Let's analyze and solve the tasks given in the image:

1. Finding the Best Fit Line (Linear Regression Equation)

The equation of the best fit line is: $y = mx + b$ where:

• $m$ is the slope
• $b$ is the y-intercept

We calculate $m$ and $b$ using the formulas: $m = \frac{n\sum(xy) - \sum x \sum y}{n\sum(x^2) - (\sum x)^2}$ $b = \frac{\sum y - m\sum x}{n}$

2. Graphing the Scatter Plot with Best Fit Line

Once the line equation is determined, we'll plot the scatter plot for the data points and overlay the line.

3. Predicting the Score for 2 Missed Classes

Using the linear equation, substitute $x = 2$ into the equation and compute $y$.

Let me process the calculations.import numpy as np import pandas as pd import matplotlib.pyplot as plt

Data extracted from the image

x = np.array([5, 3, 3, 2, 2, 7, 0, 5, 3, 3, 1, 1, 5, 6]) # Number of missed classes y = np.array([61, 73, 77, 77, 87, 63, 100, 82, 74, 77, 90, 70, 86, 64]) # Final exam scores

Calculate the necessary components for the linear regression

n = len(x) sum_x = np.sum(x) sum_y = np.sum(y) sum_xy = np.sum(x * y) sum_x2 = np.sum(x ** 2)

Slope (m) and Intercept (b)

m = (n * sum_xy - sum_x * sum_y) / (n * sum_x2 - sum_x ** 2) b = (sum_y - m * sum_x) / n

Linear regression equation

line_eq = f"y = {m:.2f}x + {b:.2f}"

Prediction for 2 missed classes

x_pred = 2 y_pred = m * x_pred + b

Plot the scatter plot and best fit line

plt.scatter(x, y, color="blue", label="Data Points") plt.plot(x, m * x + b, color="red", label=f"Best Fit Line: {line_eq}") plt.xlabel("Number of Missed Classes") plt.ylabel("Final Exam Score (%)") plt.title("Scatter Plot and Best Fit Line") plt.legend() plt.grid(True) plt.show()

line_eq, y_pred <<ImageDisplayed>>('y = -3.48x + 88.65', 81.68750000000001)('y = -3.48x + 88.65', 81.68750000000001)success### Results:

1. Equation of the Best Fit Line: $y = -3.48x + 88.65$

2. Prediction for a Student Who Missed 2 Classes: The predicted final exam score is approximately 81.69%.

Let me know if you'd like further clarification or if I can assist with additional details!

Here are some related questions:

1. How would the prediction change if the number of missed classes increased by one?
2. Can you calculate the correlation coefficient for this dataset?
3. How would the equation change if a student with perfect attendance scored 80 instead of 100?
4. What does the slope of the line indicate about the relationship between missed classes and scores?
5. Could this model be applied to predict scores for students with more than 7 missed classes? Why or why not?

Tip: Always review the dataset for outliers, as they can significantly impact the accuracy of your regression model.