Question

1) A company is about to change the way it inspects its product. Experiments were done with differing number of inspections, and the following data shows how average number of defects varies with the number of inspections:

Inspections (x)	0	1	2	3	4	5	6	7	8	9	10
Defects (y)	92	86	81	72	67	59	53	43	32	24	12

The following quantities were obtained: n = 11;   ∑x=55;  ∑y=621 ; ∑x²=385 ; ∑y²=41,977 ; ∑xy=2238, X-bar=5 ; y-bar=56.45 ; S_xx=110; S_yy=6918.73 ; S_xy= - 687

a) Find the linear regression model.

b) Construct the ANOVA table.

Answer 1

Inspections (x)	0	1	2	3	4	5	6	7	8	9	10
Defects (y)	92	86	81	72	67	59	53	43	32	24	12

a) The regression model as

Sum of X = 55
Sum of Y = 621
Mean X = 5
Mean Y = 56.4545
Sum of squares (SSX) = 110
Sum of products (SP) = -867

Regression Equation = ŷ = bX + a

b = SP/SSX = -867/110 = -7.88182

a = MY - bMX = 56.45 - (-7.88*5) = 95.86364

ŷ = -7.88182X + 95.86364

Hence regression model as

ŷ = -7.88182X + 95.86364

Graph.

b) Summary of data as

Summary of Data
	Treatments
	1	2	3	4	5	Total
N	11	11				22
∑X	55	621				676
Mean	5	56.4545				30.7273
∑X2	385	41977				42362
Std.Dev.	3.3166	26.3035				32.0642

Result Details
Source	SS	df	MS
Between-treatments	14561.64	1	14561.64	F = 41.43463
Within-treatments	7028.727	20	351.4364
Total	21590.36	21