Question4: 8 a) Describe the situation in which two variables are perfectpositiv

Question

Question4:                                                                                                                  8

a)    Describe the situation in which two variables are perfectpositively correlated?

b)    The cost of output at a factory is thought to depend on thenumber of units produced. Data have been collected for the numberof units produced each month in the last six months, and theassociated 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

a sol :-      If correlation is +1 then we saidthat correlation is prefectly possitively correlation. b sol :-       correlation between x & yis, covariance(x,y)/sqrt(variance(x)*variance(y))           consider,cov(x,y) = 3.33333                         var(x) = 1.66667                          var(y)= 6.66667                    so corr(x,y) = (3.33333)/sqrt((1.66667)*(6.66667))                                       = 1.          Herecorrelation is perfectly possitively correlated.because corr(x,y)is exactly 1.

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