Plotting the Perfect Line of Best Fit in Python

Plotting a Line of Best Fit in Python

If you’re in the field of data analytics, you may already be familiar with the concept of a line of best fit. A line of best fit is a straight line that represents the trend in a set of data points.

It’s a useful tool in predicting future trends and making sense of large amounts of data. In this article, we’ll explore how to plot a line of best fit in Python.

Basic Line of Best Fit

The most straightforward way to plot a line of best fit is to use the `np.polyfit` function from the NumPy library. This function takes two arguments: the x-axis data and the y-axis data.

It returns the coefficients of the line of best fit, with the slope being the first element and the intercept being the second element. To start, let’s define some data for our example.

We’ll use NumPy’s array function to create two arrays: one for the x-axis and one for the y-axis. Here’s the code:

``````import numpy as np
x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 5, 4, 5])``````

Now that we have our data, we can find the coefficients of the line of best fit using `np.polyfit`. We’ll pass in our `x` and `y` arrays, as well as the degree of the polynomial we want to fit.

Since we’re fitting a straight line, the degree will be 1. Here’s the code:

``coefficients = np.polyfit(x, y, 1)``

Our `coefficients` variable now contains the slope and intercept of our line of best fit.

To plot the line on a graph, we need to add our data points as well. We can do this using Matplotlib’s `scatter` function.

Here’s the code:

``````import matplotlib.pyplot as plt
plt.scatter(x, y)``````

Now, let’s add our line of best fit to the plot. We’ll use the `np.poly1d` function to create a function that takes in an x value and outputs the y value on the line of best fit.

We’ll then pass this function into Matplotlib’s `plot` function to actually draw the line on the graph. Here’s the code:

``````line_of_best_fit = np.poly1d(coefficients)
plt.plot(x, line_of_best_fit(x))``````

And that’s it! We now have a basic line of best fit plotted on a graph.

Here’s the final code:

``````import numpy as np
import matplotlib.pyplot as plt

x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 5, 4, 5])

coefficients = np.polyfit(x, y, 1)
line_of_best_fit = np.poly1d(coefficients)

plt.scatter(x, y)
plt.plot(x, line_of_best_fit(x))
plt.show()``````

Custom Line of Best Fit

While a basic line of best fit is useful, sometimes we want to customize it for more clarity or visual interest. Fortunately, Matplotlib gives us many options for customizing our lines.

Color, linestyle, and linewidth

We can change the color of our line of best fit using the `color` parameter. This parameter takes a string that represents a color name or hex code.

Here’s an example:

``plt.plot(x, line_of_best_fit(x), color='red')``

We can also change the linestyle of our line using the `linestyle` parameter. This parameter takes a string that represents a linestyle name or code.

Here’s an example:

``plt.plot(x, line_of_best_fit(x), linestyle='dashed')``

Finally, we can change the linewidth of our line using the `linewidth` parameter. This parameter takes a number that represents the width of the line in points.

Here’s an example:

``plt.plot(x, line_of_best_fit(x), linewidth=3)``

Text

Another way to customize our line of best fit is to add text to the graph. We can use Matplotlib’s `text` function to add text anywhere on the graph.

Here’s an example:

``plt.text(1, 3, 'Line of best fit')``

This code will add the text “Line of best fit” at the coordinates (1, 3) on our graph. Example 1: Plot

Basic Line of Best Fit in Python

To sum up, let’s put everything we’ve learned together and plot a customized line of best fit.

Here’s an example of data that represents the number of hours studied and the corresponding grade received on a test:

``````import numpy as np
import matplotlib.pyplot as plt

hours_studied = np.array([1, 2, 3, 4, 5])
grades = np.array([60, 70, 80, 90, 95])

line_of_best_fit = np.poly1d(coefficients)

plt.plot(hours_studied, line_of_best_fit(hours_studied), color='red', linestyle='dashed', linewidth=3)
plt.text(3, 80, 'Line of best fit')
plt.xlabel('Hours studied')
plt.show()``````

In this example, we’ve added a dashed red line of best fit with a width of 3 points.

We’ve also added the text “Line of best fit” at the coordinates (3, 80).

Conclusion

In conclusion, plotting a line of best fit in Python is a useful way to analyze data and predict trends. Through the use of NumPy and Matplotlib, we can find the coefficients of the line of best fit and customize its appearance with different colors, linestyles, and widths.

We can also add text to the graph to make it more informative. By following the steps outlined in this article, you’ll be able to plot a line of best fit in no time.

Example 2: Plot

Custom Line of Best Fit in Python

In this example, we will explore how to plot a customized line of best fit in Python. We’ll start by defining our data, finding the line of best fit, and adding our data points to the plot.

From there, we’ll customize our line by changing its color and linestyle, and by adding text to the plot. Finally, we’ll add a fitted regression equation to the plot to make it more informative.

Define Data

Before we start plotting our line of best fit, we need to define our data. Let’s say we have data that represents the number of hours a student studies per week and their corresponding GPA.

We’ll use NumPy’s array function to create two arrays: one for the x-axis (hours studied) and one for the y-axis (GPA). Here’s the code:

``````import numpy as np
import matplotlib.pyplot as plt

hours_studied = np.array([1, 2, 5, 7, 8, 10])
GPA = np.array([2.0, 2.7, 3.5, 3.8, 3.9, 4.0])``````

Find Line of Best Fit

Now that we have our data, we can find the coefficients of the line of best fit using the `np.polyfit` function. We’ll pass in our `x` and `y` arrays, as well as the degree of the polynomial we want to fit, which in this case is 1 since we’re fitting a straight line.

Here’s the code:

``coefficients = np.polyfit(hours_studied, GPA, 1)``

Now we have our line of best fit and can begin visualizing it on a plot.

Before we plot our line of best fit, let’s first add our data points to the plot using Matplotlib’s `scatter` function. Here’s the code:

``````plt.scatter(hours_studied, GPA)
plt.xlabel('Hours Studied')
plt.ylabel('GPA')
plt.title('Number of hours studied vs. GPA')
plt.show()``````

This code will create a scatter plot of our data points with hours studied on the x-axis and GPA on the y-axis. We’ve also added axis labels and a title to the plot.

Add Line of Best Fit to Plot

Now that we have our data points plotted, let’s add our line of best fit. We’ll use the `np.poly1d` function to create a function that takes in an x value and outputs the y value on the line of best fit.

Here’s the code:

``````line_of_best_fit = np.poly1d(coefficients)
plt.plot(hours_studied, line_of_best_fit(hours_studied))``````

This code will plot our line of best fit on the scatter plot. The x values will be the hours studied and the y values will be the predicted GPA based on our line of best fit.

Customize Line of Best Fit

Now that we have our line of best fit plotted, let’s customize it to make it more informative and visually appealing. We can change the color of the line by specifying a color parameter when calling the `plot` function.

Here’s the code:

``plt.plot(hours_studied, line_of_best_fit(hours_studied), color='red')``

This code will change the color of our line of best fit to red. We can also change the linestyle of the line by specifying a `linestyle` parameter.

Here’s the code:

``plt.plot(hours_studied, line_of_best_fit(hours_studied), linestyle='dashed')``

This code will change the linestyle of our line of best fit to dashed. We can also adjust the linewidth using the `linewidth` parameter.

Here’s the code:

``plt.plot(hours_studied, line_of_best_fit(hours_studied), linewidth=3)``

This code will increase the width of our line of best fit to 3 points.

Add Fitted Regression Equation to Plot

Let’s make our graph more informative by adding the fitted regression equation to the plot. We can display the equation using the Matplotlib `text` function by passing in the equation as a string.

Here’s the code:

``````equation = "y = " + str(round(coefficients[0], 2)) + "x + " + str(round(coefficients[1], 2))
plt.text(4, 3.4, equation)``````

This code will add the regression equation to the plot at the coordinates (4, 3.4). The equation will be a string representation of our line of best fit, with the slope and y-intercept rounded to 2 decimal places.

Final Code

Here’s the final code for our customized line of best fit plot:

``````hours_studied = np.array([1, 2, 5, 7, 8, 10])
GPA = np.array([2.0, 2.7, 3.5, 3.8, 3.9, 4.0])
coefficients = np.polyfit(hours_studied, GPA, 1)
line_of_best_fit = np.poly1d(coefficients)
plt.scatter(hours_studied, GPA)
plt.plot(hours_studied, line_of_best_fit(hours_studied), color='red', linestyle='dashed', linewidth=3)
equation = "y = " + str(round(coefficients[0], 2)) + "x + " + str(round(coefficients[1], 2))
plt.text(4, 3.4, equation)
plt.xlabel('Hours Studied')
plt.ylabel('GPA')
plt.title('Number of hours studied vs. GPA')
plt.show()``````

This code will plot a scatter plot of hours studied vs. GPA with a line of best fit. The line of best fit will be colored in red, dashed, and 3 points wide.

The regression equation will be displayed on the plot, making our visualization more informative.

Conclusion

In conclusion, customizing a line of best fit in Python can help you better interpret your data and increase the readability of your visualization. By using Matplotlib’s parameters, `text` function and Numpy’s `polyfit` function, we are able to change the color, linestyle and add text that helps viewers read and understand the data much easily.

With a bit of Python coding and experimentation, you can create an informative and visually appealing graph. In this article, we have explored the process of plotting a line of best fit in Python.

We have discussed how to create a basic line of best fit using NumPy’s `polyfit` function and Matplotlib’s `scatter` and `plot` functions. Additionally, we have shown how to customize the line by changing color, linestyle, and linewidth.