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

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 + bΣx²

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 =