How to Determine if Exponential Regression is Correct and Find Percent Increase

Understanding whether your regression model is exponential and calculating percent increase is essential in data analysis. Let’s dive deeper into how to correctly identify an exponential regression and compute percent increases effectively.

### Identifying Exponential Regression
Exponential regression is used when data shows a multiplicative growth pattern. Unlike linear regression, which follows the equation P = mx + b (where m is the slope, and b is the y-intercept), exponential regression follows the form P = a·b^n. Here, 'a' represents a starting value, and 'b' is the growth factor.

For example, if you're analyzing population growth, your equation might look something like P = 1000 * 1.05^n, indicating a 5% growth rate each period. If your current equation is in a linear format, like P = 3565.58n + 746.740, you need to recalculate using the exponential regression method.

To find the correct exponential regression on a graphing calculator (like a TI-84):
1. Enter your independent variable (n values) in list L1 and your dependent variable (P values) in list L2.
2. Access the STAT menu and select CALC.
3. Choose ExpReg to compute the exponential regression.
4. The calculator will then provide you with values for 'a' and 'b', allowing you to construct the correct exponential equation.

### Calculating Percent Increase
Once you have your regression model, you might also want to determine the percent increase from one value to another. The formula for percent increase is:

**Percent Increase = [(New Value - Old Value) / Old Value] × 100**

For instance, if your population grew from 4600 to 5678.78 (as in your example), the calculation would be:
1. New Value = 5678.78
2. Old Value = 4600
3. Percent Increase = [(5678.78 - 4600) / 4600] × 100 ≈ 23.94%.

This calculation helps in understanding the growth rate in percentage terms, which is often more intuitive than raw numbers. Knowing how to perform these calculations is beneficial not only in academic settings but also in real-world applications, such as finance, biology, and social sciences.

### Conclusion
By ensuring that you are using the correct exponential regression model and being able to compute percent increases, you're equipped to analyze growth trends effectively. Mastering these concepts will enhance your analytical skills and contribute to your success in various fields of study.