https://file.aiquickdraw.com/mathbot/file/1727184030878hxkra38b.jpg

The question asks for the residual for the point \((2, 5)\) given the line of best fit:

\[
\hat{y} = 2.5x - 1.5
\]

### Step 1: Calculate the predicted \(y\)-value \(\hat{y}\) using the line of best fit for \(x = 2\).

\[
\hat{y} = 2.5(2) - 1.5 = 5 - 1.5 = 3.5
\]

### Step 2: Find the residual. The residual is the difference between the actual \(y\)-value and the predicted \(y\)-value:

\[
\text{Residual} = y_{\text{actual}} - \hat{y}
\]

Here, the actual \(y\)-value is \(5\), and the predicted \(y\)-value is \(3.5\):

\[
\text{Residual} = 5 - 3.5 = 1.5
\]

### Conclusion: The residual for the point \((2, 5)\) is **1.5**, so the correct answer is:

\[
\boxed{A. 1.5}
\]

Do you need more details or have any questions?

---

Here are 5 related questions to expand on this:
1. What does a positive residual indicate about a data point in relation to the line of best fit?
2. How do you interpret a residual of zero for a particular data point?
3. What is the meaning of the slope in the equation \(\hat{y} = 2.5x - 1.5\)?
4. How would you calculate the residual for a different point, such as \((3, 6)\)?
5. Can the residual be negative, and what would that mean for the data point?

**Tip**: Residuals help us measure the accuracy of predictions from the line of best fit. A smaller residual indicates a better fit for the data point.

A set of data points has a line of best fit of ŷ = 2.5x - 1.5. What is the residual for the point (2, 5)?

Find the residual for the point (2, 5) given the line of best fit ŷ = 2.5x - 1.5. This problem involves calculating residuals using the formula y_actual - ŷ_predicted, important in statistics and regression analysis. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation