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# Curve Fitting

It is easier to understand the graphical view rather than mathematical view, that’s why Curve Fitting Statistics is useful in statistics, curve fitting statistics is a way to represent large number of data in the form of curve. Proper definition of curve fitting statistics states that it is a way to represent best fit curve of large amount of data. With the help of these fitting curves, we can easily visualize the whole data and we can easily summarize the data means we can easily judge that where data is placed and we can easily judge relationship between data. Now we will discuss how we fit curve into statistics.
We use following steps, which shows whole procedure of statistics curve fitting-
Step1: First of all, we judge what type of equation we have, means its first order, second order or n- order like
First order equation f(x) = ax + b
Second order equation f(x) = ax2 + bx + c
.
.
.
n- order equation f(x) = axn + bxn-1 + cxn-2 +................+ d.
Step 2: After evaluating the curve equation, we will analyze how many constraints are there, constraints can be any points, angle or curvature like
If f(x) = ax + b, it is like a Slope equation where this type of curve contains exactly two fit points,
And angle of this curve equation is tan θ = a.
If f(x) = ax2 + bx + c, then this type of curve contains exactly three fit points, where angle of this curve equation is tan θ = (dy / dx).
If f(x) = ax3 + bx2 + cx + d, then this type of curve contains exactly four fit points, where angle of this curve equation is tan θ = (dy / dx).
Step 3: After evaluation of these constraints, we make suitable curves like ellipse, circle, rectangle, sphere etc.
For making this kind of curve, first we find out what kind of error is there in given curve equation by following method -
Step 1: If we have a function f(x) = a + bx or y – (a + bx) = 0, then we calculate sum of Square -
Where sum of square is R2 (a, b) = ∑i=1n [y – (a + bx)]2.
Step 2: After evaluation of sum of square, we can calculate the condition where R2 (a, b) is minimum,
dR2 / dai (a, b) = -2 . ∑i=1n [y – (a + bx)],
For critical points, above condition should be 0
dR2 / dai (a, b) = 0,
dR2 / dai (a, b) = -2 . ∑i=1n [y – (a + bx)] = 0,
After evaluating above sum equation, it produces value of ‘a’ and ‘b’-
Step 3: After evaluation of ‘a’ and ‘b’, we calculate standard errors for ‘a’ and ‘b’ by following formula -
Standard error of a = SE(a) = s . √(1 / n + x2 / ssx)
Standard error of b = SE(a) = s / √ ssx
Where ssx is a regression and ‘s’ is variance.
This method is used for finding errors in curve equation.

## Polynomial Curve Fitting

Curve fitting can be thought as process of finding a function in mathematics that best fits a sequence of data points. Here we will discuss polynomial Curve Fitting This is to be done by abiding to some rules of fitness. Different techniques we use for purpose of curve fitting are: smoothing and interpolation. Various examples for curve fitting can be Linear Reg...Read More

## Least Squares Curve Fitting

Curve fitting when done by method of least squares Curve Fitting, we assume such curves that are best fit with minimum abnormalities squared (least squared error) from a given sample of data.
Suppose we have data points as (x1, y1), (x2, y2)… (xn, yn). Where, “x” is an independent variable and 'y' a dependent variable. Curve that we get after fitting F (x) h...Read More

## Curve Fitting Algorithm

Curve fitting algorithm in mathematics deals with estimating those data points in given Set of samples for which curves are best fitted. There are several techniques that we follow to implement this algorithm. Let us discuss them in brief as follows:
1.      Least squares Curve Fitting: This curve fitting technique is based on the use of least squares, which use...Read More

## Exponential Curve Fitting

Exponential Curve Fitting is a type of curve fitting method that uses Functions with expressions containing exponential terms. We have different types of exponential functions that can best suit this fitting method:
1.      Y = A BX + C
2.      Y = A eXB + C
3.      Y =  e2XA + BX + C
4.      Y = A BX
5.      Y = A eX
Where, 'e' is a mathematical term (ba...Read More

## Linear Function

Calculus is based upon the linear Functions. Linear Functions are the functions whose graphs consist of sections of one straight line throughout the function's Domain.
Linear function Statistics can be defined as the funct...Read More

## Best Fit Lines

From statistical Point of view Best fit lines Statistics very important in many aspects. If we want to draw best fit line then we need scatter-plot to find the direction. Scatter-plot is dimensional graph which display lots of point and show the relationship between two variables. These two variables are explanatory variables and response variables. Where, explanatory var...Read More

## Scatter Plots

Statistics scatter plots is a graph, which plots a Point and all these points shows some relationship between two Sets of data like we have a data of our country population and when create a graph of persons between their height and weight, it shows some dotted graph, where each dot represents each person’s height and weight.
So, this dotted graph, which represents relati...Read More