Question

Select all the statements that are true of a least-squares regression line.

a) It minimizes the sum of the squared residuals.
b) It always passes through the origin (0,0).
c) The sum of the residuals is always zero.
d) It is not affected by outliers.

Answer 1

Only statements (a) and (c) are true about a least-squares regression line; it minimizes the sum of squared residuals, and the sum of the residuals is zero. Statements (b) and (d) are false; the line does not always pass through the origin, and it can be affected by outliers.

Step-by-step explanation:

The subject of this question is the characteristics of a least-squares regression line in the context of Mathematics, particularly statistics. When dealing with a least-squares regression line, there are some key points to consider:

• (a) True: A least-squares regression line does indeed minimize the sum of the squared residuals, which is known as the sum of squared errors (SSE).
• (c) True: The sum of the residuals around the least-squares regression line is always zero, which is a result of how the line is calculated to minimize the SSE.

However, some statements are incorrect:

• (b) False: A least-squares regression line does not always pass through the origin (0,0) unless the data dictates that the best-fit line does so.
• (d) False: A least-squares regression line can be affected by outliers, which can significantly alter the slope and intercept of the line if present.