Question

The table below shows the radius y, in centimeters, created by growing algae in x days: Time (x) (days) 2 4 6 8

Answer 1

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.

PART B:
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.

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