Answer to Question #86235 in Statistics and Probability for AVENUE HEALTHCARE

Question

Perched No of welding job assignments Total cost sh ‘000’
Sept 2008 280 700
Oct 2008 800 860
Nov 2008 1,240 110
Dec 2008 1,000 960
Jan 2009 600 720
Feb 2009 920 910
Mar 2009 860 880
Apr 2009 1,200 260

REQUIRED:
Formulate an equation to estimate the total cost of the welding shop and compute the cost of undertakings 1256 assignment using

i) High-low method
ii) Simple linear regression method.

Answer 1

i) The high and low points are chosen by activity, not by cost.

Total Cost = Fixed Cost + Variable Cost

(Variable Cost) ⁄ unit = (Change in Cost) / (Change in Activity)

$$Variable Cost / unit = (-590) / 960 = -$0.61 / unit$$

Fixed Cost = Total Cost - Variable Cost

$$Fixed Cost = 110- (-0.61)*1240 = $866.40$$

$$Fixed Cost = 700 - (-0.61)*(280) = $870.80$$ $$y = 868.60 - 0.61x$$

$$x = 1256: y = 868.60 - 0.61*(1256)$$

$$y = $102.44$$

ii)

$$Xmean = 6900 / 8 =862.5$$

$$Ymean =5400 / 8 = 675$$ $$b1 = (4318400 - 6900 * 5400 / 8) / (6642000 - (6900)^2 / 8)$$

$$b1 = - 0.49$$ $$b0 = Ymean - b1 * Xmean$$

$$b0 = 1098.41$$

$$y = b0 + b1 * x$$

$$y = 1098.41 - 0.49x$$

$$x = 1256: y =1098.41 - 0.49*(1256)$$

$$y = $482.97$$