A residual in regression analysis is the difference between the actual value of a data point and the value predicted by the regression model. It can be calculated as:
[tex]\[ \text{Residual} = \text{Actual Value} - \text{Predicted Value} \][/tex]
Given that a data point has a residual of -1, let's analyze what this means step-by-step:
1. Understand the Residual Value: A residual of -1 indicates that the actual value is 1 unit less than the predicted value.
2. Relationship to the Regression Line: The regression line represents the predicted values for the data points. Therefore, if a point has a residual of -1, it lies 1 unit below the predicted value given by the regression line.
Let's evaluate the possible answers:
A. The point lies directly on the regression line: This would mean the residual is 0, which is not the case here.
B. The point lies 1 unit below the regression line: Since the residual is -1, it translates to the actual value being 1 unit less than the predicted value, which is consistent with the point lying 1 unit below the regression line.
C. The point lies 1 unit above the regression line: This would imply the residual is +1, which is opposite of what is given.
D. The predicted value for that point is -1: This option incorrectly describes what a residual of -1 means.
Therefore, the correct answer is:
B. The point lies 1 unit below the regression line.
