Which regression line properly describes the data relationship in the scatterplot?

Question

On a graph, a trend line has a positive slope. There are 4 points above the line, and 2 points below.
On a graph, a trend line has a positive slope. There is 1 point above the line, and 5 points below.
On a graph, a trend line has a positive slope. There are 3 points above the line, and 3 points below.
On a graph, a trend line has a positive slope. There are 5 points above the line, and 1 point below.

Answer 1

To determine which regression line properly describes the data relationship in a scatterplot, we generally look for the line that minimizes the distance from the line to all points in the scatterplot.

1. First option (4 points above the line, 2 points below): This indicates that while there are more points above the line than below, it may suggest a potential bias in the fitting process, as there are still many points well above the line.

2. Second option (1 point above the line, 5 points below): Having significantly more points below the line compared to points above suggests that the line may be a poor fit for the trend of the data.

3. Third option (3 points above the line, 3 points below): An equal number of points above and below the line indicates a balance, which may suggest that the line is a reasonable estimate of the trend, representing the data fairly well but with notable scatter.

4. Fourth option (5 points above the line, 1 point below): This indicates that the vast majority of data points are above the regression line, implying that it may not be representative of the general trend of the data.

Given these observations, the third option (3 points above the line and 3 points below) suggests a balanced representation of the data points around the regression line. Thus, it likely provides the best description of the data relationship in the scatterplot.

Therefore, the third option is the most appropriate regression line for the scatterplot.