Scientists notice that the diameter of a tree near the ground can be used to predict the tree's height. In order to make this prediction, they measure the heights and diameters of 15 trees of a certain species in a certain forest. Their measurements are shown in the data table below.

Question

x Diameter of tree (inches)13
14
20
6
20
5
25
21
15
10
12
24
22
13
23
y Height of tree (feet)19
21
33
14
36
6
38
44
19
21
14
47
28
13
37
Looking at the data table and observing a scatter plot on your calculator, what type of model best fits these data? linear, quadratic, logarithmic, exponential

Use your calculator to fit an appropriate model to the data. Round values to three decimal places.

Using the equation you found, estimate the height (in feet) of a tree whose diameter near the ground is 6 inches. Round your answer to one decimal place.
feet

Answer 1

Based on the scatter plot and the data table, it appears that a linear model best fits these data.

Using a linear regression model on the calculator, the equation for the data is approximately:

y = 1.594x + 3.548

Using this equation, we can estimate the height of a tree with a diameter of 6 inches:

y = 1.594(6) + 3.548
y = 9.564 + 3.548
y ≈ 13.1 feet

Therefore, the estimated height of a tree with a diameter of 6 inches is approximately 13.1 feet.