Residuals: practice

Statistics. Try each one, then open the answer. The Credit Sprint app generates unlimited new versions.

Item 1.

The least-squares line is ŷ = 38 + 3x. At x = 6 the observed y is 52. What is the residual (observed − predicted)?

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Predicted ŷ = 38 + 3(6) = 56. Residual = 52 − 56 = -4.

Item 2.

The least-squares line is ŷ = 29 + 4x. At x = 12 the observed y is 74. What is the residual (observed − predicted)?

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Predicted ŷ = 29 + 4(12) = 77. Residual = 74 − 77 = -3.

Item 3.

The least-squares line is ŷ = 13 + 0.5x. At x = 8 the observed y is 24. What is the residual (observed − predicted)?

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Predicted ŷ = 13 + 0.5(8) = 17. Residual = 24 − 17 = 7.

Item 4.

The least-squares line is ŷ = 31 + 2x. At x = 5 the observed y is 46. What is the residual (observed − predicted)?

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Predicted ŷ = 31 + 2(5) = 41. Residual = 46 − 41 = 5.

Item 5.

The least-squares line is ŷ = 32 + 3x. At x = 9 the observed y is 62. What is the residual (observed − predicted)?

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Predicted ŷ = 32 + 3(9) = 59. Residual = 62 − 59 = 3.

Item 6.

The least-squares line is ŷ = 23 + 2.5x. At x = 10 the observed y is 45. What is the residual (observed − predicted)?

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Predicted ŷ = 23 + 2.5(10) = 48. Residual = 45 − 48 = -3.