Question

Solve and write about equations of trend lines.
These scatterplots represent the monthly sales and advertising costs of a company. Which trend line is the best fit for the data?
A graph with ad costs (1,000 dollars) on the x-axis, and sales (1,000 dollars) on the y-axis. Points are grouped together and increase. A line with positive slope is drawn through 2 points. There are 7 points above the line, and 1 below.
A graph with ad costs (1,000 dollars) on the x-axis, and sales (1,000 dollars) on the y-axis. Points are grouped together and increase. A horizontal line goes through the points.
A graph with ad costs (1,000 dollars) on the x-axis, and sales (1,000 dollars) on the y-axis. Points are grouped together and increase. A vertical line goes through the points.
A graph with ad costs (1,000 dollars) on the x-axis, and sales (1,000 dollars) on the y-axis. Points are grouped together and increase. A line with positive slope is drawn through 2 points. There are 4 points above the line and 4 points below.

Answer 1

The best fit is the fourth graph (the positively sloped line with 4 points above and 4 below).

Why:
- The data show an increasing (positive) relationship, so a line with positive slope is appropriate (rules out the horizontal line).
- A vertical line can't be a regression line for predicting sales from ad costs — regression lines model y as a function of x, so distances are vertical, not horizontal.
- The first positive-slope line leaves 7 points on one side and 1 on the other, so it is poorly centered; a good trend line roughly balances the vertical deviations (residuals).
- The fourth line balances the points (4 above, 4 below) and thus better represents the central tendency of the scatter — this is what least-squares (best-fit) lines aim to do.