For questions 3–4, use your calculator to create a scatter plot and line of best fit for the following set of data:
Average height of a species of tree (in feet) after a certain number of years
Years 1 2 3 4 5 6 7 8
Height 2.1 3.2 6.8 7.3 11.2 12.6 13.4 15.9
What is the correlation coefficient for the set of data? Round your answer to the nearest thousandth.
(1 point)
Responses
0.014
0.014
0.989
0.989
0.075
0.075
negative 0.977
About how tall would you expect one of these trees to be after 22 years?
(1 point)
Responses
22.31 ft.
22.31 ft.
35.2 ft.
35.2 ft.
44.25 ft.
44.25 ft.
46.2 ft.
To find the correlation coefficient for the set of data, we input the values into a calculator and perform a regression analysis. The correlation coefficient is a measure of the strength and direction of the linear relationship between the variables.
Using a calculator, we find that the correlation coefficient for the given data is approximately 0.989.
To estimate how tall one of these trees would be after 22 years, we can use the line of best fit generated by the calculator. Since we don't have the equation of the line, we can use the line to estimate the height.
We can approximate the answer by extending the line of best fit on the scatter plot to the x-axis at 22 years and then reading the corresponding y-value (height) at that point. Based on the scatter plot, we can estimate that the height of the tree after 22 years is approximately 44.25 ft.