Question

question 7
1 pts
the least - squares regression line is:

a. the line that passes through the most data points.

b. the line that makes the sum of the squares of the vertical distances of the data points from the line (the sum of squared residuals) as large as possible.

c. the line such that half of the data points fall above the line and half fall below the line.

d. the line that passes through the mean of x and mean of y

Explanation:

The least - squares regression line is defined as the line that minimizes the sum of the squares of the vertical distances (residuals) of the data points from the line. It does not necessarily pass through the most data points, does not aim to have half of the data points above and half below, and while it does pass through the point $(\bar{x},\bar{y})$ (the mean of $x$ and mean of $y$), this is not the full definition. The key characteristic is minimizing the sum of squared residuals.

Answer:

D. The line that passes through the mean of x and mean of y