Using OLS to solve for the slope and intercept of a simple linear regression will yield a regression line that satisfies which of the following conditions?
A) $\frac { \sum _ { i = 1 } ^ { N } e _ { i } } { N }$ = 0
B) $$\frac { \sum _ { i = 1 } ^ { N } \left( Y _ { i } - b - m X _ { i } \right) X _ { i } } { N }$$ = $\bar { Y }$
C) Sum of squared residuals equals 0.
D) None of the answers is correct.

Question

Quizplus · Accepted Answer

The condition $\frac { \sum _ { i = 1 } ^ { N } e _ { i } } { N }$ = 0, where $e_i$ are the residuals, means that the average of the residuals is zero. This is a property of the Ordinary Least Squares (OLS) method, as it ensures that the regression line passes through the mean of the dependent variable, thereby minimizing the sum of squared residuals.

Using OLS to Solve for the Slope and Intercept of a Simple