What does it mean to say that a data point has a residual of 1?
A. The point lies 1 unit below the regression line.
B. The point lies 1 unit above the regression line.
C. The point lies directly on the regression line.
D. The x-coordinate of the point is 1.
Answer (2)
A residual represents the difference between the actual and predicted values in a regression model.
A residual of 1 indicates the data point's actual value is 1 unit greater than the predicted value.
This means the point lies 1 unit above the regression line.
Therefore, the answer is OB โ .
Explanation
Understanding Residuals Let's break down what a residual means in the context of regression analysis.
Defining the Residual In regression analysis, we're trying to find a line (the regression line) that best fits a set of data points. The residual is the difference between the actual (observed) value of the dependent variable (y) for a data point and the value predicted by the regression line (ลท) for that same data point. Mathematically, we can express the residual as: residual = y โ y ^ โ
Interpreting a Residual of 1 If a data point has a residual of 1, it means that the actual y-value of the point is 1 unit greater than the y-value predicted by the regression line. In simpler terms, the point lies 1 unit above the regression line.
Conclusion Therefore, the correct answer is OB. The point lies 1 unit above the regression line.
Examples
Imagine you're tracking the relationship between hours studied and exam scores. If a student studied for 10 hours and the regression line predicts a score of 70, but they actually scored 71, the residual is 1. This means their score was 1 point higher than expected based on the general trend.
A residual of 1 indicates that the actual value of a data point is 1 unit greater than its predicted value, meaning the point lies 1 unit above the regression line. Thus, the correct answer is B. The point lies 1 unit above the regression line.
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