If the predicted value when x equals 12 is
y hat equals 72.0
and the actual value at x equals 12 is measured to be y equals 73.7, find the value of the residual at this point.
residual equals blank. Fill in the blank.

The residual is calculated as the difference between the actual value and the predicted value:

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

Given:
- Actual value \( y = 73.7 \)
- Predicted value \( \hat{y} = 72.0 \)

Substitute these values into the formula:

\[
\text{Residual} = 73.7 - 72.0 = 1.7
\]

Thus, the residual is \( \boxed{1.7} \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What does a positive residual indicate about the predicted model?
2. How is the residual used in evaluating the accuracy of a regression model?
3. What is the formula for calculating the residual sum of squares (RSS)?
4. How can you interpret the residual if it equals zero?
5. What are outliers in terms of residuals?

**Tip:** Residuals help assess the fit of a regression model. Large residuals can indicate that the model is not capturing some aspect of the data properly.

If the predicted value when x equals 12 is y hat equals 72.0 and the actual value at x equals 12 is measured to be y equals 73.7, find the value of the residual at this point. Residual equals blank. Fill in the blank.

Learn how to calculate the residual by finding the difference between the actual value and the predicted value in regression analysis. In this example, the predicted value is 72.0, and the actual value is 73.7, giving a residual of 1.7. Suitable for students in 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