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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1, Problem 3P

a.

To determine

Make a scatter plot of the data.

Expert Solution

**Given information: **

To estimate ages of trees, forest rangers use a linear model that relates tree diameter to age. The model is useful because tree diameter is much easier to measure than tree age (which requires special tools for extracting a representative cross-section of the tree and counting the rings). To find the model, use the data in the table, which were collected for a certain variety of oaks.

**Calculation: **

The scatter plot of the data is given as,

Hence, the graph is shown above.

b.

To determine

Find and graph a linear function that models the data.

Expert Solution

**Given information: **

To estimate ages of trees, forest rangers use a linear model that relates tree diameter to age. The model is useful because tree diameter is much easier to measure than tree age (which requires special tools for extracting a representative cross-section of the tree and counting the rings). To find the model, use the data in the table, which were collected for a certain variety of oaks.

**Calculation: **

Using a calculator, we find the following regression line that models the data in the form of,

Using regression calculator,

Substituting

Hence, the linear function that models the data is

c.

To determine

Use the model to estimate the age of an oak whose diameter is

Expert Solution

**Given information: **

To estimate ages of trees, forest rangers use a linear model that relates tree diameter to age. The model is useful because tree diameter is much easier to measure than tree age (which requires special tools for extracting a representative cross-section of the tree and counting the rings). To find the model, use the data in the table, which were collected for a certain variety of oaks.

**Calculation: **

The diameter

Hence, the estimated age of an oak whose diameter is