https://file.aiquickdraw.com/mathbot/file/1727184087653ruekc6y0.jpg

The question is asking which of the given values cannot be an \( r^2 \)-value.

### Explanation of \( r^2 \)-value:
The \( r^2 \)-value, or the coefficient of determination, is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable(s) in a regression model. The value of \( r^2 \) ranges between 0 and 1.

- \( r^2 = 1 \) means the model perfectly explains all variability in the data.
- \( r^2 = 0 \) means the model does not explain any of the variability in the data.
- \( r^2 \) values are always between 0 and 1; they cannot be negative.

### Analysis of options:
- **A. 0**: This is a valid \( r^2 \)-value.
- **B. 0.75**: This is a valid \( r^2 \)-value.
- **C. 1**: This is a valid \( r^2 \)-value.
- **D. -0.75**: This **cannot** be an \( r^2 \)-value because \( r^2 \) cannot be negative.

### Correct Answer:
**D. -0.75**

Would you like more details on this topic, or do you have any other questions?

---

Here are 5 related questions to expand your understanding:
1. What is the relationship between the correlation coefficient \( r \) and \( r^2 \)?
2. How do you interpret the value of \( r^2 \) in a regression analysis?
3. Can \( r^2 \) be used for non-linear models, and if so, how is it interpreted?
4. What is a common limitation of using \( r^2 \) as a measure of model accuracy?
5. How can a high \( r^2 \) value be misleading in some contexts?

**Tip**: While \( r^2 \) gives a measure of how well your model fits the data, it doesn't indicate whether the model is good in practical terms. Always look at residuals and other diagnostics!

Understand which values are valid for r², the coefficient of determination, in regression analysis. Learn why r² cannot be negative and explore the statistical measures involved in model fitting. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation