In the dichotomous regression if one was to replace the regression line prediction of the outcome means (for treated/untreated) with medians, which of the following conditions would hold?
A) The sum of all the residuals would equal zero.
B) The sum of the residuals for the treated observations would equal zero.
C) The slope of the regression line would be positive.
D) The number of strictly positive residuals would equal the number of strictly negative residuals.

Question

Quizplus · Accepted Answer

When using medians in regression analysis, the method aims to minimize the absolute deviations rather than the squared deviations. This leads to a situation where the number of positive residuals is equal to the number of negative residuals, ensuring that the median is the central point of the distribution of residuals. This property does not necessarily ensure that the sum of residuals equals zero (as in mean regression), nor does it directly affect the slope of the regression line or guarantee that the sum of residuals for a specific group (treated or untreated) equals zero.

In the Dichotomous Regression If One Was to Replace the Regression