LEAST SQUARES ANALYSIS Meaning and
Definition
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Least squares analysis is a statistical technique used to find the best-fit line or curve that minimizes the sum of the squared differences between the observed and predicted values of a dependent variable. It is widely employed in regression analysis, a field of statistical modeling that explores the relationship between one or more independent variables and a dependent variable.
In least squares analysis, the goal is to estimate the unknown parameters of a mathematical model that best represent the relationship between the independent and dependent variables. The method calculates these parameter estimates by minimizing the sum of the squared residuals, which are the differences between the observed and predicted values for the dependent variable.
The analysis begins by assuming a functional form for the model, which can be linear or non-linear. The least squares approach then uses an algorithm to adjust the values of the model parameters until the sum of the squared residuals is minimized. This process is typically achieved through mathematical optimization techniques.
By minimizing the squared residuals, the least squares analysis provides the "best fit" line or curve that closely aligns with the observed data points, allowing for the estimation of unknown parameters and enabling predictions or inferences about the dependent variable.
Overall, least squares analysis is a powerful statistical tool used to analyze relationships, make predictions, and uncover patterns in data by finding the best-fit model that minimizes the discrepancy between observed and predicted values.
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