Matplotlib is easy to use and an amazing visualizing library in Python. It is built on NumPy arrays and designed to work with the broader SciPy stack and consists of several plots like line, bar, scatter, histogram, etc.
In this article, we will learn about Python plotting with Matplotlib from basics to advance with the help of a huge dataset containing information about different types of plots and their customizations.
Table Of Content
Recent Articles on Matplotlib !!!
Getting Started
Before we start learning about Matplotlib we first have to set up the environment and will also see how to use Matplotlib with Jupyter Notebook:
After learning about the environment setup and how to use Matplotlib with Jupyter let’s create a simple plot. We will be plotting two lists containing the X, Y coordinates for the plot.
Example:
Python3
import matplotlib.pyplot as plt # initializing the datax = [10, 20, 30, 40]y = [20, 30, 40, 50] # plotting the dataplt.plot(x, y) # Adding the titleplt.title("Simple Plot") # Adding the labelsplt.ylabel("y-axis")plt.xlabel("x-axis")plt.show() |
Output:
In the above example, the elements of X and Y provides the coordinates for the x axis and y axis and a straight line is plotted against those coordinates. For a detailed introduction to Matplotlib and to see how basic charts are plotted refer to the below article.
In the above article, you might have seen Pyplot was imported in code and must have wondered what is Pyplot. Don’t worry we will discuss the Pyplot in the next section.
Pyplot
Pyplot is a Matplotlib module that provides a MATLAB-like interface. Pyplot provides functions that interact with the figure i.e. creates a figure, decorates the plot with labels, and creates a plotting area in a figure.
Syntax:
matplotlib.pyplot.plot(*args, scalex=True, scaley=True, data=None, **kwargs)
Example:
Python3
# Python program to show pyplot moduleimport matplotlib.pyplot as plt plt.plot([1, 2, 3, 4], [1, 4, 9, 16]) plt.axis([0, 6, 0, 20]) plt.show() |
Output:
Refer to the below articles to get detailed information about Pyplot and functions associated with this class.
- Pyplot in Matplotlib
- Matplotlib.pyplot.plot() function in Python
- Matplotlib.pyplot.title() in Python
- matplotlib.pyplot.imshow() in Python
- Matplotlib.pyplot.legend() in Python
- Matplotlib.pyplot.subplots() in Python
- Matplotlib.pyplot.colors() in Python
- Matplotlib.pyplot.grid() in Python
>>> More Functions on Pyplot class
Matplotlib take care of the creation of inbuilt defaults like Figure and Axes. Don’t worry about these terms we will study them in detail in the below section but let’s take a brief about these terms.
- Figure: This class is the top-level container for all the plots means it is the overall window or page on which everything is drawn. A figure object can be considered as a box-like container that can hold one or more axes.
- Axes: This class is the most basic and flexible component for creating sub-plots. You might confuse axes as the plural of axis but it is an individual plot or graph. A given figure may contain many axes but given axes can only be in one figure.
Figure class
Figure class is the top-level container that contains one or more axes. It is the overall window or page on which everything is drawn.
Syntax:
class matplotlib.figure.Figure(figsize=None, dpi=None, facecolor=None, edgecolor=None, linewidth=0.0, frameon=None, subplotpars=None, tight_layout=None, constrained_layout=None)
Example 1:
Python3
# Python program to show pyplot moduleimport matplotlib.pyplot as plt from matplotlib.figure import Figure # Creating a new figure with width = 5 inches# and height = 4 inchesfig = plt.figure(figsize =(5, 4)) # Creating a new axes for the figureax = fig.add_axes([1, 1, 1, 1]) # Adding the data to be plottedax.plot([2, 3, 4, 5, 5, 6, 6], [5, 7, 1, 3, 4, 6 ,8])plt.show() |
Output:
Example 2: Creating multiple plots
Python3
# Python program to show pyplot moduleimport matplotlib.pyplot as plt from matplotlib.figure import Figure # Creating a new figure with width = 5 inches# and height = 4 inchesfig = plt.figure(figsize =(5, 4)) # Creating first axes for the figureax1 = fig.add_axes([1, 1, 1, 1]) # Creating second axes for the figureax2 = fig.add_axes([1, 0.5, 0.5, 0.5]) # Adding the data to be plottedax1.plot([2, 3, 4, 5, 5, 6, 6], [5, 7, 1, 3, 4, 6 ,8])ax2.plot([1, 2, 3, 4, 5], [2, 3, 4, 5, 6]) plt.show() |
Output:
Refer to the below articles to get detailed information about the Figure class and functions associated with it.
