Understanding Residuals Worksheet
This worksheet helps Grade 11 students understand residuals, calculate them, and interpret residual plots in the context of linear regression.
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Understanding Residuals
Name:
Date:
Score:
Read each question carefully and provide your answers in the space provided. Show all your work for calculation questions.
1. In your own words, define what a residual is in the context of linear regression.
2. Explain the difference between an observed value and a predicted value.
3. A positive residual indicates that the observed value is than the predicted value.
4. A negative residual means the observed value is than the predicted value.
5. The sum of the residuals for a least-squares regression line is always .
6. Which of the following is the formula for calculating a residual?
Predicted - Observed
Observed - Predicted
Observed + Predicted
Predicted / Observed
7. A student predicted a test score of 85, but the student actually scored 92. Calculate the residual.
8. For a different student, the observed score was 70 and the predicted score was 78. Calculate the residual and interpret its meaning.
9. Consider the following residual plot:
a) Does this residual plot suggest that a linear model is appropriate for the data? Explain why or why not.
10. A residual plot with a clear pattern (e.g., a curve) suggests that a linear model is a good fit for the data.
True
False