Regression 4. Linear Regression - Model Fitting Techniques

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 Model Fitting Technique

The term "model fitting technique" in the context of statistics and machine learning refers to the methods and algorithms used to construct a mathematical model that best describes the relationship between variables in a given dataset. Specifically, in the context of linear regression, it involves finding the coefficients (parameters) that minimize the difference between the observed data and the model's predictions.

 Model Fitting in Linear Regression

For linear regression, the process of model fitting typically involves estimating the parameters (coefficients) of the linear equation that best fits the observed data. The equation for a simple linear regression model is:

 Techniques for Model Fitting

1. Ordinary Least Squares (OLS):

   - The most common technique for fitting a linear regression model.

   - It works by minimizing the sum of the squares of the residuals (the differences between the observed values and the values predicted by the model).

2. Gradient Descent:

   - An optimization algorithm used to find the minimum of a function, often used in machine learning.

   - It iteratively adjusts the parameters to find the combination that minimizes the cost function (e.g., the sum of squared errors).

3. Regularization Methods (Ridge, Lasso):

   - Used to prevent overfitting by adding a penalty term to the cost function.

   - Ridge regression adds a penalty proportional to the square of the magnitude of the coefficients.

   - Lasso regression adds a penalty proportional to the absolute value of the coefficients, leading to feature selection.

4. Maximum Likelihood Estimation (MLE):

   - A method that estimates the parameters of a statistical model by maximizing the likelihood function.

   - MLE tries to find the parameter values that make the observed data most probable.

 Importance of Model Fitting

- Accurate model fitting is crucial for making reliable predictions and inferences.

- It helps in understanding the relationship between variables and in forecasting future observations.

- Poor model fitting can lead to incorrect conclusions and predictions.

In summary, model fitting techniques are fundamental to developing an effective statistical model or machine learning algorithm. They are used to find the optimal parameters that best describe the data, taking into account the specific characteristics and assumptions of the chosen model.

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