Let me analyze the image and extract the necessary data to solve the problem.The problem involves finding the best fit line, graphing the data, and predicting a value based on the given data. Here’s a step-by-step breakdown:

Provided Data:

• $x$ (number of classes missed): $5, 3, 3, 2, 0, 7, 0, 5, 5, 3, 1, 5, 1, 6$
• $y$ (final exam scores): $61, 73, 77, 77, 87, 63, 100, 82, 74, 77, 90, 70, 86, 64$

1. Find the Best Fit Line:

The equation for a linear regression line is: $y = mx + b$ Where $m$ is the slope and $b$ is the intercept.

Let me calculate the best-fit line based on the provided $x$ and $y$ values.

2. Graph Scatter Plot and Best-Fit Line:

The scatter plot will display the $x$-$y$ points, and the regression line will show the trend.

3. Prediction for $x = 2$:

Using the equation of the regression line, calculate the predicted score for a student who missed 2 classes.

Let me calculate the regression line and the prediction.import numpy as np import matplotlib.pyplot as plt

Given data

x = np.array([5, 3, 3, 2, 0, 7, 0, 5, 5, 3, 1, 5, 1, 6]) y = np.array([61, 73, 77, 77, 87, 63, 100, 82, 74, 77, 90, 70, 86, 64])

Calculate the best fit line using linear regression

coefficients = np.polyfit(x, y, 1) # Linear regression (degree 1) m, b = coefficients # Slope and intercept

Define the regression line

y_pred = m * x + b

Predict the score for a student who missed 2 classes (x=2)

x_new = 2 y_new = m * x_new + b

Plot scatter plot and regression line

plt.figure(figsize=(8, 6)) plt.scatter(x, y, label="Data points", color="blue") plt.plot(x, y_pred, label=f"Best fit line: y = {m:.2f}x + {b:.2f}", color="red") plt.scatter(x_new, y_new, color="green", label=f"Prediction for x={x_new}: y={y_new:.2f}", zorder=5) plt.xlabel("Number of Classes Missed (x)") plt.ylabel("Final Exam Score (y)") plt.title("Scatter Plot with Best Fit Line") plt.legend() plt.grid(True) plt.show()

m, b, y_new <<ImageDisplayed>>(-4.200854700854707, 91.01709401709398, 82.61538461538457)(-4.200854700854707, 91.01709401709398, 82.61538461538457)success### Results:

1. Best-Fit Line Equation: $y = -4.20x + 91.02$

2. Prediction for $x = 2$: When a student misses 2 classes ($x = 2$), the predicted final exam score is: $y = 82.62$

3. Graph Description:

   • Blue points represent the actual data.
   • The red line represents the best-fit line ($y = -4.20x + 91.02$).
   • The green point shows the predicted value for $x = 2$.

Do you want further details or help interpreting the results?
Here are 5 related questions you might consider:

1. What does the slope of $-4.20$ indicate about the relationship between missed classes and exam scores?
2. How could you verify the accuracy of the regression model?
3. What is the $R^2$ value for this regression, and how well does the line fit the data?
4. How would predictions change if a quadratic model were used instead of linear regression?
5. What other factors (besides missed classes) might affect the final exam score?

Tip: Always review the residuals of your regression model to ensure no major patterns are overlooked.