Multiregressiomallin

Multiregressiomalli, or multiple regression model in English, is a statistical technique used to analyze the relationship between a dependent variable and two or more independent variables. The primary goal is to understand how changes in the independent variables affect the dependent variable. This is achieved by fitting a linear equation to the observed data, where the dependent variable is expressed as a weighted sum of the independent variables, plus an error term. The weights, known as regression coefficients, indicate the strength and direction of the relationship between each independent variable and the dependent variable, while holding other independent variables constant.

The process of building a multiregressiomalli involves selecting appropriate independent variables, estimating the coefficients, and then evaluating the model's fit and the significance of the predictors. Statistical tests, such as the F-test for overall model significance and t-tests for individual coefficients, are used to assess the reliability of the findings. Common metrics like R-squared are employed to measure the proportion of variance in the dependent variable that is explained by the independent variables. Multiregressiomalli is widely applied in various fields, including economics, social sciences, and engineering, for prediction, explanation, and forecasting. Assumptions such as linearity, independence of errors, homoscedasticity, and normality of residuals are crucial for the validity of the model's inferences.