Non-linear regression extends beyond simple linear relationships to model more complex patterns in data. The most common types of non-linear regression models include:
For instance, population growth might follow an exponential model, while oscillating phenomena like sound waves could be modeled using a sine function.
Choosing the appropriate non-linear regression model depends on the nature of the data and the underlying relationship between variables. Here are some common guidelines:
In the context of AI and machine learning, least squares regression is a fundamental technique for training models on numerical data.
Modern technology, such as graphing calculators and statistical software, can quickly perform least squares regression for various model types. Students are expected to be proficient in using such tools to evaluate different regression models.
The Sum of Square Residuals (SSres) is a measure of the total deviation of the response values from the fit to the response values. It is calculated as:
$$ SSres = \sum_{i=1}^n (y_i - \hat{y}_i)^2 $$
Where:
A smaller SSres indicates a better fit of the model to the data.
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