- Matplotlib.figure.Figure() in Python
- Matplotlib.figure.Figure.add_axes() in Python
- Matplotlib.figure.Figure.clear() in Python
- Matplotlib.figure.Figure.colorbar() in Python
- Matplotlib.figure.Figure.get_figwidth() in Python
- Matplotlib.figure.Figure.get_figheight() in Python
- Matplotlib.figure.Figure.subplots() in Python
>>> More Functions in Figure Class
Axes Class
Axes class is the most basic and flexible unit for creating sub-plots. A given figure may contain many axes, but a given axes can only be present in one figure. The axes() function creates the axes object. Let’s see the below example.
Syntax:
matplotlib.pyplot.axis(*args, emit=True, **kwargs)
Example 1:
Python3
# Python program to show pyplot moduleimport matplotlib.pyplot as plt from matplotlib.figure import Figure # Creating the axes object with argument as # [left, bottom, width, height]ax = plt.axes([1, 1, 1, 1]) |
Output:
Example 2:
Python3
# Python program to show pyplot moduleimport matplotlib.pyplot as plt from matplotlib.figure import Figure fig = plt.figure(figsize = (5, 4)) # Adding the axes to the figureax = fig.add_axes([1, 1, 1, 1]) # plotting 1st dataset to the figureax1 = ax.plot([1, 2, 3, 4], [1, 2, 3, 4]) # plotting 2nd dataset to the figureax2 = ax.plot([1, 2, 3, 4], [2, 3, 4, 5])plt.show() |
Output:
Refer to the below articles to get detailed information about the axes class and functions associated with it.
- Matplotlib – Axes Class
- Matplotlib.axes.Axes.update() in Python
- Matplotlib.axes.Axes.draw() in Python
- Matplotlib.axes.Axes.get_figure() in Python
- Matplotlib.axes.Axes.set_figure() in Python
- Matplotlib.axes.Axes.properties() in Python
>>> More Functions on Axes Class
Setting Limits and Tick labels
You might have seen that Matplotlib automatically sets the values and the markers(points) of the x and y axis, however, it is possible to set the limit and markers manually. set_xlim() and set_ylim() functions are used to set the limits of the x-axis and y-axis respectively. Similarly, set_xticklabels() and set_yticklabels() functions are used to set tick labels.
Example:
Python3
# Python program to show pyplot moduleimport matplotlib.pyplot as plt from matplotlib.figure import Figure x = [3, 1, 3] y = [3, 2, 1] # Creating a new figure with width = 5 inches# and height = 4 inchesfig = plt.figure(figsize =(5, 4)) # Creating first axes for the figureax = fig.add_axes([0.1, 0.1, 0.8, 0.8]) # Adding the data to be plottedax.plot(x, y)ax.set_xlim(1, 2)ax.set_xticklabels(( "one", "two", "three", "four", "five", "six")) plt.show() |
Output:
Multiple Plots
Till now you must have got a basic idea about Matplotlib and plotting some simple plots, now what if you want to plot multiple plots in the same figure. This can be done using multiple ways. One way was discussed above using the add_axes() method of the figure class. Let’s see various ways multiple plots can be added with the help of examples.
Method 1: Using the add_axes() method
The add_axes() method figure module of matplotlib library is used to add an axes to the figure.
Syntax:
add_axes(self, *args, **kwargs)
Example:
Python3
# Python program to show pyplot moduleimport matplotlib.pyplot as plt from matplotlib.figure import Figure # Creating a new figure with width = 5 inches# and height = 4 inchesfig = plt.figure(figsize =(5, 4)) # Creating first axes for the figureax1 = fig.add_axes([0.1, 0.1, 0.8, 0.8]) # Creating second axes for the figureax2 = fig.add_axes([0.5, 0.5, 0.3, 0.3]) # Adding the data to be plottedax1.plot([5, 4, 3, 2, 1], [2, 3, 4, 5, 6])ax2.plot([1, 2, 3, 4, 5], [2, 3, 4, 5, 6])plt.show() |
Output:
The add_axes() method adds the plot in the same figure by creating another axes object.
