Description: Explained variance is a statistical concept that refers to the proportion of the total variance in a dataset that can be attributed to a specific model. In simpler terms, it measures how much of the observed variability in the data can be explained by the independent variables in a regression model. This concept is fundamental in regression analysis, where the goal is to understand the relationship between a dependent variable and one or more independent variables. Explained variance is commonly expressed as a percentage and is calculated as the ratio of the regression sum of squares to the total sum of squares. A high explained variance value indicates that the model is effective in capturing the variability in the data, while a low value suggests that the model is not adequately capturing the relationship between the variables. This indicator is crucial for assessing the quality of a predictive model and for making comparisons between different models. In summary, explained variance is a key tool in statistics that allows researchers and analysts to quantify the effectiveness of their models in representing complex data.
History: The concept of explained variance originated in the context of statistics and regression analysis, which developed throughout the 20th century. Although the foundations of statistics date back centuries, the formal use of regression and variance was consolidated in the 1920s with the work of statisticians like Ronald A. Fisher, who introduced methods of analysis of variance (ANOVA) and linear regression. These methods allowed researchers to quantify the relationship between variables and assess the effectiveness of their models.
Uses: Explained variance is primarily used in regression analysis to assess the quality of predictive models. It is an essential tool in various disciplines, such as economics, biology, psychology, and engineering, where the goal is to understand the relationship between variables and predict outcomes. Additionally, it is used in model selection, helping analysts determine which variables are most relevant in explaining variability in the data.
Examples: A practical example of explained variance can be seen in a study analyzing the impact of multiple factors on a given outcome, such as income. If the regression model shows that 70% of the variance in that outcome can be explained by these factors, it means that they are significant in understanding differences in the outcome. Another example is found in predicting prices in various markets, where explained variance can indicate how well a model that includes features can predict selling prices.
