for the following data 
A) come up with a exponential regression model and state r & r^2
B) sketch the residuals of the exponential model v Day d
Day d       |4|13|18|21|25|30|40|
Number n|90|68|56|54|48|38|26|

### A) Exponential Regression Model:

The exponential regression model is:

\[
n(d) = 106.18 \cdot e^{-0.0341 \cdot d}
\]

Where:
- \( a = 106.18 \)
- \( b = -0.0341 \)

The correlation coefficient \( r = -0.996 \), indicating a very strong negative linear relationship between the natural log of \( n \) and \( d \). The coefficient of determination \( r^2 = 0.991 \), meaning 99.1% of the variance in \( n \) is explained by the model.

### B) Residual Plot:

The residuals plot (displayed above) shows the difference between the actual values of \( n \) and the values predicted by the exponential model, plotted against the days. Residuals are close to zero, suggesting the model fits the data well.

---

Would you like more details or have any questions about this?  
Here are some additional related questions you might find helpful:

1. How do you interpret the \( r^2 \) value in this context?
2. What does the negative \( b \)-value imply about the trend in the data?
3. How could you assess if the exponential model is the best fit for the data?
4. What are residuals, and why are they important in regression analysis?
5. How do outliers affect the residuals and the overall model fit?

**Tip**: Always check the residuals plot when fitting a model—it helps assess how well the model captures the data trends.

A) come up with a exponential regression model and state r & r^2 B) sketch the residuals of the exponential model v Day d Day d |4|13|18|21|25|30|40| Number n|90|68|56|54|48|38|26|

Learn how to fit an exponential regression model for the dataset of days and numbers, with a detailed explanation of the correlation coefficient (r) and coefficient of determination (r^2). Also, explore the residual analysis to assess the model's accuracy. This problem covers advanced mathematical concepts suitable for high school or college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation