Residuals in Data Analysis
A Grade 10 math worksheet focusing on understanding, calculating, and interpreting residuals in linear regression.
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Residuals in Data Analysis
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Read each question carefully and provide your answers in the space provided. Show all your work for calculation questions.
1. A residual is the difference between an observed y-value and its predicted y-value.
2. When a linear model perfectly predicts an observed value, the residual will be .
3. A positive residual indicates that the observed value is the predicted value.
4. A negative residual indicates that the observed value is the predicted value.
Consider the following observed data point (x=3, y=10) and a regression line with the equation ŷ = 2x + 3.
5. Calculate the predicted y-value (ŷ) for x=3.
6. Calculate the residual for this data point.
7. What does the sign of this residual tell you about the observed value relative to the regression line?
8. A good linear model should have residuals that are randomly scattered around zero.
True
False
9. If a residual plot shows a clear pattern (e.g., a curve), it suggests that a linear model is the best fit for the data.
True
False
10. Which of the following residual plots would indicate that a linear model is a good fit for the data?
Residuals show a clear U-shaped pattern.
Residuals are randomly scattered above and below zero.
Residuals show a clear increasing or decreasing trend.
Residuals are all positive.
A student collected data on the number of hours studied (x) and the score on a math test (y). The regression line for this data is ŷ = 5x + 50.
11. If a student studied for 4 hours and scored 75 on the test, calculate the residual for this student.
12. What does this residual indicate about the student's performance compared to the prediction?