Spearman’s rank correlation coefficient

THIS IS AIMED AT ENABLING A STUDENT TO CALCULATE THE SPEARMAN’S RANK CORRELATION COEFFICIENT FROM GIVEN DATA AND TO RELATE IT TO BUSINESS AS AN AREA OF APPLICATION.
CASE 1: RANKING NON-REPEATING DATA
CASE 2: RANKING REPEATING DATA
CASE 3: LINK BETWEEN SPEARMAN RANK AND BUSINESS PROFITS
1. (a) What do you understand by the word correlation?
(b)Explain with examples the types of correlation.
(c) State and explain the formula used to calculate spearmans rank correlation coefficient.
(d)(i)Calculate the square of deviation between the given variables in the table below.
P
Q
12
11
32
24
14
65
25
23
16
27
09
18
(ii) Write the rank of X and of Y of the given table
X
Y
29
24
34
44
29
24
11
24
13
35
(e) Copy and fill the comments column of the tables below that have the range of spearmans rank correlation coefficient values.
(i)
RANK
COMMENT
0 0.19
0.2 0.39
0.4 0.59
0.6 0.79
0.8 0.999
(ii)
RANK
COMMENT
-0 to -0.19
-0.2 to -0.39
-0.4 to -0.59
-0.6 to -0.79
-0.8 to -0.999
(f) Below is a table showing the quantity of two commodities sold within eight days.
Use it to answer the questions that follow.
Week
1
2
3
4
5
6
7
8
Commodity1
200
150
180
60
190
210
160
75
Commodity2
300
80
110
200
70
48
90
120
Profits($)
9000
3850
4350
4900
4250
4110
4200
3525
By calculating the spearmans rank correlation coefficient find and explain the relationship between.
(i) Commodity 1 and commodity 2
(ii) Commodity 1 and profits
(iii) Commodity 2 and profits
(g) Using the table in (f) above calculate the profit made from selling a single commodity of each.