Regression lines and residuals

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Milo plotted a puppy's weight. The dot at x = 13 has a residual of 1, but its label is smudged. What is that dot's y-value?

   24.2
2. 2.

   Pia plotted reading time against chapter length. The dot at x = 14 has a residual of 1.2, but its label is smudged. What is that dot's y-value?

   36.5
3. 3.

   Ren plotted the temperature against cricket chirps. The dot at x = 24 has a residual of -1.8, but its label is smudged. What is that dot's y-value?

   58
4. 4.

   Tala plotted a tomato plant's height with its least-squares line. Which dot has the residual farthest from 0? Write it as (x, y).

   (4, 32.8)
5. 5.

   Zee plotted a candle's height as it burns with its least-squares line. Which dot has the residual farthest from 0? Write it as (x, y).

   (5, 18.4)
6. 6.

   Ari plotted the height of a stack of paper cups with its least-squares line. Which dot has the residual farthest from 0? Write it as (x, y).

   (6, 16.3)
7. 7.

   Bo plotted an ice block melting in the sun with its least-squares line. Which dot has the residual farthest from 0? Write it as (x, y).

   (20, 203.6)
8. 8.

   Esme plotted snow depth as the sun comes out and listed the residuals from the least-squares line. Is a line a good model for these data?

   • No: the line should pass through the first and last dots to be a good model.
   • No: the residuals run in a pattern of signs, so a curve would fit better.
   • Yes: some residuals are positive and some are negative.
   • Yes: the residuals add up to 0.
9. 9.

   Jun plotted a tomato plant's height and listed the residuals from the least-squares line. Is a line a good model for these data?

   • No: the residuals are not all 0.
   • No: the line should pass through the first and last dots to be a good model.
   • Yes, because the residuals add up to 0.
   • Yes: the residuals are small and jump above and below 0 with no pattern.
10. 10.

    Kira plotted a puppy's weight and listed the residuals from the least-squares line. Is a line a good model for these data?

    • No: the line should pass through the first and last dots.
    • No: the residuals run in a pattern of signs, so a curve would fit better.
    • Yes: the residuals add up to 0.
    • Yes: some residuals are positive and some are negative, so the line fits well.