To create a residual plot, we first need to understand how residuals are calculated. A residual is the difference between the observed value (Y) and the predicted value (Ŷ) for each data point. The formula is:
\[ \text{Residual} = Y - Ŷ \]
In the case you provided, we have the following points:
- (1, 1)
- (0, 1.5)
- (2, 3)
- (3, 3)
- (4, 5)
- (5, 5.5)
To determine how many values would be located below the residual = 0 line, we'd need to know the trend or the regression line (the predicted values, Ŷ, for each X value) to calculate the residual for each point. Assuming you have a regression line (which you usually would derive from the scatter plot), you would then compute the residuals for each X coordinate, comparing the Y values to the Ŷ values.
Without an exact regression model or predicted values (Ŷ) given, we wouldn’t be able to compute the residuals directly. However, we can reason about this:
- If a data point lies above the regression line, its residual will be positive (Y > Ŷ).
- If a data point lies on the regression line, its residual will be zero (Y = Ŷ).
- If a data point lies below the regression line, its residual will be negative (Y < Ŷ).
To summarize, once you compute or know the predicted values for each X based on the regression line, you can determine how many points have a positive, negative, or zero residual. You would look for how many of those residuals are negative, which indicates how many points lie below the residual = 0 line.
If you provide the regression line or predicted values, I can help calculate the residuals and determine how many are below zero.