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

what is the result if 816.537 is rounded to the nearest tenth


Specified a system of equations, (1), we will have one of the three probabilities for the number of solutions. 1.   No solution. 2.   Accurately one solution. 3.   Infinit

How many arrangements can be made from the letters of the word " VENUS " such that the order of the vowels remains the same?

Find out the linear approximation for at x =8 .  Utilizes the linear approximation to approximate the value of  and Solution Since it is just the tangent line there

DECISION THEORY People constantly make decisions in their private lives as well as in their work. Some decisions are qualitative in terms of their implications and signi

1. Build an equation for a hyperboloid of two sheets with the following properties: a. The central axis of the hyperboloid is the y-axis b. The two sheets are 4 units apart, an

When Ms. Jones retired, she received a lump sum of $1,000,000 from her pension plan.  She then invested this sum in an annuity account that would pay her an equal amount at the end

theory about solving sequencing problem using graphical method