Regression analysis

Definition

Regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables. In this context, it often involves fitting exponential models to data to predict growth or decay trends.

5 Must Know Facts For Your Next Test

1. Regression analysis can be used to determine the parameters of an exponential function that best fits a given set of data points.
2. The least squares method is commonly employed in regression analysis to minimize the sum of squared differences between observed and predicted values.
3. An exponential regression model takes the form $y = ab^x$ where $a$ and $b$ are constants determined through regression analysis.
4. Logarithmic transformations may be applied to linearize an exponential model, making it easier to apply linear regression techniques.
5. Residual plots help assess the fit of an exponential regression model by showing the difference between observed and predicted values.

Review Questions

• What is the purpose of using regression analysis in fitting exponential models?
• How does the least squares method contribute to regression analysis?
• What form does an exponential regression model take, and how are its parameters determined?

Related terms

Exponential Function: A mathematical function in which an independent variable appears in the exponent, typically written as $f(x) = ab^x$.

Least Squares Method: A standard approach in regression analysis that minimizes the sum of squared differences between observed values and those predicted by a model.

Residual Plot: A graph showing the residuals (differences between observed and predicted values) on the vertical axis against an independent variable on the horizontal axis, used to assess the fit of a model.