Method 2: Using subplot() method.
This method adds another plot to the current figure at the specified grid position.
Syntax:
subplot(nrows, ncols, index, **kwargs)
subplot(pos, **kwargs)
subplot(ax)
Example:
Python3
import matplotlib.pyplot as plt # data to display on plots x = [3, 1, 3] y = [3, 2, 1] z = [1, 3, 1] # Creating figure object plt.figure() # adding first subplot plt.subplot(121) plt.plot(x, y) # adding second subplot plt.subplot(122) plt.plot(z, y) |
Output:
Note: Subplot() function have the following disadvantages –
- It does not allow adding multiple subplots at the same time.
- It deletes the preexisting plot of the figure.
Method 3: Using subplots() method
This function is used to create figure and multiple subplots at the same time.
Syntax:
matplotlib.pyplot.subplots(nrows=1, ncols=1, sharex=False, sharey=False, squeeze=True, subplot_kw=None, gridspec_kw=None, **fig_kw)
Example:
Python3
import matplotlib.pyplot as plt # Creating the figure and subplots# according the argument passedfig, axes = plt.subplots(1, 2) # plotting the data in the 1st subplotaxes[0].plot([1, 2, 3, 4], [1, 2, 3, 4]) # plotting the data in the 1st subplot onlyaxes[0].plot([1, 2, 3, 4], [4, 3, 2, 1]) # plotting the data in the 2nd subplot onlyaxes[1].plot([1, 2, 3, 4], [1, 1, 1, 1]) |
Output:
Method 4: Using subplot2grid() method
This function give additional flexibility in creating axes object at a specified location inside a grid. It also helps in spanning the axes object across multiple rows or columns. In simpler words, this function is used to create multiple charts within the same figure.
Syntax:
Plt.subplot2grid(shape, location, rowspan, colspan)
Example:
Python3
import matplotlib.pyplot as plt # data to display on plots x = [3, 1, 3] y = [3, 2, 1] z = [1, 3, 1] # adding the subplotsaxes1 = plt.subplot2grid ( (7, 1), (0, 0), rowspan = 2, colspan = 1) axes2 = plt.subplot2grid ( (7, 1), (2, 0), rowspan = 2, colspan = 1) axes3 = plt.subplot2grid ( (7, 1), (4, 0), rowspan = 2, colspan = 1) # plotting the dataaxes1.plot(x, y)axes2.plot(x, z)axes3.plot(z, y) |
Output:
Refer to the below articles to get detailed information about subplots
- How to create multiple subplots in Matplotlib in Python?
- How to Add Title to Subplots in Matplotlib?
- How to Set a Single Main Title for All the Subplots in Matplotlib?
- How to Turn Off the Axes for Subplots in Matplotlib?
- How to Create Different Subplot Sizes in Matplotlib?
- How to set the spacing between subplots in Matplotlib in Python?
- Matplotlib Sub plotting using object oriented API
- Make subplots span multiple grid rows and columns in Matplotlib
What is a Legend?
A legend is an area describing the elements of the graph. In simple terms, it reflects the data displayed in the graph’s Y-axis. It generally appears as the box containing a small sample of each color on the graph and a small description of what this data means.
Creating the Legend
A Legend can be created using the legend() method. The attribute Loc in the legend() is used to specify the location of the legend. The default value of loc is loc=”best” (upper left). The strings ‘upper left’, ‘upper right’, ‘lower left’, ‘lower right’ place the legend at the corresponding corner of the axes/figure.
The attribute bbox_to_anchor=(x, y) of legend() function is used to specify the coordinates of the legend, and the attribute ncol represents the number of columns that the legend has. Its default value is 1.
Syntax:
matplotlib.pyplot.legend([“blue”, “green”], bbox_to_anchor=(0.75, 1.15), ncol=2)
Example:
Python3
import matplotlib.pyplot as plt # data to display on plots x = [3, 1, 3] y = [3, 2, 1] plt.plot(x, y)plt.plot(y, x) # Adding the legendsplt.legend(["blue", "orange"])plt.show() |
Output:
Refer to the below articles to get detailed information about the legend –
- Matplotlib.pyplot.legend() in Python
- Matplotlib.axes.Axes.legend() in Python
- Change the legend position in Matplotlib
- How to Change Legend Font Size in Matplotlib?
