OLSanalüüsis

OLSanalüüs, also known as Ordinary Least Squares, is a fundamental method in regression analysis used to estimate the unknown parameters of a linear regression model. The core idea behind OLS is to find the line that best fits a set of data points by minimizing the sum of the squared differences between the observed values and the values predicted by the linear model. These differences are often referred to as residuals.

In a simple linear regression, the model takes the form Y = β₀ + β₁X + ε, where Y is the dependent variable, X is the independent variable, β₀ is the intercept, β₁ is the slope, and ε represents the error term. OLS aims to find the values of β₀ and β₁ that minimize the sum of squared residuals (SSR): SSR = Σ(Yᵢ - (β₀ + β₁Xᵢ))². By calculating these estimates, OLS provides a way to quantify the relationship between variables and make predictions.

The method relies on several assumptions, including linearity, independence of errors, homoscedasticity (constant variance of errors), and normality of errors. If these assumptions are met, the OLS estimators are considered BLUE (Best Linear Unbiased Estimators), meaning they have the smallest variance among all linear unbiased estimators. Violations of these assumptions can lead to biased or inefficient estimates, requiring alternative methods or transformations of the data. OLS is widely used across various fields, including economics, finance, social sciences, and engineering, due to its simplicity and interpretability.