To determine the number of values that would be located below the residual = 0 line, we need to understand what residuals represent. Residuals are calculated as the difference between the observed values (the actual data points) and the predicted values (the values estimated by the line of best fit).
Points located above the residual = 0 line have positive residuals, which means their observed values are greater than predicted values. Conversely, points below the residual = 0 line have negative residuals, meaning their observed values are less than predicted values.
From your description, since the line is sloping upward and passes through various quadrants, it suggests that the actual data points can be positioned both above and below the line of best fit.
If we assume that there are five points near the line, and given the general behavior of a regression line through a set of data, it is likely that there would be a mix of points both above and below the line.
However, the specific number of points below the residual = 0 line requires examining the scatterplot visually or knowing more information about the distribution of the points in relation to the line of best fit. Since it’s not given explicitly, we could make some logical assumptions based on typical distributions.
In many cases with five points:
- It could be that around 2-3 points might be above the line while the rest would be below, as regression lines often balance out over a set of data that is roughly linear.
Given the options:
- If we guess that it is common to have a few points below and a few above with such data, 2 or 3 might be reasonable estimates.
Since we need to choose one:
- 2 is a common estimate, considering typical distributions around a linear regression line.
So the correct response would be:
2