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
can the superheat be in percentage?

Q. Steam Generator Master Pressure Control? The combined header pressure is controlled by a regular P.I.D. controller which ultimately trims the water flow to each boiler. A

Evolution of Specific volume of wet saturated steam -thermodynamics : Specific volume of wet saturated steam (V we t ) It is volume occupied by unit mass of wet satu

Measurement in Production System: This unit explain the performance measurement in an organisation. More than just a passive means for assessing what has already occurred, the

explain the following terms in brief:- point function and path funtion

Energy - thermodynamics: The energy can be defined as the capacity of doing work. The energy possessed by system may be of two kinds. 1. Stored energy: for example potent

Concept of plane stress: Define the concept of plane stress. Sol.:   In cubical element of strained material is acted on by stresses acting on only 2 pairs of parallel plane

In designing rotating space stations to give for artificial-gravity environments, one of the constraints that must be considered is motion sickness. Studies have shown that the neg

The Winged-Edge Representation Perhaps the oldest data structure for a b-rep is Baumgart's winged-edge data structure. It is quite different from that of a wire-frame model, be

How does an Ignition system works ?