a) Analysis of Variance for Light output, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Glass type 5865 5865 753 6.37. Temperature 97335 97335 98567 695.6. Glass type*temperature 955 955 7638 98.73. Error 8 6579 6579 366 Total 6 833 S = 9.85 R-Sq =.73% R-Sq(adj) =.6% La interaccion es significativa y también los factores individuales b)no es posible hacer modelo debido a que el tipo de vidrio es una variable categorica c)
Percent 9 5 Plots for Light output Normal Probability Plot - Versus Fits 95 9 8 Probability Plot of RESI Normal Mean 8.85E- StDev 5.9 N 7 A D.5 P-Value.76 - - Histogram - 5 75 5 Fitted Value Versus Order 5 Percent 7 6 5 3 Frequency 9 6 3-3 - - 3 - - es sí son normales 6 8 6 8 6 Observation Order 5 - -3 - - RESI 3 El experimento no fue aleatorizado por lo cual no puede checarse aleatoridad en residuales Datos aberrantes: Unusual Observations for Light output Light Obs output Fit SE Fit St Resid 5 7. 35.. 35.. R 3. 35.. -35. -. R R denotes an observation with a large standardized residual.
a) Analysis of Variance for strength, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P % hardwood 7.7639 7.7639 3.889.6. cooking time.5.5.5 55.. pressure 9.3739 9.3739 9.6869 6.5. % hardwood*cooking time.87.87.8.85.8 % hardwood*pressure 6.9 6.9.58.7.5 cooking time*pressure.95.95.975 3..75 % hardwood*cooking time*pressure.9733.9733.933.35.9
Error 8 6.58 6.58.3656 Total 35 66.389 S =.66 R-Sq = 9.8% R-Sq(adj) = 8.7% Factores individuales son significativos y la interacción % hardwood*pressure Percent 9 5 Plots for strength Normal Probability Plot..5. -.5 Versus Fits -. -.5..5. -. 96 98 Fitted Value Histogram. Versus Order Frequency 9 6 3.5. -.5 b) -.8 -....8 -. 5 5 5 Observation Order 3 35 Probability Plot of RESI Normal Percent 95 9 8 7 6 5 3 Mean.838E- StDev.336 N 36 AD.9 P-Value.6 5 -. -.5. RESI.5. es no son normales No hay datos aberrantes Aleatorización no puede checarse ya que el experimento no fue aleatorizado
Main Effects Plot for strength Data Means. 98.5 98. 97.5 % hardwood cooking time Mean. pressure 8 3 98.5 98. 97.5 c) 5 65 Interaction Plot for strength Data Means 3 5 65 % hardwood 98 % hardwood 8 cooking time 96 98 cooking time 3 96 pressur e Condiciones optimas: %hardwood:, cooking time, pressure 65
a) Analysis of Variance for warping, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Temperature 3 56.9 56.9 5.3 7.67. Cooper content 3 698.3 698.3 3.78 3.33. Temperature*Cooper content 9 3.78 3.78.6.86.33 Error 6 8.5 8.5 6.78 Total 3 76.79 Ambos factores afectan
Percent 9 5 Plots for warping Normal Probability Plot - Versus Fits -5. -.5..5 5. - 5 Fitted Value 5 3 8 Histogram Versus Order Frequency 6 - b) -3 - - 3-6 8 6 8 Observation Order 6 8 3 3 Probability Plot of RESI Normal 95 9 Mean.6E-6 StDev.87 N 3 AD.666 P-Value.7 8 7 Percent 6 5 3 5 - -3 - - RESI 3 5 La prueba de normalidad la pasa muy justa, no se ven bien distribuidos losresiduales Main Effects Plot for warping Data Means 3. Temperature Cooper content 7.5 5. Mean.5. 7.5 c) 5. 5 75 5 6 8 La temperatura no se comporta linealmente
Interaction Plot for warping Data Means 3 5 Temperature 5 75 5 Mean 5 6 8 Cooper content Dado que la interacción no es significativa, no afecta dónde debe estar la temperatura para elegir el contenido de cobre bajo. d) Misma respuesta que c)
a) The regression equation is Y (strength) = +.88 X (% hardwood) b) Analysis of Variance Source DF SS MS F P Regression 6. 6. 6.. Error 8 38.8.9 Total 9 3.9 La regresión es significativa
