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 compute the \( R^2 \)-value (coefficient of determination) for the best-fitting function—whether linear, quadratic, or exponential—you would generally follow these steps:

1. **Fit each model** (linear, quadratic, or exponential) to the given data using least-squares regression.
2. **Calculate the total sum of squares (SST)**, which measures the variance in the data points.
3. **Calculate the residual sum of squares (SSR)**, which measures the variance that remains after fitting the model.
4. Use the formula for \( R^2 \):
   \[
   R^2 = 1 - \frac{SSR}{SST}
   \]
   where:
   - \( SSR \) is the sum of squared differences between the observed values and the values predicted by the model.
   - \( SST \) is the sum of squared differences between the observed values and their mean.

   The closer the \( R^2 \)-value is to 1, the better the model fits the data. A negative \( R^2 \)-value suggests that the model does not fit the data well at all.

If you provide the dataset, I can compute the \( R^2 \)-value and determine which function (linear, quadratic, or exponential) provides the best fit for the data.

Would you like to upload the data for this computation?

### Example Questions:
1. What is the specific formula for calculating SST and SSR for a quadratic function?
2. How does the \( R^2 \)-value differ between linear and exponential regressions?
3. Can you compute an \( R^2 \)-value if I have a small dataset of only three points?
4. How do outliers affect the \( R^2 \)-value of a model?
5. What are other metrics that could complement the \( R^2 \)-value for model evaluation?

**Tip**: The \( R^2 \)-value only measures the fit quality of the model, not whether the model is appropriate for predicting future values.

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 compute the R2-value (coefficient of determination) for linear, quadratic, and exponential regression models. This process involves fitting each model using least-squares regression, calculating the total and residual sum of squares, and using the R2 formula. Suitable for Grades 10-12 students and anyone interested in data analysis and model evaluation.

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