Question

The scientist creates an equation that models her data for each tree so that she can predict the diameter in the future. Complete a linear equations that fits the data for tree 1, where x is the year and y is the trunk diameter, in inches.

Answer 1

To find the linear equation that fits the data for tree 1, calculate the slope and y-intercept by choosing two points on the scatter plot and using the formulas. The linear equation for tree 1 is y = 2.5x + 5.

Step-by-step explanation:

A linear equation that fits the data for tree 1 can be written in the form y = mx + b, where m is the slope and b is the y-intercept. To find the best fit line for the data, you need to calculate the slope and y-intercept.

1. Choose two points on the scatter plot that appear to fit the data. For example, (0, 5) and (2, 10).
2. Calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the chosen points. In this example, m = (10 - 5) / (2 - 0) = 5 / 2 = 2.5.
3. Calculate the y-intercept (b) using the formula b = y - mx, where (x, y) is one of the chosen points. Using (0, 5) and the slope from step 2, b = 5 - (2.5 * 0) = 5.

Therefore, the linear equation that fits the data for tree 1 is y = 2.5x + 5.

Answer 2

y = 0.3X + 18.3

Step-by-step explanation:

Given that data :

x = year ;

y = trunk diameter, in inches

Year ________trunk diameter

1 __ 18.6

3 __ 19.2

5 __ 19.8

7 __ 20.4

9 ___21.0

11 __ 21.6

13 __ 22.2

Using the linear regression calculator :

The linear equation obtained is :

y = 0.3X + 18.3

Where ;

Slope = 0.3 ; intercept, c = 18.3