In statistic regressions, does "standard error" mean the residual (vertical distance of each point from the regression line)?
No, the "standard error" in statistical regressions and hypothesis testing refers to the variability or uncertainty in the estimated regression coefficients rather than the distance of each point from the regression line (i.e., the residuals).
The standard error of the regression coefficient is a measure of how much the estimated coefficient is expected to vary if the same regression analysis is repeated on multiple samples from the same population. It captures the uncertainty associated with estimating the true value of the regression coefficient based on a limited dataset.
To calculate the standard error, you typically use the formula:
SE = s / √(n - k - 1)
Where:
- SE is the standard error
- s is the standard deviation of the residuals (i.e., the average distance of each observed point from the regression line)
- n is the number of observations in the dataset
- k is the number of independent variables in the regression model
In summary, the standard error in statistical regressions quantifies the variability or uncertainty in estimating the regression coefficients. It is not directly related to the residual (vertical distance of each point from the regression line), but rather reflects the overall precision and reliability of the coefficient estimates.