We have already discussed two different methods, for getting the best fit line to scatter. Read: Matplotlib plot a line Matplotlib best fit line to scatter Plt.title('2nd degree best fit curve using numpy.polyfit()') # Plotting the data points and the best fit 2nd degree curve Y_line = theta + theta * pow(X, 1) + theta * pow(X, 2) # the parameters theta0, theta1 and theta2 # Now, calculating the y-axis values against x-values according to # Calculating the parameters using the least square method # Preparing X and y data from the given data # Preparing the data to be computed and plotted Now, let’s implement this algorithm using python and plot the resulted line. X) -1 is the inverse of the resulted matrix from (X T.

y) Here, X T is the transpose of the matrix X, and (X T.

We can calculate and get the optimal parameter values (theta0 and theta1) for the given data points by using the least square method equation in vector form, that is as follows: Now, the equation in vector form will be like this: y = X. Let, X be the matrix of 2XN where 1st column consists of value 1 for each row and 2nd column consists of the x-coordinate values of the N data points.Let, theta be the column vector of 2 rows with each parameter of the line ( theta0 and theta1) be as the row value of the vector.Let, the y be the column vector of N rows where each row represents the y-coordinate of each data point.Let, N be the number of data points given.Now, let’s change this equation into the vector form: Let’s change this into y = theta0 + (theta1 * x) Here, theta0 and theta1 are the parameters representing the c (intercept) and m (slope) respectively of the line. The equation of the line is: y = (m * x) + c We will be doing it by applying the vectorization concept of linear algebra.įirst, let’s understand the algorithm that we will be using to find the parameters of the best fit line. First, we need to find the parameters of the line that makes it the best fit. We can plot a line that fits best to the scatter data points in matplotlib. Read: Matplotlib subplot tutorial Matplotlib best fit line The simple regression analysis is the method of specifying a relationship between a single numeric dependent variable (Here, y) and a numeric independent variable (Here, x). The most commonly used method to find the parameters of a line to best fit the given data points is the least square method in regression analysis. We will be using the slope-intercept form of the line throughout this post. On comparing this equation with the slope-intercept form of a line.

We can convert a normal form to the slope-intercept form as follows: Intercept is the parameter of the line that decides the position of the line on the graph. c is the constant value that represents the y-intercept of the line on the graph.Slope is the parameter of the line that decides the angle of the line on the graph. m is the coefficient of the variable x which represents the slope of the line on the graph.Collectively, these are known as the parameters of a line which decides the line’s shape and position on the graph.īut, the most commonly used form of a line is the intercept-slope form, which is as follows: A and B are the coefficients of variable x and y, and C is the constant.Here, x and y are the variables that represent the x-axis and y-axis values of data points.The normal equation of the line is as follow: The best fit line or optimal relationship can be achieved by minimizing the distances of the data points from the purposed line.Ī linear equation represents a line mathematically. The best fit line in a 2-dimensional graph refers to a line that defines the optimal relationship of the x-axis and y-axis coordinates of the data points plotted as a scatter plot on the graph. Matplotlib best fit line using numpy.polyfit().

Matplotlib scatter c