|
Q. 6. Fit a straight line to the data given
by the following table: (June
2001)
Independent Variable
x |
Dependent
Variable
y |
| 1 |
6 |
| 2 |
5 |
| 4 |
9 |
| 5 |
11 |
| 6 |
13 |
| 8 |
17 |
Solution.
| x |
y |
x2
|
x X y |
|
1 |
6 |
1 |
6 |
|
2 |
5 |
4 |
10
|
|
4 |
9 |
16
|
36
|
|
5 |
11 |
25
|
55
|
|
6 |
13 |
36
|
78
|
|
8 |
17 |
64
|
136
|
|
å
x = 26 |
å
y = 61 |
å
x2 = 146 |
å
xy = 321 |
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 321) - (26 X 61)]
|
| or b = |
|
| |
[(6 X 146) - (26)2]
|
or b = 1.7
a = (1/6) X [(61 - (1.7 X 26)] = 2.8
Therefore, y = 2.8 + 1.7x
|
