Total Sum of Squares (SST)
Total Sum of Squares (SST) is a measure of the total variability in the dependent variable around its mean. It is an important benchmark in regression analysis used to assess how much of the total variation is explained by the regression model as opposed to the residual error.
Standard Error of Estimate
The standard error of the estimate (s_e) is the square root of the mean square error and represents the typical distance that the observed data points fall from the regression line. It provides insight into the precision of predictions made by the regression model.
Adjusted Coefficient of Determination
The adjusted coefficient of determination adjusts R^2 for the number of explanatory variables in the model, taking into account the number of predictors relative to the number of observations. This adjustment provides a more accurate measure of model performance, particularly when comparing models with different numbers of predictors.
Coefficient of Determination (R^2)
The coefficient of determination, R^2, quantifies the proportion of the total variation in the dependent variable that is explained by the regression model. It is a measure of how well the independent variables collectively account for the variability in the outcome.
Residual Error
Residual error, in regression modeling, is the difference between the observed values and the values predicted by the model. It quantifies the variability in the dependent variable that remains unexplained after fitting the model to the data.
Sum of Squares (SS)
Sum of Squares (SS) is a measure of the total variation in the data. In the context of regression, it is divided into regression sum of squares, which represents the variability captured by the model, and error (residual) sum of squares, which represents the portion of variability not explained by the model.
Degrees of Freedom (DF)
Degrees of Freedom (DF) represent the number of independent values that can vary in an analysis without breaking any constraints. In regression ANOVA tables, DF are allocated to the regression model and the residual error, reflecting the number of parameters estimated and the amount of information available for error estimation.
Analysis of Variance (ANOVA) in Regression
The ANOVA approach in regression is used to decompose the total variability of the dependent variable into components attributable to the regression (explained variance) and residual error (unexplained variance). This decomposition helps in testing the overall significance of the regression model.
Regression Analysis
Regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It helps in estimating the nature of the association, predicting values, and understanding which factors contribute significantly to the variation in the outcome.
Mean Square (MS)
Mean Square (MS) is obtained by dividing the sum of squares by its corresponding degrees of freedom. In regression analysis, the mean square for the residual error is particularly important as it provides an estimate of the variance of the error term in the model.