
(0.5, 25)

The (x,y) relation are apparently not linearized. It seems to by y=a.exp(b.x). How to calculate to derive the equation of y in term of y=f(x)?

Thank you.
Bundit

 

[Ackbach]

My recommendation: Excel. Plot the points up in Excel, and try fitting trendlines of various types to your data. Warning: six points isn't going to give you that much information. Do you need to interpolate or extrapolate?

The best fit I found (without going to very high-order polynomials) was
$$y=303.31x^{2}-151.14x+24.221,$$
with an $R^{2}$-value of $0.9895$. You can do a bit better with a cubic:
$$y=1357.5x^{3}-1205.6x^{2}+387.32x-36.859,$$
with an $R^{2}$ value of $0.9968$.

 

[TheBigBadBen]

To compare, here is the exponential best fit from wolfram alpha

exponential fit (0.23, 4.5) (0.25, 6.5) (0.35, 8.8) (0.43, 15) (0.45, 17) (0.5, 25) - Wolfram|Alpha

with R^2 value 0.9969

 

[bundit]

My recommendation: Excel. Plot the points up in Excel, and try fitting trendlines of various types to your data. Warning: six points isn't going to give you that much information. Do you need to interpolate or extrapolate?

The best fit I found (without going to very high-order polynomials) was
$$y=303.31x^{2}-151.14x+24.221,$$
with an $R^{2}$-value of $0.9895$. You can do a bit better with a cubic:
$$y=1357.5x^{3}-1205.6x^{2}+387.32x-36.859,$$
with an $R^{2}$ value of $0.9968$.

Thank you,Ackbach.
By the way, can you brief me the definition of R^2 in your quote.?

Thanks.
Bundit

 

[blue_raver22]

,

Thank you for your question. To find the function that best fits the given coordinate points, you can use a method called curve fitting. This involves finding a mathematical equation that closely approximates the data points.

One approach to do this is by using a regression analysis, where you can use a computer program or a graphing calculator to find the equation that best fits the data points. There are different types of regression methods, such as linear, exponential, and logarithmic, that can be used depending on the nature of the data.

In your case, since the relation between x and y appears to be exponential, you can use an exponential regression to find the equation. This will give you the values of a and b in the equation y = a.exp(b.x), which you can then use to calculate the function y = f(x).

I hope this helps. Let me know if you have any further questions.