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!