numpy as np import matplotlib.pyplot as plt

Data

x = np.array([1, 5, -4, 0, -2, 3, -7]) y = np.array([2, -3, 16, 8, 12, -1, 21])

Using numpy to compute the line of best fit (slope and intercept)

slope, intercept = np.polyfit(x, y, 1)

Create the line of best fit equation

line_of_best_fit = f"y = {slope:.2f}x + {intercept:.2f}"

Output the equation of the line

line_of_best_fitThe equation of the line of best fit for the given data is:

$y = -2.16x + 6.62$

Would you like further details on how to derive this equation, or do you have any additional questions? Here are some related questions you might find helpful:

1. How do you interpret the slope and y-intercept of the line of best fit?
2. What other methods can be used to find the equation of the line of best fit?
3. How do you determine the strength of the correlation between x and y from the line of best fit?
4. How would the equation change if the data points were altered?
5. What are the potential limitations of using a line of best fit?

Tip: The slope represents the rate of change of $y$ with respect to $x$, while the y-intercept represents the value of $y$ when $x = 0$.