- How Change the vertical spacing between legend entries in Matplotlib?
- Use multiple columns in a Matplotlib legend
- How to Create a Single Legend for All Subplots in Matplotlib?
- How to manually add a legend with a color box on a Matplotlib figure ?
- How to Place Legend Outside of the Plot in Matplotlib?
- How to Remove the Legend in Matplotlib?
- Remove the legend border in Matplotlib
Creating Different Types of Plots
Line Graph
Till now you all must have seen that we are working with only the line charts as they are easy to plot and understand. Line Chart is used to represent a relationship between two data X and Y on a different axis. It is plotted using the pot() function. Let’s see the below example
Example:
Python3
import matplotlib.pyplot as plt # data to display on plots x = [3, 1, 3] y = [3, 2, 1] # This will plot a simple line chart# with elements of x as x axis and y# as y axisplt.plot(x, y)plt.title("Line Chart") # Adding the legendsplt.legend(["Line"])plt.show() |
Output:
Refer to the below article to get detailed information about line chart.
- Line chart in Matplotlib
- Line plot styles in Matplotlib
- Plot a Horizontal line in Matplotlib
- Plot a Vertical line in Matplotlib
- Plot Multiple lines in Matplotlib
- Change the line opacity in Matplotlib
- Increase the thickness of a line with Matplotlib
- Plot line graph from NumPy array
- How to Fill Between Multiple Lines in Matplotlib?
Bar chart
A bar plot or bar chart is a graph that represents the category of data with rectangular bars with lengths and heights that is proportional to the values which they represent. The bar plots can be plotted horizontally or vertically. A bar chart describes the comparisons between the discrete categories. It can be created using the bar() method.
Syntax:
plt.bar(x, height, width, bottom, align)
Example:
Python3
import matplotlib.pyplot as plt # data to display on plots x = [3, 1, 3, 12, 2, 4, 4] y = [3, 2, 1, 4, 5, 6, 7] # This will plot a simple bar chartplt.bar(x, y) # Title to the plotplt.title("Bar Chart") # Adding the legendsplt.legend(["bar"])plt.show() |
Output:
Refer to the below articles to get detailed information about Bar charts –
- Bar Plot in Matplotlib
- Draw a horizontal bar chart with Matplotlib
- Create a stacked bar plot in Matplotlib
- Stacked Percentage Bar Plot In MatPlotLib
- Plotting back-to-back bar charts Matplotlib
- How to display the value of each bar in a bar chart using Matplotlib?
- How To Annotate Bars in Barplot with Matplotlib in Python?
- How to Annotate Bars in Grouped Barplot in Python?
Histograms
A histogram is basically used to represent data in the form of some groups. It is a type of bar plot where the X-axis represents the bin ranges while the Y-axis gives information about frequency. To create a histogram the first step is to create a bin of the ranges, then distribute the whole range of the values into a series of intervals, and count the values which fall into each of the intervals. Bins are clearly identified as consecutive, non-overlapping intervals of variables. The hist() function is used to compute and create histogram of x.
Syntax:
matplotlib.pyplot.hist(x, bins=None, range=None, density=False, weights=None, cumulative=False, bottom=None, histtype=’bar’, align=’mid’, orientation=’vertical’, rwidth=None, log=False, color=None, label=None, stacked=False, \*, data=None, \*\*kwargs)
Example:
Python3
import matplotlib.pyplot as plt # data to display on plots x = [1, 2, 3, 4, 5, 6, 7, 4] # This will plot a simple histogramplt.hist(x, bins = [1, 2, 3, 4, 5, 6, 7])# Title to the plotplt.title("Histogram")# Adding the legendsplt.legend(["bar"])plt.show() |
Output:
Refer to the below articles to get detailed information about histograms.
- Plotting Histogram in Python using Matplotlib
- Create a cumulative histogram in Matplotlib
- How to plot two histograms together in Matplotlib?
- Overlapping Histograms with Matplotlib in Python
- Bin Size in Matplotlib Histogram
- Compute the histogram of a set of data using NumPy in Python
- Plot 2-D Histogram in Python using Matplotlib
Scatter Plot
Scatter plots are used to observe the relationship between variables and use dots to represent the relationship between them. The scatter() method in the matplotlib library is used to draw a scatter plot.
