To find the least-squares regression line (linear regression) of the form:

$\hat{y} = mx + b$

where $x$ represents the number of absences (explanatory variable) and $y$ represents the final exam score (response variable), we need to calculate:

1. The slope ($m$).
2. The intercept ($b$).

Steps:

1. Calculate the means of $x$ and $y$.
2. Find the slope $m$ using the formula:

$m = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sum{(x_i - \bar{x})^2}}$

3. Find the intercept $b$ using the formula:

$b = \bar{y} - m\bar{x}$

Let's compute that now.The least-squares regression line is:

$\hat{y} = -2.922x + 89.151$

This equation predicts the final exam score ($\hat{y}$) based on the number of absences ($x$).

Would you like further details or have any questions?

Here are some related questions to explore:

1. How can you interpret the slope of the regression line?
2. What is the predicted score for 5 absences?
3. What would the model predict for 0 absences?
4. How does the regression model perform with high numbers of absences?
5. How can you test if this regression model fits the data well?

Tip: The slope of a regression line shows how much the response variable changes for each one-unit change in the explanatory variable.