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1. "Regression is the measure of
the average relationship between two or more variables
in terms of the original units of the data."
- Blair
2. "One of the most frequently used technique
in economics and business research, to find a relation
between two or more variables that are related casually,
is regression analysis." - Taro Yamane
The regression equation of y on x is expressed as
follows:
y = a + bx
where:
y = dependent variable
x = independent variable
a and b are constants
a = (1/n) (å y - bå
x)
| |
[n å
xy - (å x X
å y)]
|
| b = |
|
| |
[n å
x2 - (å
x)2]
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Q. 5. Fit a straight line to the data given
by the following table: (June
2002)
Independent Variable
x |
Dependent
Variable
y |
|
2 |
3 |
|
4 |
17 |
|
6 |
38 |
|
7 |
49 |
|
9 |
80 |
|
11 |
120 |
Solution.
| x |
y |
x2
|
x X y |
|
2 |
3 |
4 |
6 |
|
4 |
17 |
16 |
68 |
|
6 |
38 |
36 |
228 |
|
7 |
49 |
49 |
343 |
|
9 |
80 |
81 |
720 |
|
11 |
120 |
121 |
1320 |
|
å
x = 39 |
å
y = 307 |
å
x2 = 307 |
å
xy = 2685 |
Equation of straight line:
y = a + bx
Here, n = 6
| |
[n å
xy - (å x X
å y)]
|
| b = |
|
| |
[n å
x2 - (å
x)2]
|
| |
[(6 X 2685) - (39 X 307)]
|
| or b = |
|
| |
[(6 X 307) - (39)2]
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or b = 12.88
a = (1/6) X [(307 - (12.88 X 39)] = -32.55
Therefore, y = -32.55 + 12.88x
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