Residuals & Residual Plots (Grade 12)
Free printable Grade 12 General Mathematics worksheet: calculate residuals and interpret residual plots for a fitted linear model (ACMGM058).
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Grade 12 · Math worksheet
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Date
Math
Bivariate Data: Residuals & Residual Plots (Year 11-12 General Mathematics)
Find the residual for each indicated data point (residual = actual y minus predicted y), then answer the questions about what a residual plot reveals. Residuals are computed from the least-squares line.
- 1.The least-squares line for (1, 51), (2, 57), (3, 66), (4, 69), (5, 79) is y = 44 + 6.8x. Find the residual for the data point (5, 79). Residual = actual y minus predicted y. Give your answer to 2 decimal places.
- 2.The least-squares line for (0, 82), (1, 74), (2, 70), (3, 65), (4, 61) is y = 80.6 - 5.1x. Find the residual for the data point (4, 61). Residual = actual y minus predicted y. Give your answer to 2 decimal places.
- 3.The least-squares line for (1, 29), (2, 25), (3, 21), (4, 18), (5, 14) is y = 32.5 - 3.7x. Find the residual for the data point (2, 25). Residual = actual y minus predicted y. Give your answer to 2 decimal places.
- 4.The least-squares line for (1, 10), (2, 16), (3, 18), (4, 23), (5, 27) is y = 6.5 + 4.1x. Find the residual for the data point (1, 10). Residual = actual y minus predicted y. Give your answer to 2 decimal places.
- 5.The least-squares line for (0, 83), (1, 83), (2, 72), (3, 71), (4, 68), (5, 69) is y = 82.62 - 3.31x. Find the residual for the data point (5, 69). Residual = actual y minus predicted y. Give your answer to 2 decimal places.
- 6.A residual plot for a fitted line shows the residuals scattered randomly about zero with no clear pattern. What does this indicate about the linear model?
- 7.A residual plot shows a clear curved (U-shaped) pattern in the residuals. What does this suggest about fitting a straight line to the data?
- 8.What is plotted on the horizontal and vertical axes of a residual plot?
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