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The \( R^2 \)-values for the different models that fit the data are as follows:

- **Linear model**: \( R^2 = 0.9834 \)
- **Quadratic model**: \( R^2 = 0.9998 \)
- **Exponential model**: \( R^2 = 0.9830 \)

The quadratic model provides the best fit to the data, with an \( R^2 \)-value of \( 0.9998 \).

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:
1. How do you calculate the \( R^2 \)-value for a model?
2. What is the significance of a higher \( R^2 \)-value?
3. Can a model have an \( R^2 \)-value of exactly 1? What does it mean?
4. Why does the quadratic model fit better than the linear and exponential models?
5. How does polynomial regression differ from simple linear regression?

**Tip**: When comparing models, always consider both the goodness of fit (like \( R^2 \)) and how well the model generalizes to new data.

What is the R^2-value of the linear, quadratic, or exponential function that best fits the data? Include at least 4 digits in your response.

Discover the best-fit model for a set of data points by comparing R^2-values for linear, quadratic, and exponential functions. This tutorial covers how to calculate and interpret R^2-values, using data points (x, y) to find the most accurate model. Ideal for high school students in Grades 10-12.

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