What is the residual?

Answer: 3 Residual = observed - predicted = 11 - 8 = 3.

What is the residual?

Answer: -3 y-hat = 2(6) + 5 = 17. Residual = 14 - 17 = -3.

What is the residual?

Answer: -2 Residual = observed - predicted = 20 - 22 = -2.

AP Statistics · Topic 2.7

Residuals Practice

Part of Exploring Two-Variable Data.(DAT-1.D)

Practice questions

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Sample questions

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Sample 1difficulty 1/5
$A regression model predicts y-hat = 8 for an observation whose actual y-value is 11.$
$What is the residual?$
- A
  $3$
  check_circle
- B
  $11$
- C
  $-3$
- D
  $8$
Why
$Residual = observed - predicted = 11 - 8 = 3.$
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Sample 2difficulty 2/5
$A regression predicts y-hat = 2x + 5. For x = 6, the observed y is 14.$
$What is the residual?$
- A
  $-17$
- B
  $-3$
  check_circle
- C
  $17$
- D
  $3$
Why
$y-hat = 2(6) + 5 = 17. Residual = 14 - 17 = -3.$
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Sample 3difficulty 2/5
$For the line y-hat = 10 + 3x with observation (x=4, y=20).$
$What is the residual?$
- A
  $20$
- B
  $22$
- C
  $-2$
  check_circle
- D
  $2$
Why
$Residual = observed - predicted = 20 - 22 = -2.$
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Sample 4difficulty 2/5
$Consider the residuals from a least-squares regression line.$
$Which statement is always true?$
- A
  $All residuals are positive$
- B
  $Residuals equal predicted values$
- C
  $The sum of squared residuals equals 0$
- D
  $The sum of the residuals equals 0$
  check_circle
Why
$The least-squares method produces residuals that sum to 0 (when an intercept is included).$
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Sample 5difficulty 3/5
$Output for predicting weight from height shows residual SD s = 10.$
$Which interpretation of s is best?$
- A
  $The line passes within 10 inches of every point$
- B
  $Typical prediction error is about 10 lb$
  check_circle
- C
  $10 lb equals the slope of the line$
- D
  $About 10% of observations are below the line$
Why
$s estimates the typical (root-mean-square) size of residuals, i.e., the typical prediction error.$
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