Spearman's rank correlation coefficient
Question
(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 spearman’s rank correlation coefficient.
(d)(i)Calculate the square of deviation between the given variables in the table below.
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 | |
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 spearman’s 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 | ||||||||
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 spearman’s rank correlation coefficient, find and explain the relationship between.
Commodity 1 and commodity 2
Commodity 1 and profits
Commodity 2 and profits
(g) Using the table in (f) above, calculate the profit made from selling a single commodity of each.