Q1: Describe the situation in which twovariables are perfect positively correlat

Question

Q1: Describe the situation in which twovariables are perfect positively correlated?

Q2: The cost of output at a factory is thought todepend on the number of units produced. Data have been collectedfor the number of units produced each month in the last six months,and the associated costs, as follows;

Output
(‘000s of units) X

Cost
($’000) Y

2

9

3

11

1

7

4

13

3

11

5

15

                   Calculate the correlation coefficient and comment on yourresult.

Output
(‘000s of units) X

Cost
($’000) Y

2

9

3

11

1

7

4

13

3

11

5

15

Explanation / Answer

PART 1 >>>> In real life with experimentaldata, it is nearly impossible to ever get a perfect correlation dueto random measurement errors. The only way to get a trulyperfect positive correlation is in math class with an exactfunction like

y = 2x + 5.   If you make a table of x and y valuesfor this function, it will be a perfect postitive correlation.

PART 2>>>>       This data fits the eqn   y = 2 x + 5 perfectly, with r =1.   This is an unrealistic result since it is highlyunusual for actual data to obey a linear function perfectly.

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