Correlation and Regression)
1. Calculate Karl Pearson's Coefficient of correlation for the following data of the sales(x) and expenses(y) in lakes of rupees of 7 firms
| x |
17 |
15 |
25 |
28 |
19 |
18 |
20 |
| y |
12 |
14 |
18 |
20 |
14 |
11 |
16 |
2. Calculate Karl Pearson's Coefficient or correlation for the following data relating to overhead expenses and cost of production.
| Overhead( Rs. '000) |
70 |
80 |
100 |
105 |
120 |
101 |
105 |
| Cost (Rs.'000) |
14 |
15 |
18 |
20 |
20 |
25 |
22 |
3. Calculate Karl Pearson's Coefficient of correlation for the following data
Σx = 20, Σy = 40, Σx2 = 240, Σy2 = 410, Σxy = 200, n = 10
4. Calculate Product moment Coefficient of correlation for the following data.
Σx = 125, Σy = 100 Σx2 = 650, Σy2 = 436, Σxy = 520, n = 12
5. Calculate Product moment Coefficient of correlation 1-6r the following data.
Σ (X - x)2 =136, Σ(Y - y-)2 = 138, Σ(X -x-)(Y - y-) = 122, n =10
6. Calculate Karl Pearson's Coefficient of correlation for the following data,
Σ(X - x-)2 = 40, Σ( Y - y-)2 = 20, (X - x-)(Y - y-) = -26
7. Calculate Spearman's rank correlation coefficient of correlation between the supply and demand of certain commodities from the following data.
| Supply |
52 |
34 |
47 |
65 |
43 |
35 |
54 |
| Demand |
65 |
59 |
66 |
68 |
82 |
60 |
57 |
8. Find the Spearman's rank correlation coefficient for the following data.
| A |
70 |
66 |
78 |
50 |
70 |
55 |
| B |
52 |
90 |
77 |
65 |
80 |
45 |
9 The coefficient of rank correlation between the marks in Economics and marks m Statistics obtained, by a group 01 students is 0.8. If the sum of squares of the differeiices in ranks is given tube 33, find the number of students in the group.
10. The sum of squares of the differences between ranks found to be 66. The coefficient of rank correlation is 0.6. Find the number of pairs in data.
11. Find the two regression equation given the following data.
Σx= 49, Σy = 73, Σx2 = 359, Σy2 = 695, Σxy = 417, n = 8
12. The data for 10 years on sales(y) and advertising expenditure (x) of , a particular commodity is given below:
Σx =15, Σy = 110, Σx2= 250, Σy2 = 3200, Σxy = 400, n = 10