An experiment is conducted to study the effect of the chemical environment and t

Question

An experiment is conducted to study the effect of the chemical environment and the temperature on the yield strength of a material. The following data shows the results obtained when tested with two chemical agents, A and B, and two temperatures, 25°C and 37°C. Iemp Yield strength (MPa) replicate Chemical 4 25 37 25 37 138.4130.89 94.646 96.653116.9 88.215 92.312147.28116.48 88.802114.3790.737 120.18129.43139.76132.75137.23121.73 123.5128.94102.8699.941161.68136.44 a. Estimate all main effects and interactions b. Find the standard errors on all effects and test the hypothesis if any of them can be neglected. Use 95% confidence interval for hypothesis testing c. Create a regression model for the experiment. d. Test if any of the regression coefficients can be neglected using 95% confidence interval. Rewrite the regression equation with only significant coefficients

Explanation / Answer

Factorial Regression: aa versus A, B

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value

Model 3 74.93 24.98 0.05 0.984

Linear 2 64.76 32.38 0.07 0.935

A 1 10.22 10.22 0.02 0.886

B 1 54.54 54.54 0.11 0.741

2-Way Interactions 1 10.17 10.17 0.02 0.886

A*B 1 10.17 10.17 0.02 0.886

Error 20 9675.04 483.75

Total 23 9749.98

Model Summary

S R-sq R-sq(adj) R-sq(pred)

21.9944 0.77% 0.00% 0.00%

Coded Coefficients

Term Effect Coef SE Coef T-Value P-Value VIF

Constant 118.76 4.49 26.45 0.000

A -1.31 -0.65 4.49 -0.15 0.886 1.00

B -3.01 -1.51 4.49 -0.34 0.741 1.00

A*B -1.30 -0.65 4.49 -0.15 0.886 1.00

Regression Equation in Uncoded Units

aa = 118.76 - 0.65 A - 1.51 B - 0.65 A*B

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