The table below shows the radius y, in centimeters, created by growing algae in x days: Time (x) (days) 2 4 6 8 Radius (y) (cm) 4 7 10 14 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, 0.97, 0.5, 0.02.] (4 points) Part B: What is the value of the slope of the graph of radius versus time between 6 and 8 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)

Accepted Solution

PART A: This is how you define the corelation coefficient
(1) Make a table and count the mean of x and y
(2) Substract the value of x with the mean of x and it results a, and substract the value of y with the mean of y and it results b (check my attachment, column 3 and 4)
(3) Multiply the value of a and b, it results ab (column 5)
(4) Square the value of a and write the results on a² (column 6), square the value of b and write the results on b² (column 7)
(5) Count the correlation coefficient with the way i work (check below the table)
(6) The correlation coefficient is 0.99 or you can write it as 1.

Describe the relationship: The radius of algae and the the time are in strong positive correlation. If the time is added, the radius of algae will also increase.

We know from the question that,
(x₁,y₁) = (6,10)
(x₂,y₂) = (8,14)

You can count the slope with this formula
m = (y₂ - y₁)/(x₂ - x₁)
m = (14-10)/(8-6)
m = 4/2
m = 2
The slope is 2. The slope represents the rate of radius increase on the sixth day to the eighth.

It shows correlation, because time is not the cause of radius increase, but time can impact the extension of the radius.