A data table is shown below. 
 
x	y
8	1.72
24	11.99
11	2.91
19	7.70
17	6.12
9	2.13
14	4.46
23	11.07
22	10.15

What is the R2-value of the linear, quadratic, or exponential function that best fits the data? Include at least 4 digits in your response.

To determine the \( R^2 \)-value for the function that best fits the data (linear, quadratic, or exponential), the following steps are required:

1. **Enter the data**: 
   We input the data points for \( x \) and \( y \).

2. **Fit models**: 
   We fit three types of models to the dataTo determine the \( R^2 \)-value for the function that best fits the data (linear, quadratic, or exponential), the following steps are required:

1. **Enter the data**: 
   We input the data points for \( x \) and \( y \).

2. **Fit models**: 
   We fit three types of models to the  linear, quadratic, and exponential.

3. **Calculate the \( R^2 \)-value**:
   For each model, compute the coefficient of determination \( R^2 \), which indicates how well the model fits the data.

### Data:
| x  | y    |
|----|------|
| 8  | 1.72 |
| 24 | 11.99|
| 11 | 2.91 |
| 19 | 7.70 |
| 17 | 6.12 |
| 9  | 2.13 |
| 14 | 4.46 |
| 23 | 11.07|
| 22 | 10.15|

Let me proceed with the calculations to determine the \( R^2 \)-value for each model.The \( R^2 \)-values for the different models fitted to the data are as follows:

- **Linear model**: \( R^2 = 0.9834 \)
- **Quadratic model**: \( R^2 = 0.9998 \)
- **Exponential model**: \( R^2 = 0.9927 \)

The **quadratic function** provides the best fit with an \( R^2 \)-value of \( 0.9998 \).

Would you like more details on any of these models or how to interpret the results?

Here are some follow-up questions:
1. What is the equation of the quadratic function that best fits the data?
2. How do you interpret the \( R^2 \)-value?
3. What are the limitations of using an exponential model in this case?
4. Can I show the residuals for each of these models?
5. How can outliers affect the \( R^2 \)-value?

**Tip**: The \( R^2 \)-value closer to 1 indicates a better fit, but always consider the nature of the data before choosing the best model.

A data table is shown below. 
x    y
8    1.72
24   11.99
11   2.91
19   7.70
17   6.12
9    2.13
14   4.46
23   11.07
22   10.15

What is the R2-value of the linear, quadratic, or exponential function that best fits the data? Include at least 4 digits in your response.

Learn how to calculate the R^2 value to find the best-fitting model (linear, quadratic, or exponential) for a given data set. The quadratic model provides the best fit with an R^2 value of 0.9998. This analysis uses key concepts like regression analysis, curve fitting, and the coefficient of determination.

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