The ordinary least squares regression line always passes through the point $( \bar { x } , \bar { y } )$

Question

Quizplus · Accepted Answer

The ordinary least squares regression line is the line that minimizes the sum of the squared differences between the predicted values and the actual values. This line is determined by calculating the slope and y-intercept using the formula:

slope = r * (sy/sx)
y-intercept = ŷ - slope * x̂

where r is the correlation coefficient, sy is the standard deviation of y, sx is the standard deviation of x, and (x̂, ŷ) is the mean of the x and y variables.

Since (x̂, ŷ) is used to calculate the y-intercept, the regression line will always pass through the point (x̂, ŷ) or (\bar { x } , \bar { y } ) in this case, which is the point that represents the average of the x and y variables. Therefore, the statement is true.

The Ordinary Least Squares Regression Line Always Passes Through the Point