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Home > CCA > Chapter 6 > Lesson 6.2.2 > Problem 6-73

6-73.
  1. Sam collected data in problem 6-4 by measuring the pencils of her classmates. She recorded the length of the painted part of each pencil and its weight. Her data is listed in the table below. Homework Help ✎

  2. Length of paint (cm)

    13.7

    12.6

    10.7

    9.8

    9.3

    8.5

    7.2

    6.3

    5.2

    4.5

    3.8

    Weight (g)

    4.7

    4.3

    4.1

    3.8

    3.6

    3.4

    3.0

    2.8

    2.7

    2.3

    2.3

    1. Graph the data on your calculator and sketch the graph on your paper.

    2. What is the equation of the LSRL? Sketch it on your scatterplot.

    3. Create a residual plot and sketch it on your paper.

    4. Interpret your residual plot. Does it seem appropriate to use a linear model to make predictions about the weight of a pencil?

    5. The teacher’s pencil, when it was new, had 16.8 cm of paint and weighed 6 g. What was the residual? Consider the precision of the original data and use an appropriate number of decimal places.

    6. What does a positive residual mean in this context?

If you entered the data correctly, your calculator should have given you an answer of y = 1.300 + 0.248x.

Does the points on the residual plot appear to have a pattern?
If a linear model fits the data well, no interesting pattern will be made by the residuals.

residual = actual − predicted
You will need to calculate the predicted weight of 16.8 cm of paint using the equation in part (b).

Is the predicted weight of the pencil greater than or less than its actual weight?