Mathematics and Statistics
(Commerce) Part - II
STANDARD TWELVE
Chapter 3
Linear Regression
Q. 1 The HRD manager of company wants to find measures which he can use to fix the monthly income of persons applying job in the production department as an experimental project, he collected data of 7 persons from the department referring to years of service and their incomes.
|
Years of service (X) |
11 |
7 |
9 |
5 |
8 |
6 |
10 |
|
Monthly Income (Rs. 1000’s) (Y) |
10 |
8 |
6 |
5 |
9 |
7 |
11 |
II) What initial start would you recommend for applying job after having served in similar capacity in another company for 13 year?
Q. 2 Calculate the regression equation of X on Y and Y on X for the following data:
|
X |
10 |
12 |
13 |
17 |
18 |
|
Y |
5 |
6 |
7 |
9 |
13 |
Q. 3 For a certain bivariate data on 5 pairpairs of observation given
∑ x = 20, ∑ y = 20, ∑ x2 = 90, ∑ y2 = 90, ∑ xy = 76
Calculate I) cov(x, y) ii) bxy and byx iii) r
Q. 4 From the following data estimate y when x =125
|
X |
120 |
115 |
120 |
125 |
126 |
123 |
|
Y |
13 |
15 |
14 |
13 |
12 |
14 |
Q. 5 The following table give the aptitude test scores and productivity index of 10 workers selected at random.
|
Aptitude score (X) |
60 |
62 |
65 |
70 |
72 |
48 |
53 |
73 |
65 |
82 |
|
Productivity Index (Y) |
68 |
60 |
62 |
80 |
85 |
40 |
52 |
62 |
60 |
81 |
(i) The productivity index of a worker whose test score is 95.
(ii) The test score when productivity index is 75.
6. Compute the appropriate regression equation for the following data:
|
X [Independent Variable] |
2 |
4 |
5 |
6 |
8 |
11 |
|
Y[Dependent Variable] |
18 |
12 |
10 |
8 |
7 |
5 |
Q.7 The following are the marks obtained by the students in Economics (X) and Mathematics (Y)
|
X |
59 |
60 |
61 |
62 |
63 |
|
Y |
78 |
82 |
82 |
79 |
81 |
Q.8 For the following bivariate data obtain the equations of two regression lines:
|
X |
1 |
2 |
3 |
4 |
5 |
|
Y |
5 |
7 |
9 |
11 |
13 |
Q. 9 From the following data obtain the equation of two regression lines:
|
X |
6 |
2 |
10 |
4 |
8 |
|
Y |
9 |
11 |
5 |
8 |
7 |
Q. 10 For the following data, find the regression line of Y on X
|
X |
1 |
2 |
3 |
|
Y |
2 |
1 |
6 |
Q. 11 From the following data, find the regression equation of Y on X and estimate Y when X = 10.
|
X |
1 |
2 |
3 |
4 |
5 |
6 |
|
Y |
2 |
4 |
7 |
6 |
5 |
6 |
Q. 12 The following sample gives the number of hours of study (X) per day for an examination and marks (Y) obtained by 12 students.
|
X |
3 |
3 |
3 |
4 |
4 |
5 |
5 |
5 |
6 |
6 |
7 |
8 |
|
Y |
45 |
60 |
55 |
60 |
75 |
70 |
80 |
75 |
90 |
80 |
75 |
85 |
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 Part - II STANDARD TWELVE Chapter 3-Linear regression){kind=link}
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