1 of 51 of 5 Items
Question
Multiple Choice
Which type of correlation is suggested by the scatter plot?
A scatter plot has a cluster of points with a general downward trend.
(1 point)
Responses
positive correlation
positive correlation
negative correlation
negative correlation
equal correlation
equal correlation
no correlation
The correct answer is: negative correlation
2 of 52 of 5 Items
Question
Which type of correlation is suggested by the scatter plot?
A scatter plot has a cloud of points scattered over the graph.
(1 point)
Responses
positive correlation
positive correlation
negative correlation
negative correlation
equal correlation
equal correlation
no correlation
no correlation
The correct answer is: no correlation
3 of 53 of 5 Items
Question
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
Image with alt text: negative 0.977
To find the correlation coefficient for the set of data, you can use a calculator or statistical software. Since you are asked to round your answer to the nearest thousandth, you could perform this calculation manually. The correlation coefficient is a measure of the strength and direction of a linear relationship between two variables.
Given the data:
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
After calculating the correlation coefficient using the formula, if you get a value that is rounded to -0.977, then the correct response is:
negative 0.977
4 of 54 of 5 Items
Question
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 predict how tall a tree would be after 22 years based on the line of best fit from the data provided, you would need to use the equation of the line.
First, you need to calculate the equation of the line of best fit based on the data given:
Based on the data provided in the previous question, if you calculated the equation of the line of best fit for the data:
Height = 1.5468 * Years + 0.2664
Then, plug in the year 22 into the equation to predict the height:
Height = 1.5468 * 22 + 0.2664
Height = 34.4688 + 0.2664
Height = 34.7352 ft
Therefore, the predicted height of the tree after 22 years would be approximately 34.7352 ft.
Since this value is not provided as an option, the closest choice is 35.2 ft.
Therefore, the correct response is 35.2 ft.