Syntax:
matplotlib.pyplot.scatter(x_axis_data, y_axis_data, s=None, c=None, marker=None, cmap=None, vmin=None, vmax=None, alpha=None, linewidths=None, edgecolors=None)
Example:
Python3
import matplotlib.pyplot as plt # data to display on plots x = [3, 1, 3, 12, 2, 4, 4]y = [3, 2, 1, 4, 5, 6, 7] # This will plot a simple scatter chartplt.scatter(x, y) # Adding legend to the plotplt.legend("A") # Title to the plotplt.title("Scatter chart")plt.show() |
Output:
Refer to the below articles to get detailed information about the scatter plot.
- matplotlib.pyplot.scatter() in Python
- How to add a legend to a scatter plot in Matplotlib ?
- How to Connect Scatterplot Points With Line in Matplotlib?
- How to create a Scatter Plot with several colors in Matplotlib?
- How to increase the size of scatter points in Matplotlib ?
Pie Chart
A Pie Chart is a circular statistical plot that can display only one series of data. The area of the chart is the total percentage of the given data. The area of slices of the pie represents the percentage of the parts of the data. The slices of pie are called wedges. The area of the wedge is determined by the length of the arc of the wedge. It can be created using the pie() method.
Syntax:
matplotlib.pyplot.pie(data, explode=None, labels=None, colors=None, autopct=None, shadow=False)
Example:
Python3
import matplotlib.pyplot as plt # data to display on plots x = [1, 2, 3, 4] # this will explode the 1st wedge# i.e. will separate the 1st wedge# from the charte =(0.1, 0, 0, 0) # This will plot a simple pie chartplt.pie(x, explode = e) # Title to the plotplt.title("Pie chart")plt.show() |
Output:
Refer to the below articles to get detailed information about pie charts.
- matplotlib.axes.Axes.pie() in Python
- Plot a pie chart in Python using Matplotlib
- How to set border for wedges in Matplotlib pie chart?
- Radially displace pie chart wedge in Matplotlib
3D Plots
Matplotlib was introduced keeping in mind, only two-dimensional plotting. But at the time when the release of 1.0 occurred, the 3D utilities were developed upon the 2D and thus, we have a 3D implementation of data available today.
Example:
Python3
import matplotlib.pyplot as plt # Creating the figure objectfig = plt.figure() # keeping the projection = 3d# creates the 3d plotax = plt.axes(projection = '3d') |
Output:
The above code lets the creation of a 3D plot in Matplotlib. We can create different types of 3D plots like scatter plots, contour plots, surface plots, etc. Let’s create a simple 3D line plot.
Example:
Python3
import matplotlib.pyplot as plt x = [1, 2, 3, 4, 5]y = [1, 4, 9, 16, 25]z = [1, 8, 27, 64, 125]# Creating the figure objectfig = plt.figure()# keeping the projection = 3d# creates the 3d plotax = plt.axes(projection = '3d')ax.plot3D(z, y, x) |
Output:
Refer to the below articles to get detailed information about 3D plots.
- Three-dimensional Plotting in Python using Matplotlib
- 3D Scatter Plotting in Python using Matplotlib
- 3D Surface plotting in Python using Matplotlib
- 3D Wireframe plotting in Python using Matplotlib
- 3D Contour Plotting in Python using Matplotlib
- Tri-Surface Plot in Python using Matplotlib
- Surface plots and Contour plots in Python
- How to change angle of 3D plot in Python?
- How to animate 3D Graph using Matplotlib?
- Draw contours on an unstructured triangular grid in Python using Matplotlib
Working with Images
The image module in matplotlib library is used for working with images in Python. The image module also includes two useful methods which are imread which is used to read images and imshow which is used to display the image.
Example:
Python3
# importing required libraries import matplotlib.pyplot as plt import matplotlib.image as img # reading the image testImage = img.imread('g4g.png') # displaying the image plt.imshow(testImage) |
Output:
Refer to the below articles to get detailed information about working with images using Matplotlib.
- Working with Images in Python using Matplotlib
- Working with PNG Images using Matplotlib
- How to Display an Image in Grayscale in Matplotlib?
- Plot a Point or a Line on an Image with Matplotlib
- How to Draw Rectangle on Image in Matplotlib?
- How to Display an OpenCV image in Python with Matplotlib?
