Question

Multiple regression is used by accountants in cost analysis to shed light on the factors that cause costs to be incurred and the magnitudes of their effects.

A petroleum company wanted to evaluate different blends of its gasoline - made by inserting different additives into the manufacturing process. To test this the firm acquired thirty identical cars (make and model) from an auto company and randomly assigned the cars to one of the three blends. The cars were then driven for 30 eight hour days on a dynamometer simulating city and highway driving conditions and the mileage obtained (MPG) was measured at the conclusion of the study. The results are below and require analysis to obtain a decision as to whether one of the blends or more was superior to the others.

Gasoline Blends

Blend A	Blend B	Blend C
28.6	25.6	29.6
27.6	26.6	28.6
31	31	32.5
29.2	29.4	29.8
30.2	29.5	29.6
28.9	30	29.4
29.1	29.6	32
30.2	27.5	31.2
28.6	31.1	31.9
28.4	29.1	28.2

Answer 1

	A	B	C
count, ni =	10	10	10
mean , x̅ i =	29.180	28.94	30.28
std. dev., si =	1.014	1.817	1.507
sample variances, si^2 =	1.028	3.303	2.271
total sum	291.8	289.4	302.8		884	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	29.47
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	0.082	0.277	0.662
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	0.822	2.774	6.615		10.21067
SS(within ) = SSW = Σ(n-1)s² =	9.256	29.724	20.436		59.4160

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   30
df within = N-k =   27
  
mean square between groups , MSB = SSB/k-1 =    5.1053
  
mean square within groups , MSW = SSW/N-k =    2.2006
  
F-stat = MSB/MSW =    2.3200

anova table	0.146648794
	SS	df	MS	F	p-value	F-critical
Between:	10.21	2	5.11	2.32	0.1176	3.35
Within:	59.42	27	2.20
Total:	69.63	29

F =2.32  

p value = 0.1176

       α =    0.05
conclusion :    p-value>α , do not reject null hypothesis    

So, none of them superior to the others.   

..............

          

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