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 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.

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.

Determine the best fit model (linear, quadratic, or exponential) for a given data set. Learn how the R^2-value of each model is calculated. The quadratic model provides the best fit with an R^2-value of 0.9998, nearly perfect. Explore regression analysis, model comparison, and fitting processes.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation