  ### Home > CCA > Chapter 7 > Lesson 7.1.6 > Problem7-78

7-78.

Each team in Ms. Zaleski’s class cut a circular disks from cardboard file folders. They could cut the disks any size they chose. The weight and radius were recorded. The information is shown in the table below. Since students chose the radius, consider radius the independent variable.

 Radius (cm)  Weight (g) $9.6$ $9$ $7.7$ $6.3$ $5.3$ $4.7$ $3.7$ $2.4$ $1.3$ $5.4$ $4.6$ $3.4$ $2.3$ $1.6$ $1.2$ $0.8$ $0.3$ $0.1$
1. Make a scatterplot for the data and sketch it onto your paper. Describe the association between weight and radius.

Look at your graph. Does it appear that the two are strongly correlated? Does it seems to match any sort of function?

2. The weight of the cardboard disk depends on its area. What kind of equation do you suggest to model this data?

Think of the equation for the area of a circle. That equation gives you a hint as to what kind of equation to use.

3. Model the data with a regression equation. Does the y-intercept of your model make sense in this context?

Use either a power regression or a quadratic regression to model the data.

Would something with no area weigh anything?

4. What do you predict a 7-cm disk will weigh? Use appropriate precision in your answer.

Use your equation from part (c) to solve this problem.

Use the eTool below to solve problem.
Click on the link at right for the full eTool version: CCA 7-78 HW eTool