Question

The table below shows the surface area y in square inches, of a shrinking puddle in x hours

Time (x) (hours) 2 5 8 11

Surface area (y) 25 15 9 2
(Square inches)

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 are puddle. [choose the value of the correlation coefficient from -1,-0.99,-0.5,-0.02]

Part b - what is the value of the slope of the graph of surface area versus time between 5 and 8 hours and what does the slope represent?

Part c- does the data in the table represent correlation or causation?

Answer 1

Part A
Correlation coefficient: -.99
This tells us that as time goes on (value of x increases) the area of the puddle goes down (value of y decreases)

Part B
y₂ - y₁
------- = slope
x₂ - x₁
9 - 15
--------
5 - 8
-6/-3 = 2
So the slope equals -2, regardless of the fact that we got 2 as an answer there, we know that it is a negative slope

Part C
The data represents causation because an increase in the value of x results in a decrease in the value of y, this shows an example of direct causation between x and y.

Answer 2

Explanation:

Given is a table showing the surface area y in square inches, of a shrinking puddle in x hours

x y

2 25

5 15

8 9

11 2

r -0.993835256

Hence correlation coefficient is option B) -0.99

Part b:

Time Sur area

x y

2 25

5 15

8 9

11 2

r -0.993835256

slope -0.395083406

Intercept 11.53731343

slope =-0.395

Between 5 and 8, slope =
`(change in y)/(change in x) \\=(9-15)/(8-5) \\=-2`

Slope represents the change of y with respect to 1 unit change in x.

Part c:

Yes correlation strong and negative.