Question

The table below shows the surface area y, in square feet, of a shrinking lake in x days:

Time (x)
(days) 10 20 30 40
Surface area (y)
(square feet) 100 90 80 70


Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the lake. [Choose the value of the correlation coefficient from −1, −0.99, −0.5, −0.02.] (4 points)

Part B: What is the value of the slope of the graph of surface area versus time between 20 and 30 days, and what does the slope represent? (3 points)

Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)

Answer 1

Based on the data, the most likely correlation coefficient would be -1.
The slope between 20 and 30 days is -1, and it represents the change in the surface area of the lake per day.
The data represents correlation, not causation.

Since the data would form a perfectly straight line through the points, the correlation coefficient would be -1 for a perfect decreasing fit.
To find the slope, find the change in the surface area between those days, the change in the days, and write it as surface area/days: 80-90=-10; 30-20=10; -10/10=-1
This is not causation because there could be lurking variables we cannot see.