Model fitting is the process of adjusting a statistical model so that it best captures the patterns in a given dataset. It involves optimizing the model parameters to minimize the difference between observed data and model predictions, often using techniques like least squares or maximum likelihood estimation.

Model Fitting

Model fitting

A statistical model is a mathematical representation of observed data, capturing relationships between variables and allowing predictions or inferences about the data. It is essential for understanding patterns, testing hypotheses, and making decisions based on data-driven insights.

statistical model

Optimizing model parameters

difference between observed data and model predictions

Least Squares is a mathematical optimization technique used to find the best-fitting curve or line to a given set of data points by minimizing the sum of the squares of the differences between the observed and predicted values. It is widely used in regression analysis and curve fitting to ensure that the model has the least possible error in predicting the dependent variable from the independent variables.

least squares

Maximum Likelihood Estimation (MLE) is a statistical method for estimating the parameters of a model by maximizing the likelihood function, thereby making the observed data most probable under the assumed statistical model. It is widely used due to its desirable properties such as consistency, efficiency, and asymptotic normality, which make it a cornerstone of statistical inference and machine learning.

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