Derive a regression forecasting equation, Mechanical Engineering

Derive a regression forecasting equation:

The general manager of a company producing road rollers is convinced that the demand for road rollers is associated to the number of road construction tenders issued in the state during the previous years. The past data gathered is shown in the Table.

1957_Derive a regression forecasting equation.png

1. Derive a regression forecasting equation.

2. Estimate the demand for road roller when the number of tenders issued is 28.

3. Calculate the standard deviation of regression and the correlation coefficient.

Solution

 (a)       First of all, it is useful to prepare the following Table.

1848_Derive a regression forecasting equation1.png

n = no. of observations = 8

x = 184 /8 = 23 ;         Y = 80/8 = 10

b = 2146 - 8 (23) (10) / (5006 - 8 (23) (23)) = 0.35

and      a = 10 - 0.395 (23) = 0.91

∴   Y = 0.91 + 0.395 X is the regression forecasting equation.

(b) For       X = 28

Y = 0.91 + 0.395 (28) ≅ 12 road rollers

(c) Standard deviation

[ (∑Y 2  - a ∑Y - b ∑ X Y)/(n-2)] = [950 - (0.9) (80) - (0.395) (2146))/(8-2)](1/2)

= 2.2 road rollers

Correlation coefficient

676_Derive a regression forecasting equation2.png

=  8 (2146) - (184) (80) /{[8 (5006) - (184)2 ] [8 (950) - (80)2 ]}1/ 2

  = 0.90

The value of r is quite close to 1 indicating a very good correlation.

Posted Date: 1/31/2013 6:59:31 AM | Location : United States







Related Discussions:- Derive a regression forecasting equation, Assignment Help, Ask Question on Derive a regression forecasting equation, Get Answer, Expert's Help, Derive a regression forecasting equation Discussions

Write discussion on Derive a regression forecasting equation
Your posts are moderated
Related Questions
what is coriolis component of acceleration?

derivation of elongation of bar due to its self weight

Q. Define Zirconium and its alloys? Zirconium and its alloys were developed primarily for the nuclear industry, but have found many industrial corrosion-resistant applications

Explain the meaning of A raft foundation A raft foundation, as also combined footing, cannot be considered to be the opposite of a slab supported on the columns with a defined

Q. Design Loading - Unloading Facilities in plant layout? Loading and unloading areas should be separated. These facilities should be situated on the edge of the site near road

Q. 11: What is relation between the maximum tensile stress and the maximum compressive stress in any section of beam? Sol.: L et us assume inverted angle section of the beam a

Difference between press forminig and hammer forming

Ask quesinstantaneous stress formulation #Minimum 100 words accepted#

How is bearing capacity of soil varied? The bearing capacity of soil varies not only with its strength but also with the magnitude and distribution of the load. When a load Q,