### Home > INT1 > Chapter 4 > Lesson 4.2.2 > Problem4-74

4-74.

Sam collected data in problem 4-4 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.

  Length (cm)  Weight (g) $13.7$ $12.6$ $10.7$ $9.8$ $9.3$ $8.5$ $7.2$ $6.3$ $5.2$ $4.5$ $3.8$ $4.7$ $4.3$ $4.1$ $3.8$ $3.6$ $3.4$ $3.0$ $2.8$ $2.7$ $2.3$ $2.3$
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.

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

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?

Do 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.

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

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

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

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