The data below represent the number of days​ absent, x, and the final​ grade, y, for a sample of college students at a large university. Complete parts​ (a) through​ (e) below.
No. of​ absences, x
0
1
2
3
4
5
6
7
8
9
 
Final​ grade, y
89.3
86.5
83.5
81.1
78.1
73.8
64.5
68.8
65.9
63.1
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Part 1
​(a) Find the​ least-squares regression line treating the number of​ absences, x, as the explanatory variable and the final​ grade, y, as the response variable.
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​(Round to three decimal places as​ needed.)

The least-squares regression line, treating the number of absences \( x \) as the explanatory variable and the final grade \( y \) as the response variable, is given by:

\[
\hat{y} = 89.304 - 3.076x
\]

Where \( \hat{y} \) is the predicted final grade, and \( x \) is the number of absences.

Do you need any further details or have any questions?

Here are five related questions:
1. How can you interpret the slope of the regression line?
2. What does the intercept represent in this context?
3. How would you predict the grade for a student with 5 absences using this model?
4. What is the significance of the \( R^2 \) value in this regression analysis?
5. How can outliers affect the least-squares regression line?

**Tip:** Always check the residuals to assess how well your regression model fits the data!

The data below represent the number of days​ absent, x, and the final​ grade, y, for a sample of college students at a large university. Complete parts​ (a) through​ (e) below. Part (a) Find the​ least-squares regression line treating the number of​ absences, x, as the explanatory variable and the final​ grade, y, as the response variable.

Learn how to calculate the least-squares regression line for a dataset representing the number of days absent and final grades of college students. Understand the relationship between absences and grades using statistical formulas and concepts such as the least-squares method, slope, and intercept. Suitable for college-level statistics courses.

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