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Grade 9 · Math · Algebra 1

9th grade Regression lines and residuals worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Regression lines and residuals

Grade 9 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

  1. Milo plotted a puppy's weight. The line predicts 18.4 at x = 10, and the dot there is at y = 19.4. What is the residual at x = 10?

  2. Noah plotted a tomato plant's height. The line predicts 42 at x = 5, and the dot there is at y = 40.4. What is the residual at x = 5?

  3. Pia plotted a candle's height as it burns. The line predicts 19.5 at x = 3, and the dot there is at y = 17.4. What is the residual at x = 3?

  4. Ren plotted reading time against chapter length. The line predicts 44.1 at x = 18, and the dot there is at y = 45.1. What is the residual at x = 18?

  5. Tala plotted the temperature against cricket chirps. The calculator's line is y = 1.2x + 31. What does the line predict for x = 28?

  6. Zee plotted the height of a stack of paper cups. The calculator's line is y = 1.8x + 6.4. What does the line predict for x = 7?

  7. Ari plotted kite height against string let out. The calculator's line is y = 0.6x - 3. What does the line predict for x = 35?

  8. Esme plotted snow depth as the sun comes out. The residual for the dot at x = 4 is -0.8. What does that mean?

    • The dot is 0.8 centimeters above the line; the line predicted too little.
    • The dot is 0.8 centimeters below the line; the line predicted too much.
    • The line is off by 0.8 centimeters at every x.
    • The dot is 0.8 hours to the left of the line.

  9. Jun plotted a puppy's weight. The residual for the dot at x = 15 is 1.4. What does that mean?

    • The dot is 1.4 pounds above the line; the line predicted too little.
    • The dot is 1.4 pounds below the line; the line predicted too much there.
    • The dot is 1.4 weeks to the right of the line.
    • The line is off by 1.4 pounds at every x.

  10. Luz plotted a tomato plant's height. The residual for the dot at x = 7 is 1.6. What does that mean?

    • The dot is 1.6 centimeters below the line; the line predicted too much.
    • The dot is 1.6 weeks to the right of the line.
    • The line is off by 1.6 centimeters at every x.
    • The dot is 1.6 centimeters above the line; the line predicted too little.
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9th grade Regression lines and residuals worksheet – printable
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About this worksheet

Regression lines and residuals. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find a residual as observed minus predicted, and say what its sign means.
  • I can say what the slope and the y-intercept of a fitted line mean in the story, or that the intercept means nothing real.
  • I can use the residuals to judge whether a line is a good model.

Standard: S-ID.B.6a–c, S-ID.C.7

Words to know

least-squares (regression) line: The calculator's best line through the dots.

predicted value: The line's y at a given x.

residual: Observed y minus predicted y: the up-or-down gap to the line.

slope (in a story): The typical change in y for one more unit of x.

y-intercept (in a story): The predicted y when x is 0, if that makes sense.

residual pattern: Signs that run in groups, showing the data bend away from the line.

Common mistakes

Your child subtracted in the wrong order, so the residual's sign flipped. A residual is the actual value minus the predicted value; a dot above the line has a positive residual.

Your child multiplied by the slope but left out the y-intercept. Say the line out loud: slope times x, then plus the y-intercept.

Your child multiplied x by the wrong number in the line's equation. The number right next to x is the slope; it is the one that multiplies x.

Questions parents ask

What is the most common mistake with regression lines and residuals?

Your child subtracted in the wrong order, so the residual's sign flipped. A residual is the actual value minus the predicted value; a dot above the line has a positive residual.

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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