Find the​ least-squares

regression

line treating number of absences as the explanatory variable and the final exam score as the response variable.

ModifyingAbove y with caretyequals=enter your response herexplus+enter your response here

​(Round to three decimal places as​ needed.)
Number of absences, x	Final exam score, y

0	90.2

1	87.2

2	82.9

3	80.7

4	77.9

5	73.9

6	64.5

7	71.6

8	65.4

9	65.7

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.

Find the least-squares regression line treating number of absences as the explanatory variable and the final exam score as the response variable. Round to three decimal places as needed. Number of absences (x), Final exam score (y): (0, 90.2), (1, 87.2), (2, 82.9), (3, 80.7), (4, 77.9), (5, 73.9), (6, 64.5), (7, 71.6), (8, 65.4), (9, 65.7)

Find the least-squares regression line for the number of absences as the explanatory variable and final exam scores as the response variable. Learn how to calculate the slope and intercept of the regression line using the least-squares method. Suitable for students in Grades 10-12.

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