Regression lines and residuals

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Milo plotted the temperature against cricket chirps and fit a least-squares line. What is the residual for the dot at x = 30?

   -1.4
2. 2.

   Pia plotted the height of a stack of paper cups and fit a least-squares line. What is the residual for the dot at x = 6?

   -2.3
3. 3.

   Ren plotted kite height against string let out and fit a least-squares line. What is the residual for the dot at x = 60?

   2.6
4. 4.

   Zee plotted a candle's height as it burns. The least-squares line is y = -1.5x + 24. What does the slope -1.5 mean?

   • Over all the data, the height falls 1.5 centimeters in total.
   • When x is 0, the height is about 1.5 centimeters.
   • For each extra hour, the height tends to fall about 1.5 centimeters.
   • For each extra hour, the height tends to rise about 1.5 centimeters.
5. 5.

   Ari plotted an ice block melting in the sun. The least-squares line is y = -11.5x + 420. What does the slope -11.5 mean?

   • For each extra minute, the mass tends to rise about 11.5 grams.
   • When x is 0, the mass is about 11.5 grams.
   • Over all the data, the mass falls 11.5 grams in total.
   • For each extra minute, the mass tends to fall about 11.5 grams.
6. 6.

   Bo plotted reading time against chapter length. The least-squares line is y = 2.2x + 4.5. What does the slope 2.2 mean?

   • Over all the data, the reading time rises 2.2 minutes in total.
   • For each extra page, the reading time tends to rise about 2.2 minutes.
   • When x is 0, the reading time is about 2.2 minutes.
   • The reading time is exactly 2.2 minutes more each page, with no scatter.
7. 7.

   Esme plotted a tomato plant's height. The least-squares line is y = 6.5x + 9.5. What does the y-intercept 9.5 mean, if anything?

   • At x = 0, the day it was planted, the height was about 9.5 centimeters.
   • The height changes about 9.5 centimeters each week.
   • It has no real meaning, because x = 0 does not match a real time in the story.
8. 8.

   Jun plotted snow depth as the sun comes out. The least-squares line is y = -2.4x + 30. What does the y-intercept 30 mean, if anything?

   • The snow depth changes about 30 centimeters each hour.
   • At x = 0, the moment the snow stopped, the snow depth was about 30 centimeters.
   • It has no real meaning, because x = 0 is not a real time.
9. 9.

   Kira plotted lemonade sales against the temperature. The least-squares line is y = 2.5x - 128. What does the y-intercept -128 mean, if anything?

   • At x = 0, the number of cups sold would be about −128 cups.
   • The number of cups sold changes about 128 cups each degree.
   • Nothing real: x = 0 is far outside the data, and the number of cups sold cannot be −128.
10. 10.

    Luz plotted kite height against string let out. The least-squares line is y = 0.6x - 3. What does the y-intercept -3 mean, if anything?

    • Nothing real: x = 0 is far outside the data, and the kite height cannot be −3.
    • At x = 0, the kite height would be about −3 meters.
    • The kite height changes about 3 meters each meter of string.