Example of Regression Equation
An investment company advertised the sale of pieces of land at different prices. The given table shows the pieces of land their costs and acreage
Piece of land

(x)Acreage Hectares

(y) Cost £ 000

xy

x^{2}

A

2.3

230

529

5.29

B

1.7

150

255

2.89

C

4.2

450

1890

17.64

D

3.3

310

1023

10.89

E

5.2

550

2860

27.04

F

6.0

590

3540

36

G

7.3

740

5402

53.29

H

8.4

850

7140

70.56

J

5.6

530

2969

31.36


Σx =44.0

Σy = 4400

Σxy= 25607

Σx^{2} = 254.96

Required
Find out the regression equations of
i. y on x and thus estimate the cost of a piece of land along with 4.5 hectares
ii. Estimate the expected average if the piece of land costs of £ 900,000
Σy = an + bΣxy
Σxy = a∑x + bΣx^{2}
By substituting of the suitable values in the above equations we have
4400 = 9a + 44b ........ (i)
25607 = 44a + 254.96b ........(ii)
By using multiplying equation .... (i) by 44 and equation ...... (ii) by 9 we have
193600 = 396a + 1936b ........ (iii)
230463 = 396a + 2294.64b ........(iv)
By using subtraction of equation .... (iii) from equation ...... (iv) We have
36863 = 358.64b
102.78 = b
by substituting for b in equation........ (i)
4400 = 9a + 44( 102.78)
4400  4522.32 = 9a
122.32 = 9a
13.59 = a
Hence the equation of the regression line of y on x is
Y = 13.59 + 102.78x
When the acreage or hectares is 4.5 then the cost
(y) = 13.59 + (102.78 x 4.5)
= 448.92
= £ 448, 920
Note that
Where the regression equation is described by
y= a + bx
Whereas a is the intercept on the y axis and
b is the slope of the line or else regression coefficient
n is the sample size
After that,
intercept a = (Σy  bΣx)/n
Slope b =