Difference between explained variation and total variation in economics
In economics, explained variation and total variation are terms used in statistical analysis to understand the relationship between variables.
Explained variation is the part of the total variation in the dependent variable that can be attributed to the independent variable(s) being considered. It represents the portion of the variation in the dependent variable that is already explained by the independent variable(s) in the statistical model. Explained variation is typically measured using the coefficient of determination (R-squared) in regression analysis.
On the other hand, total variation is the overall variability of the dependent variable, regardless of whether it can be explained by the independent variable(s) or not. It represents the total amount of variation that exists in the dependent variable, including both the variation that can be explained and the random or unexplained variation. Total variation is typically measured using the sum of squared residuals (SSR) in regression analysis.
The difference between explained variation and total variation can be seen as the unexplained or residual variation. If the explained variation is high, close to 1 or 100%, it means that the independent variable(s) can account for most of the variation in the dependent variable. Conversely, if the explained variation is low, close to 0 or 0%, it means that the independent variable(s) have little influence on the dependent variable, and most of the variation is due to other factors or random errors.
Understanding the relationship between explained variation and total variation is crucial in empirical analysis, as it provides insights into the effectiveness and significance of the independent variable(s) in explaining the behavior of the dependent variable.
In economics, explained variation and total variation are used to measure the amount of variability in a data set and understand the relationship between variables.
1. Total Variation: Total variation is a measure of the overall variability in a data set. It represents the sum of the squared differences between each data point and the mean of the data set. In other words, it quantifies the total dispersion of data around the average.
2. Explained Variation: Explained variation, also known as explained sum of squares or the coefficient of determination (R-squared), measures the proportion of the total variation that can be explained by a regression model or explanatory variable(s). It represents the portion of the variation in the dependent variable that is captured by the independent variable(s) in the model.
To calculate the explained variation, you need to estimate a regression model and obtain the sum of squared residuals (SSR) or the sum of squared errors (SSE). The explained variation is then calculated by subtracting the SSR or SSE from the total variation.
Mathematically, the explained variation (EV) can be represented as:
EV = Total Variation - SSR (or SSE)
The ratio of the explained variation to the total variation gives you the R-squared value, which ranges from 0 to 1. A higher R-squared value indicates a stronger relationship between the variables, whereas a lower R-squared value suggests a weaker relationship or a high degree of unexplained variation.
In summary, total variation measures the overall dispersion of data points, while explained variation quantifies the proportion of that total variation that can be attributed to specific factors or explanatory variables in a regression model.