To determine the best description of the residual plot based on the given information about the scatterplot, we need to understand what "residuals" represent. Residuals are the differences between the observed values and the predicted values from the regression line.
Given that the scatterplot has a line, we can infer that there will be residuals above and below the line depending on how well the line fits the data points.
Here’s how to interpret the options based on residuals:
- Points below the x-axis indicate negative residuals (observed values are less than predicted).
- Points on the x-axis indicate zero residuals (observed values equal predicted values).
- Points above the x-axis indicate positive residuals (observed values are greater than predicted).
Now let's analyze the options provided:
- (a) 3 dots left of the y-axis, 3 dots on the y-axis, and 4 dots right of the y-axis - This focuses on horizontal placement rather than vertical (residuals).
- (b) 3 dots below the x-axis and 7 dots above the x-axis - This indicates there are significantly more positive residuals than negative, suggesting a good fit with the majority being above the line.
- (c) 4 dots below the x-axis, 3 dots on the x-axis, and 3 dots above the x-axis - Here, we have a balance between negative and zero residuals, with a few above.
- (d) 3 dots below the x-axis, 3 dots on the x-axis, and 4 dots above the x-axis - There are equal amounts of negative and zero residuals and more positive residuals.
Without the visual reference, the choice that suggests an imbalance favoring positive residuals (indicating observed values often exceed predicted ones) would suggest more information about the fit of the regression line. The best match would be:
(b) a residual plot with 3 dots below the x-axis and 7 dots above the x-axis.