Question

these scatterplots represent the monthly sales and advertising costs of a company. which trend line is the best fit for the data?

Explanation:

Step1: Analyze the first scatter - plot

The line in the first scatter - plot passes through the origin. But looking at the data points, there is no indication that when ad costs are \(0\) (i.e., \(x = 0\)), sales are \(0\). So this line is not a good fit.

Step2: Analyze the second scatter - plot

The line in the second scatter - plot is horizontal. A horizontal line implies that sales do not change with an increase in advertising costs, which is not in line with the general relationship (more advertising usually leads to more sales, at least in a positive - correlation sense). So this line is not a good fit.

Step3: Analyze the third scatter - plot

The line in the third scatter - plot is vertical. A vertical line does not represent a function (fails the vertical line test for a relationship between two variables \(x\) (ad costs) and \(y\) (sales)). So this line is not a good fit.

Step4: Analyze the fourth scatter - plot

The line in the fourth scatter - plot has a positive slope (as advertising costs increase, sales increase) and is positioned such that it balances the data points around it. It is a reasonable approximation of the trend of the data points.

Answer:

The fourth scatter - plot (the one with a non - zero positive slope that balances the data points around it) has the best - fit trend line.