Suzuki finds that there exists a relationship between the population and luxury cars for sale in the city. The data collected is:
Population in the city in lakhs |
15 |
22 |
25 |
36 |
42 |
No. of luxury cars in hundreds |
65 |
80 |
96 |
130 |
185 |
The demand of luxury car for a city with a population of 60 lakhs is:
Concept:
Let the equation of regression line be
y = a + bx
∑y = na + b∑x …... (1)
∑xy = a∑x + b∑x2 .....(2)
Calculation:
Given:
Population (x) |
No. of cars (y) |
xy |
x2 |
15 |
65 |
975 |
225 |
22 |
80 |
1760 |
484 |
25 |
96 |
2400 |
625 |
36 |
130 |
4680 |
1296 |
42 |
185 |
7770 |
1764 |
∑x = 140 |
∑y = 556 |
∑xy = 17585 |
∑x2 = 4394 |
By Regression method:
∑y = na + b∑x
556 = 5a + 140b ......(3)
∑xy = a∑x + b∑x2
17585 = 140a + 4394b ......(4)
Solving (3) and (4)
a = -7.94 and b = 4.2552
The equation becomes
y = -7.94 + 4.2552x
For x = 60 lakh
y = -7.94 + (4.2552 × 60)
y = 247.372
∴ the demand for luxury cars is (247.372 × 100) = 24737 ≈ 24752.