Let's analyze the regression equation:

$\hat{y} = -2.971x + 89.129$

Where:

• $x$ is the number of absences
• $y$ is the final exam score

Slope Interpretation:

The slope of the regression line is $-2.971$. This means that for every additional absence, a student's final exam score drops by 2.971 points on average. This interpretation aligns with option B or C.

Y-Intercept Interpretation:

The y-intercept is $89.129$. This represents the predicted final exam score for a student with zero absences. Therefore, the average final exam score of students who miss no classes is 89.129. This interpretation aligns with A or C.

Final Choice:

Since both the slope and the y-intercept have meaningful interpretations in this case, the correct choice is:

C. For every additional absence, a student's final exam score drops 2.971 points on average. The average final exam score of students who miss no classes is 89.129.

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Would you like to explore the detailed calculation for the least-squares regression, or do you have any questions?

Here are 5 related questions to expand on this:

1. How is the least-squares regression line calculated using data points?
2. Can you explain what residuals are in the context of regression analysis?
3. How does a large number of absences impact the exam score based on this model?
4. What is the coefficient of determination ($R^2$) and how can it be interpreted in this scenario?
5. How would the interpretation of the y-intercept change if the y-intercept value was much higher or lower?

Tip: Always check if the intercept and slope have real-world meaning in the context of your data! Not all models make sense with a y-intercept interpretation.