Regressioyhtälöt

Regressioyhtälöt are mathematical equations used to model the relationship between a dependent variable and one or more independent variables. The goal of a regression equation is to describe how changes in the independent variables are associated with changes in the dependent variable. These equations are fundamental tools in statistical analysis and are widely used in various fields, including economics, social sciences, and engineering, to understand and predict phenomena.

The simplest form is the simple linear regression equation, which models the relationship between two variables as a straight line. This equation typically takes the form Y = a + bX, where Y is the dependent variable, X is the independent variable, 'a' is the intercept (the value of Y when X is zero), and 'b' is the slope (the change in Y for a one-unit change in X). Multiple linear regression extends this concept to include more than one independent variable, allowing for the analysis of more complex relationships.

In practice, when fitting a regression equation to data, there is often a component of random error, which is not explained by the independent variables. This error term is typically included in the full regression equation as 'e', resulting in Y = a + bX + e for simple linear regression. The process of finding the best-fitting regression equation involves estimating the parameters (coefficients like 'a' and 'b') that minimize the difference between the observed values of the dependent variable and the values predicted by the equation. Common methods for this estimation include the method of least squares.