matplotlib import pyplot as plt import numpy as np

Data from the table

x = np.array([83, 87, 91, 93, 97, 97, 101, 104]) y = np.array([102, 115, 107, 122, 125, 127, 120, 127])

Scatter plot

plt.scatter(x, y, color='blue', label='Data Points')

Line of best fit

coefficients = np.polyfit(x, y, 1) # Linear fit (degree 1) line_of_best_fit = np.poly1d(coefficients)

Plot the line of best fit

x_fit = np.linspace(min(x), max(x), 100) y_fit = line_of_best_fit(x_fit) plt.plot(x_fit, y_fit, color='red', label=f"Best Fit: y = {coefficients[0]:.2f}x + {coefficients[1]:.2f}")

Labels and legend

plt.xlabel('x') plt.ylabel('y') plt.title('Scatter Plot with Line of Best Fit') plt.legend() plt.grid() plt.show()

coefficientsThe scatter plot has been created, and the line of best fit is shown in red. The equation of the line of best fit is:

$y = 1.09x + 15.59$

Let me know if you'd like further explanation or additional analysis!

Here are 5 related questions to consider:

1. What is the correlation coefficient of this dataset, and how strong is the linear relationship?
2. Can we use the line of best fit to predict $y$ for a given $x$?
3. How would the results change if there were an outlier in the data?
4. What happens to the line of best fit if the data is normalized or standardized?
5. How do residuals help measure the goodness of fit for this model?

Tip: The slope of the line of best fit indicates how much $y$ changes for a unit change in $x$. In this case, $y$ increases by about 1.09 for every 1-unit increase in $x$.