Question

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)

Answer 1

PART A:

The data is plotted in the graph below. The line best fit is drawn to show the trend of the data. Since the plots form a cluster that follows the line best fit and there are no outliers, the most likely coefficient is 0.94 which is a strong positive correlation.

PART B:

The value of slope between x = 5 and x = 10 is
Slope = (3-1) ÷ (10-5) = 2/5

The slope represents the rate of change of the radius, which is 2/5 for every 5 days

PART C:

The data in the table represents correlation, that the algae grow longer as the days increase. It might not be necessary a causation because the growth of algae doesn't necessarily depend on the number of days.