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Grade 11 · Math · Precalculus

11th grade Slope of a fit line from r and the spreads worksheet

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Slope of a fit line from r and the spreads

Grade 11 Math Worksheet - Challenge Me

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

  1. Pia's class compares practice-test scores (x) with final-test scores (y), r = 0.8. A student is 2 spreads above the mean on x, z = 2. How many spreads from ȳ is the predicted y?

  2. Tala's class compares practice-test scores (x) with final-test scores (y), r = 0.5. A student is 2 spreads below the mean on x, z = -2. How many spreads from ȳ is the predicted y?

  3. Zee's class compares practice-test scores (x) with final-test scores (y), r = 0.6. A student is 1.5 spreads above the mean on x, z = 1.5. How many spreads from ȳ is the predicted y?

  4. Jun's class compares practice minutes (x) with free throws made (y). The fit line is ŷ = 20 + 3x. One dot is (15, 70). What is its residual?

  5. Luz's class compares temperature in °F (x) with ice melt minutes (y). The fit line is ŷ = 60 − 1.5x. One dot is (20, 34). What is its residual?

  6. Milo's class compares miles from school (x) with bus ride minutes (y). The fit line is ŷ = 12 + 4x. One dot is (6, 33). What is its residual?

  7. r = 0.8; spread of x = 4; spread of y = 10. Noah's class compares practice minutes (x) with free throws made (y). Now the class wants a line that predicts x from y, using the table shown. What is its slope?

  8. r = 0.5; spread of x = 4; spread of y = 5. Pia's class compares sunlight hours (x) with bean plant height (y). Now the class wants a line that predicts x from y, using the table shown. What is its slope?

  9. r = -0.6; spread of x = 10; spread of y = 5. Tala's class compares temperature in °F (x) with ice melt minutes (y). Now the class wants a line that predicts x from y, using the table shown. What is its slope?

  10. r = 0.9; spread of x = 6; spread of y = 4. Zee's class compares miles from school (x) with bus ride minutes (y). Now the class wants a line that predicts x from y, using the table shown. What is its slope?

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11th grade Slope of a fit line from r and the spreads worksheet – printable
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About this worksheet

Slope of a fit line from r and the spreads. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find the slope and intercept of the fit line from r, the means and the spreads.
  • I can predict y, find r from a slope, and find a residual.
  • I can predict in standard units and find the line for predicting x from y.

Standard: S-ID.B.6, S-ID.C.7, S-ID.C.8

Words to know

r (correlation): A number from -1 to 1 for how tightly dots follow a line.

spread: The standard deviation: the typical distance from the mean.

x̄, ȳ: The means of x and of y, the balance point of the dots.

fit line ŷ = a + bx: The least-squares line; ŷ is its prediction.

residual: Actual y minus predicted y.

Common mistakes

Put the spread of x on top. The slope is r × (spread of y ÷ spread of x): the line rises in y units per x unit.

Used spread of y ÷ spread of x without multiplying by r. The fit line rises only r of a spread of y for each spread of x.

Added b × x̄ to ȳ. The line passes through the means, so a = ȳ − b × x̄.

Questions parents ask

What is the most common mistake with slope of a fit line from r and the spreads?

Put the spread of x on top. The slope is r × (spread of y ÷ spread of x): the line rises in y units per x unit.

Are these 11th 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.

More precalculus

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