Example of regression equation, Mathematics

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

x2

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

Σx2 = 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 + 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 =

2321_Example of Regression Equation.png

Posted Date: 2/16/2013 7:20:42 AM | Location : United States







Related Discussions:- Example of regression equation, Assignment Help, Ask Question on Example of regression equation, Get Answer, Expert's Help, Example of regression equation Discussions

Write discussion on Example of regression equation
Your posts are moderated
Related Questions
Example of Product moment correlation The given data was acquired during a social survey conducted in a described urban area regarding the yearly income of described families

GIVE EXAMPLE OF ROW EQUIVALENT

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to


A two-digit number is seven times the sum of its digits.  The number formed by reversing the digits is 18 less than the  original number. Find the original number.

a recipe good for 4 servings require 1/8 tsp. black pepper and 1/2 tsp. of salt. how much black pepper and how much salt needed for 2 servings?

A drug has a decay rate of k = - ¼ ln(¾) / hr. How soon after an initial dose of 1600 mg will the drug reach its minimum therapeutic value of 900 mg in the body?

how do i compute an algebra number

Data entry is performed in 2-person teams. Each 2-person team can enter 520 surveys per day. A selection of 7540 surveys must be entered by day''s end. How many total employees, wo

A dealer sells a toy for Rs.24 and gains as much percent as the cost price of the toy. Find the cost price of the toy. Ans:    Let the C.P be x ∴Gain = x % ⇒ Gain = x