- Calculate the area of an image using Matplotlib
Customizing Plots in Matplotlib
- Style Plots using Matplotlib
- Change plot size in Matplotlib – Python
- How to Change the Transparency of a Graph Plot in Matplotlib with Python?
- How to Change the Color of a Graph Plot in Matplotlib with Python?
- How to Change Fonts in matplotlib?
- How to change the font size of the Title in a Matplotlib figure ?
- How to Set Tick Labels Font Size in Matplotlib?
- How to Set Plot Background Color in Matplotlib?
- How to generate a random color for a Matplotlib plot in Python?
- Add Text Inside the Plot in Matplotlib
- How to add text to Matplotlib?
- How to change Matplotlib color bar size in Python?
- How to manually add a legend with a color box on a Matplotlib figure ?
- How to change the size of axis labels in Matplotlib?
- How to Hide Axis Text Ticks or Tick Labels in Matplotlib?
- How To Adjust Position of Axis Labels in Matplotlib?
- Hide Axis, Borders and White Spaces in Matplotlib
More articles on Matplotlib
- How to Create an Empty Figure with Matplotlib in Python?
- Change the x or y interval of a Matplotlib figure
- How to add a grid on a figure in Matplotlib?
- How to change the size of figures drawn with matplotlib?
- Place plots side by side in Matplotlib
- How to Reverse Axes in Matplotlib?
- How to remove the frame from a Matplotlib figure in Python?
- Use different y-axes on the left and right of a Matplotlib plot
- How to Add a Y-Axis Label to the Secondary Y-Axis in Matplotlib?
- How to plot a simple vector field in Matplotlib ?
- Difference Between cla(), clf() and close() Methods in Matplotlib
- Make filled polygons between two horizontal curves in Python using Matplotlib
- How to Save a Plot to a File Using Matplotlib?
- How to Plot Logarithmic Axes in Matplotlib?
- How to put the y-axis in logarithmic scale with Matplotlib ?
- How to draw 2D Heatmap using Matplotlib in python?
- Plotting Correlation Matrix using Python
- Plot Candlestick Chart using mplfinance module in Python
- Autocorrelation plot using Matplotlib
- Stem and Leaf Plots in Python
- Python | Basic Gantt chart using Matplotlib
Exercises, Applications, and Projects
- How to Plot List of X, Y Coordinates in Matplotlib?
- How to put the origin in the center of the figure with Matplotlib ?
- How to Draw a Circle Using Matplotlib in Python?
- How to Plot Mean and Standard Deviation in Pandas?
- How to plot a complex number in Python using Matplotlib ?
- 3D Sine Wave Using Matplotlib – Python
- Plotting A Square Wave Using Matplotlib, Numpy And Scipy
- How to Make a Square Plot With Equal Axes in Matplotlib?
- Plotting a Sawtooth Wave using Matplotlib
- Visualizing Bubble sort using Python
- Visualization of Merge sort using Matplotlib
- Visualization of Quick sort using Matplotlib
- Insertion Sort Visualization using Matplotlib in Python
- 3D Visualisation of Quick Sort using Matplotlib in Python
- 3D Visualisation of Merge Sort using Matplotlib
- 3D Visualisation of Insertion Sort using Matplotlib in Python
- How to plot a normal distribution with Matplotlib in Python ?
- Normal Distribution Plot using Numpy and Matplotlib
- How to Create a Poisson Probability Mass Function Plot in Python?
- Find all peaks amplitude lies above 0 Using Scipy
- How to plot ricker curve using SciPy – Python?
- How to Plot a Confidence Interval in Python?
- How To Highlight a Time Range in Time Series Plot in Python with Matplotlib?
- How to Make a Time Series Plot with Rolling Average in Python?
- Digital Band Pass Butterworth Filter in Python
- Digital Band Reject Butterworth Filter in Python
- Digital High Pass Butterworth Filter in Python
- Digital Low Pass Butterworth Filter in Python
- Design an IIR Notch Filter to Denoise Signal using Python
- Design an IIR Bandpass Chebyshev Type-2 Filter using Scipy – Python
- Visualizing Tiff File Using Matplotlib and GDAL using Python
- Plotting Various Sounds on Graphs using Python and Matplotlib
- COVID-19 Data Visualization using matplotlib in Python
- Analyzing selling price of used cars using Python
