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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.

1 answer

To determine the best fit trend line for the scatterplot data representing the monthly sales and advertising costs, we need to analyze the options given regarding how well each line fits the data.

  1. First option: A line with a positive slope passing through 2 points, with 7 points above the line and 1 below. The presence of significantly more points above the line suggests that the line may not be the best representation of the overall trend, as it indicates that sales tend to be higher than predicted by the line.

  2. Second option: A horizontal line goes through the points. A horizontal line indicates no correlation between advertising costs and sales, which is unlikely if the data shows a positive trend.

  3. Third option: A vertical line goes through the points. A vertical line indicates a perfect correlation in the independent variable (ad costs), which is typically not applicable in this context as it suggests that sales do not change regardless of advertising costs.

  4. Fourth option: A line with a positive slope drawn through 2 points, with 4 points above the line and 4 points below. This suggests a more balanced relationship between the sales and advertising costs, indicating that while sales increase with ad spending, there is some variability around the trend line.

Given these options, the fourth option seems to be the best fit, as it reflects the overall upward trend in sales relative to advertising costs while still accounting for some variability in the data. A line with a positive slope and an equal number of points above and below suggests a more accurate representation of the relationship between the two variables.