a) The regression equation is y = 35 -.7 x -.5 x b) S = 5.979 R-Sq = 86.% R-Sq(adj) = 77.% Analysis of Variance Source DF SS MS F P Regression 6.6 68.8 9.35.5 Error 3 95. 65. Total 5. Regresión significativa c) Predictor Coef SE Coef T P Constant 35. 7.75.7.8 x -.7.69 -.9.356 x -.539.8953 -.7.8 Ninguna de las pendientes es estadísticamente igual a cero porque los p-valores son mayores a.5
The regression equation is y =. - 38. x +.7 x + 35. x^ +. x^ - 9. xx Predictor Coef SE Coef T P Constant. 6.59.9.39 x -38.3.5 -.9.383 x.7.69.6.953 x^ 3.98.56.6.56 x^.66 3.58 3.5.3 xx -9.986 8.7 -..97 S = 6. R-Sq =.% R-Sq(adj) = 98.9% Analysis of Variance Source DF SS MS F P Regression 5 359.6 78.5 9.3. Error 6 9. 36.5 Total 353.7
Es una buena regresión porque R es grande, pero podemos notar que la regresión está dominada por x solamente, los demás regresores no son significativos. Analysis of Variance for Num orders (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 3 5.5 5.5 6.833 5.6.3 A.5.5.5.8.78 B.5.5.5.75. C 36. 36. 36...9 -Way Interactions 3 9.5 9.5 63.75.5. A*B.5.5.5.8.6 A*C... 33.33. B*C 9. 9. 9. 6.33. 3-Way Interactions....33.8 A*B*C....33.8 Error 8.. 3. Pure Error 8.. 3. Total 5 69.75 Significativos: C, A*B, A*C, B*C
Plots for Num orders Normal Probability Plot Versus Fits Percent 9 5 - -3. -.5..5 3. - 5 8 5 Fitted Value 5 Histogram Versus Order 3 Frequency - - - - 3 5 6 7 8 9 Observation Order 3 5 6 Probability Plot of RESI Normal Percent 95 9 8 7 6 5 3 Mean StDev.65 N 6 AD.5 P-Value.7 5-3 - - RESI 3 es normales, pero falta resolución en el instrumento de medición vs fits ligeramente forma de embudo c) Main Effects Plot for Num orders Data Means 9 A B 8 7 Mean 6 9 - C - 8 7 6 -
Cube Plot (data means) for Num orders 7.5 55. 7..5 B 7.5 6.5-5. - A 3. - C Se recomienda trabajar en A alto, B alto, C alto
a) Estimated Effects and Coefficients for crack length (coded units) Term Effect Coef SE Coef T P Constant.988.536 38.. A 3.9.59.536 9.97. B 3.976.988.536 39.7. C -3.596 -.798.536-35.7. D.958.979.536 9.. A*B.93.967.536 9.. A*C -.8 -..536-39.79. A*D.76.38.536.76.59 B*C.96.8.536.95.355 B*D.7..536.7.65 C*D -.77 -.38.536 -.76.56 A*B*C 3.37.569.536 3.5. A*B*D.98.9.536.97.35 A*C*D.9..536.9.85 B*C*D.36.8.536.35.78 A*B*C*D..7.536..89 b) Analysis of Variance for crack length (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 333.96 333.96 83.37 7.8. A 7. 7. 7. 898.3. B 6.6 6.6 6.6 558.7. C 3.6 3.6 3.6 7.8. D 3.66 3.66 3.66 377.8. -Way Interactions 6 58.69 58.69 6.35 35.7. A*B 9.97 9.97 9.97 368.7. A*C 8.96 8.96 8.96 583.6. A*D.7.7.7.58.59 B*C.7.7.7.9.355 B*D.8.8.8..65 C*D.7.7.7.58.56 3-Way Interactions 78.8 78.8 9.7.86. A*B*C 78.75 78.75 78.75 97.33. A*B*D.77.77.77.95.35 A*C*D.3.3.3..85 B*C*D....3.78 -Way Interactions.....89 A*B*C*D.....89 Error 6...8 Pure Error 6...8 Total 3 57.6 Significativos: A,B,C,D,AB,AC,ABC c) Y =.988 +.59x+.988x-.798x3+.979x+.967xx-.xx3+.569xxx3
d) Percent 9 5 Plots for crack length Normal Probability Plot... -. Versus Fits -.5 -.5..5.5 -. 5 5 Fitted Value 8 Histogram. Versus Order Frequency 6.. -. -.3 -. -.....3 -. 6 8 6 8 6 8 3 3 Observation Order Probability Plot of RESI Normal Percent 95 9 8 7 6 5 3 Mean -8.3667E-7 StDev.7 N 3 A D.786 P-Value.37 5 -.5 -.5. RESI.5.5 es no pasan prueba de normalidad e) Todos los factores individualmente afectan la respuesta (son significativos) f)
3 Main Effects Plot for crack length Data Means A B Mean - C - D 3 - - Interaction Plot for crack length Data Means - - - A 6 A - B 8 6 B - C 8 6 C - 8 D
Cube Plot (data means) for crack length 9.365 3.85.65 5.353.86 7.5 3.767 9.735 B.77.33.95 6.5-6.765 - A.963 - C 8.756 6.9595 - D Recomendación para minimizar: A bajo, B alto, C alto, D bajo