Question

Run	A	B	C	D	E	F	G	Y1	Y2
1	-	-	-	-	-	-	-	75.20	73.76
2	-	-	-	+	+	+	+	73.50	77.92
3	-	+	+	-	-	+	+	73.50	77.92
4	-	+	+	+	+	-	-	69.80	67.78
5	+	-	+	-	+	-	+	88.20	81.76
6	+	-	+	+	-	+	-	80.30	82.84
7	+	+	-	-	+	+	-	82.00	86.06
8	+	+	-	+	-	-	+	78.00	83.94

A.) Complete the table calculating ybar, s and In/s

B.) Identify the significant factors affecting the response (y)

C.) Identify significant factors affecting dispersion

D.) What is the predictions equation

Answer 1

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Model 7 427.445 61.064 6.74 0.008
Linear 7 427.445 61.064 6.74 0.008
A 1 339.665 339.665 37.50 0.000
B 1 13.104 13.104 1.45 0.263
C 1 4.285 4.285 0.47 0.511
D 1 36.966 36.966 4.08 0.078
E 1 0.152 0.152 0.02 0.900
F 1 15.210 15.210 1.68 0.231
G 1 18.063 18.063 1.99 0.196
Error 8 72.460 9.057
Total 15 499.905

Model Summary

S R-sq R-sq(adj) R-sq(pred)
3.00956 85.51% 72.82% 42.02%

Coded Coefficients

Term Effect Coef SE Coef T-Value P-Value VIF
Constant 78.280 0.752 104.04 0.000
A 9.215 4.607 0.752 6.12 0.000 1.00
B -1.810 -0.905 0.752 -1.20 0.263 1.00
C -1.035 -0.518 0.752 -0.69 0.511 1.00
D -3.040 -1.520 0.752 -2.02 0.078 1.00
E 0.195 0.098 0.752 0.13 0.900 1.00
F 1.950 0.975 0.752 1.30 0.231 1.00
G 2.125 1.063 0.752 1.41 0.196 1.00

Regression Equation in Uncoded Units

Y = 78.280 + 4.607 A - 0.905 B - 0.518 C - 1.520 D + 0.098 E + 0.975 F + 1.063 G

Alias Structure (up to order 3)

Factor Name

A A
B B
C C
D D
E E
F F
G G

Aliases

I - ABC - ADE - AFG - BDF - BEG - CDG - CEF
A - BC - DE - FG + BDG + BEF + CDF + CEG
B - AC - DF - EG + ADG + AEF + CDE + CFG
C - AB - DG - EF + ADF + AEG + BDE + BFG
D - AE - BF - CG + ABG + ACF + BCE + EFG
E - AD - BG - CF + ABF + ACG + BCD + DFG
F - AG - BD - CE + ABE + ACD + BCG + DEG
G - AF - BE - CD + ABD + ACE + BCF + DEF

from above graph it is clear that effect A only significant