Class WeightedRegressionOptions<T>
Configuration options for weighted regression models, which assign different importance to different observations.
public class WeightedRegressionOptions<T> : RegressionOptions<T>Type Parameters
T
- Inheritance
-
WeightedRegressionOptions<T>
- Inherited Members
Remarks
Weighted regression is an extension of standard regression techniques that allows different observations to have different levels of influence on the model. By assigning weights to each observation, you can control how much each data point contributes to the parameter estimation process. This approach is particularly useful when dealing with heteroscedasticity (non-constant variance in errors), outliers, or when some observations are known to be more reliable or important than others. Common applications include time series analysis where recent observations may be weighted more heavily than older ones, or situations where observations have different measurement precision. This class inherits from RegressionOptions and adds parameters specific to weighted regression.
For Beginners: Weighted regression lets you give some data points more influence than others.
In standard regression:
- All observations have equal influence on the model
- This assumes all data points are equally important and reliable
Weighted regression solves this by:
- Allowing you to assign different weights to different observations
- Giving more influence to observations with higher weights
- Reducing the impact of less reliable or less important data points
This approach is useful when:
- Some observations are more reliable than others
- Recent data is more relevant than older data
- Certain observations are known to be outliers
- Data points have different levels of measurement precision
For example, in time series forecasting, you might assign higher weights to recent observations to make your model more responsive to recent trends.
This class lets you configure how the weighted regression model is structured.
Properties
Order
Gets or sets the order of the regression model.
public int Order { get; set; }Property Value
- int
A non-negative integer, defaulting to 1.
Remarks
This property specifies the order of the regression model, which determines the highest power of the independent variable included in the model. For example, an order of 1 corresponds to a linear regression (y = a + bx), an order of 2 corresponds to a quadratic regression (y = a + bx + cx²), and so on. A higher order allows the model to capture more complex nonlinear relationships but increases the risk of overfitting. The default value of 1 provides a simple linear model suitable for many applications. The optimal order depends on the underlying relationship between the variables and can be determined using techniques such as cross-validation or information criteria.
For Beginners: This setting determines the complexity of the relationship between variables.
The regression order:
- Defines the highest power of the independent variable in the equation
- Determines the shape of the curve that can be fitted to your data
- Higher orders can model more complex, nonlinear relationships
The default value of 1 means:
- The model is a straight line (linear regression): y = a + bx
- This is appropriate for many relationships that are approximately linear
Common values and their equations:
- 1: Linear (y = a + bx)
- 2: Quadratic (y = a + bx + cx²)
- 3: Cubic (y = a + bx + cx² + dx³)
When to adjust this value:
- Increase it when the relationship between variables is clearly nonlinear
- Keep at 1 for simple linear relationships
- Be cautious with high orders as they can lead to overfitting
For example, if plotting your data shows a clear curved relationship, you might increase this to 2 to fit a quadratic curve.
Weights
Gets or sets the weights assigned to each observation.
public Vector<T> Weights { get; set; }Property Value
- Vector<T>
A vector of weights, defaulting to an empty vector.
Remarks
This property specifies the weights assigned to each observation in the regression model. Each weight determines the relative influence of the corresponding observation on the parameter estimation process. Higher weights give more influence to the corresponding observations, while lower weights reduce their influence. The weights should be non-negative, with zero weights effectively excluding the corresponding observations from the model. The default value is an empty vector, which means that weights must be explicitly provided before fitting the model. The length of the weights vector should match the number of observations in the dataset. Common weighting schemes include equal weights (standard regression), inverse variance weights (to account for heteroscedasticity), exponential decay weights (for time series), and robust weights (to reduce the influence of outliers).
For Beginners: This setting specifies how much influence each data point has on the model.
The weights vector:
- Contains a weight value for each observation in your dataset
- Higher weights give that observation more influence on the model
- Lower weights reduce an observation's influence
- Zero weights effectively remove observations from consideration
The default value is an empty vector, which means:
- You must provide weights before fitting the model
- If you don't set weights, all observations will have equal influence
Common weighting approaches:
- Equal weights (1, 1, 1, ...): Standard regression with equal influence
- Time-based weights (e.g., 0.2, 0.4, 0.7, 1.0): More recent data has more influence
- Reliability weights: More reliable measurements get higher weights
- Robust weights: Automatically reduce weights for potential outliers
When to adjust this value:
- Set specific weights when some observations should have more influence than others
- Use time-based weights for time series where recency matters
- Use inverse variance weights when observations have different precision
For example, in a time series model of monthly sales, you might use weights like [0.5, 0.6, 0.7, 0.8, 0.9, 1.0] to give more recent months more influence.