Question
A simple linear regression model was constructed to predict exam scores using quiz scores in STAT 200 . According to that model, Mel's predicted exam score was 43 points. Mel's actual exam score was 54 points. Compute the residual for Mel's exam score
Ask by Ward Hart. in the United States
Feb 03,2025
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Tutor-Verified Answer
Answer
Mel's residual is 11 points.
Solution
In linear regression, a **residual** is the difference between the actual observed value and the value predicted by the model. It measures the error in the prediction for a particular data point.
**Residual Calculation:**
\[
\text{Residual} = \text{Actual Exam Score} - \text{Predicted Exam Score}
\]
Plugging in Mel's scores:
\[
\text{Residual} = 54 - 43 = 11
\]
**Conclusion:**
Mel's residual for the exam score is **11 points**.
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The residual is calculated by taking the difference between the actual exam score and the predicted exam score. In Mel's case, you would subtract the predicted score (43 points) from the actual score (54 points): Residual = Actual Score - Predicted Score Residual = 54 - 43 = 11. So, Mel's residual is 11 points! This positive residual suggests that Mel performed better on the exam than what was predicted by the model—way to go, Mel! If you're diving into regression, remember that a positive residual indicates an underestimation, while a negative one indicates an overestimation. Catching these insights can really enhance your understanding of data prediction!
