The table below shows the radius y, in inches, created by growing algae in x days:
time (x)
(days) 5 10 15 20
radius (y)
(inches) 1 3 9 22
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 radius of the algae. [choose the value of the correlation coefficient from 1, 0.94, 0.5, 0.02.] (4 points)
part b: what is the value of the slope of the graph of radius versus time between 5 and 10 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)

Part A. The correlation coefficient, denotes as R^2, is a measure of how well does the data point correlate with a given model or equation. The closer the R^2 is to 1, the better is the correlation. However, R2=1 is ideal for scatter plots. Using the MS Excel to execute the regression, the data points was fitted to a quadratic equation. The R2=0.9983. From the choices, the closest answer would be 1. But as stated previously, a value of 1 is ideal only. Therefore, the answer is most likely 0.94,

Part B. To determine the slope, the equation would be Δy/Δx. For x=5 and x=10, the slope would be

Slope = (3-1)/(10-5) = 2/5 or 0.4. This is the instantaneous rate of change at the interval of 5 to 10 days.

Part C. The difference between causation and correlation is identifiable if you know the direct relationship between the variables. In this case, the increase in radius is not caused by time. The problem does not state so. But we know from the trend shown on a graph, that there is a correlation between these variables. Therefore, the answer is correlation.