To determine how many values would be located below the residual = 0 line in a residual plot, we need to understand the concept of residuals.
Residuals are the differences between the observed values (y-values of your points) and the predicted values (y-values of the line at the corresponding x-values). The residual is calculated as:
\[ \text{Residual} = \text{Observed value} - \text{Predicted value} \]
A residual value of 0 means the observed value and predicted value are equal. If a point has a residual less than 0, it lies below the residual = 0 line, meaning the observed value is less than the predicted value.
In this scenario, you have one point on the line where the residual would be 0. The five nearby points can either be above or below the line. Typically, in a scatterplot like this:
- Since the line is sloping upwards and passes through various quadrants,
- If we assume the points near the line are randomly placed, they could be both above and below the line.
Considering the potential configurations of the five points, we can make an educated guess. Given the upward slope of the line, it often happens that you will find a balance of the points being above and below the line.
If we analyze the typical distributions in scatter plots, a reasonable assumption would be that there might be 2 or 3 points below the line.
Without further information about the exact position of the five points near the line, you cannot give a definitive answer, but common behavior suggests:
3 points below the residual = 0 line might be a good guess based on typical scatter plots and the distribution of residuals around a regression line.
Thus, the answer would be 3.