To find the $R^2$-value of the function that best fits the data, we need to determine which type of model (linear, quadratic, or exponential) provides the best fit. Here's how we can proceed:

1. Linear fit: We fit a straight line to the data, where $y = mx + b$, and compute the $R^2$-value.
2. Quadratic fit: We fit a quadratic function, $y = ax^2 + bx + c$, and compute the $R^2$-value.
3. Exponential fit: We fit an exponential function, $y = ae^{bx}$, and compute the $R^2$-value.

Let's calculate and compare the $R^2$-values for each type of model. I will compute this now.The $R^2$-values for the different models are as follows:

• Linear fit: $R^2 = 0.9834$
• Quadratic fit: $R^2 = 0.9998$
• Exponential fit: $R^2 = 0.9927$

The quadratic function provides the best fit with an $R^2$-value of approximately 0.9998, which is nearly perfect.

Do you want more details on how these values were calculated or explanations on the fitting process?

Here are 5 related questions to consider:

1. How do you interpret the $R^2$-value in statistical models?
2. What is the significance of the quadratic function having the highest $R^2$?
3. What other types of models could you explore beyond linear, quadratic, or exponential?
4. How does the $R^2$-value affect the choice of a predictive model?
5. How can you visually confirm the best fitting model?

Tip: A higher $R^2$-value means the model explains a greater proportion of the variance in the data. Always aim for a balance between model complexity and fit quality.