A set of data is known, and how to derive a function between the two

If it is not the test data processing in the university, it can be solved by using Excel. After establishing a chart based on the above two sequences in excel, you can choose the way to fit the curve to the coordinates after observation, I can basically use linear curve fitting to observe, and the equation for fitting the curve given by excel is:

f(x)=, and its fitting accuracy r 2=

If fitted with a polynomial, the equation for the 3rd order curve is:

f(x)=, fitting accuracy r 2=

Of course, you can also choose polynomial 2nd curve fitting, logarithmic fit, etc., but by looking at the images, I think the two fitting curves given above are very close.

If it is the fitting of the experimental data in the university, it needs to be carried out in strict accordance with the data processing method:

1.To determine the validity, excluding the value of the change, you can choose 3 sigma level standards.

2.The coordinate system is mapped and observed, and the curve category is fitted according to the image trend conjecture.

3.Set the equation and use the curve fitting formula (I don't remember exactly, you can check other curve fitting data) to fit, and find r 2 and coherence values.

4.If it is within the range of accuracy satisfaction, it can be used, if not, continue to improve the accuracy (e.g., fit with a higher order curve equation) until the requirement is satisfied.

In fact, I don't have to do it so much after the university experiment, and many math software can easily do it, such as mathlab or even Lindu, Lingo and other software.

Of course, if you are only a middle school student, just guess that it is a linear curve, let the equation:

f(x)=ax+b, use the knowledge in middle school physics to make a straight line on the image, select the point and bring in the evaluation.

Images of these data are made in Cartesian coordinate systems to see the distribution trend of the images.

Make points of these data in a Cartesian coordinate system, connect lines, then observe the image, guess what function it is based on the image, and then derive the function expression based on what you have learned.

Let n equations form a system of equations.

The coefficients and constant terms are set to unknowns, and only x and f(x) are known conditions.

x=[2:15]；

y=[Copy the data, space space];

plot(x,y,'o'Draw a scatter plot.

p=polyfit(x,y,2)

Just confirm it, p is the coefficient of polynomial fitting, and you can choose the polynomial twice in this place.

According to the trend, this should be a gradual convergence to, and should be a tired exp(-x)+

MATLAB can be fitted with special functions, which you can find in relevant books and directly look up commands, and you can get this curve. I won't remember the exact name either.

Use log to get the following number x y for two sets of numbers, and then use the trend line in excel.

y = -r² =

I don't know if that's right

Regression analysis methods do!

The so-called regression analysis method is based on mastering a large amount of observation data, using mathematical statistical methods to establish the regression relationship function expression between the dependent variable and the independent variable (called the regression equation). In regression analysis, when the causal relationship under study involves only the dependent variable and an independent variable, it is called univariate regression analysis; When the causal relationship under study involves a dependent variable and two or more independent variables, it is called multiple regression analysis. In addition, regression analysis is divided into linear regression analysis and nonlinear regression analysis according to whether the expression of the function describing the causal relationship between the independent variable and the dependent variable is linear or nonlinear.

Linear regression analysis is usually the most basic analysis method, and nonlinear regression problems can be solved by mathematical means.

Specifically, you can check out books on statistical regression.

It seems to be very deep, and there is no solution!