Question

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

Time (x)
(days) 5 10 15 20
Surface area (y)
(square feet) 90 85 70 61


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, −0.98, −0.5, −0.02.] (4 points)

Part B: What is the value of the slope of the graph of surface area versus time between 15 and 20 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

The scatter graph of the data is shown in the first picture below

The 'line of best fit' shows a negative gradient

Part A: The most likely coefficient is -0.98.
If the coefficient is -1, then each point would be exactly on the straight line (which they are not as shown on the graph). The graph however still shows a strong negative coefficient. It can be seen from the close distance of each point from the line of best fit. So -0.5 and -0.02 is unlikely as they show weak negative correlation

Part B: Refer to the second picture to see the horizontal and vertical distance between day 15 and day 20

The horizontal distance is 5 units
The vertical distance is read between 61 and 71.5, hence it's 10.5
The slope = Vertical distance ÷ Horizontal Distance = 10.5÷5 = 2.1
The 'downhill' slope shows a negative gradient, hence the value of the slope is -2.1
The value of the slope shows that the surface area of the lake shrinks by 2.1 for every one day

Part C: The data in the table represents the relation between two variables. Since one variable doesn't cause the change in the other variable, the data table represents correlation rather than a causation.