RESEARCH METHODOLOGY

Detailed explanation-1: -It gives us an idea of how well the regression line fits the data points. So, the standard deviation is to the mean as the Standard Error of the Estimate is to the regression line.

Detailed explanation-2: -The ‘usual’ definition of the standard deviation is with respect to the mean of the data. In a regression, the mean is replaced by the value of the regression at the associated value of the independent variable.

Detailed explanation-3: -Standard error of the regression = (SQRT(1 minus adjusted-R-squared)) x STDEV. S(Y). So, for models fitted to the same sample of the same dependent variable, adjusted R-squared always goes up when the standard error of the regression goes down.

Detailed explanation-4: -Standard deviation describes variability within a single sample, while standard error describes variability across multiple samples of a population. Standard deviation is a descriptive statistic that can be calculated from sample data, while standard error is an inferential statistic that can only be estimated.