A chemist wants to know what aspects of cloth produc6on affect how easily it wri
ID: 3231961 • Letter: A
Question
A chemist wants to know what aspects of cloth produc6on affect how easily it wrinkles. He looks at 32 pieces of cloth and their curing time, curing temperature, formaldehyde concentration, and catalyst ratio and measured their wrinkle resistance score. Use the following data to perform a multiple regression analysis and fill in the outlined boxes.
a) Create the line of best fit and calculate s and adjusted R2.
b) Perform a test of overall significance for the model at 95% confidence.
c) Predict the wrinkle resistance for a cloth made at 40 degrees Celsius, a concentration of .8, a ratio of 2:1, and for21 seconds. Knowing a score of 5 is a good indicator of wrinkle resistance, is this a good fabric?
d) Create a 95% confidence interval for time and do a test of significance with the same confidence level.
e) A reduced model is created that only includes ratio and temperature. Write out this reduced model and then test
Analysis of Variance Source DF Adj SS Adj MS F-Value Regression 4 47.9096 Error 17.7953 0.6591 Total 31 65.7049 Coefficients TValue 95% Cl Coef SE Coef Term Constant (-2.2665, 0.7544) 0.7560 0.7361 Conc 0.15453 0.06334 (0.02457, 0.28448) 2.44 Ratio 0.21705 0.03164 (0.15214, 0.28197) 6.86 Temp 0.010806 0.004622 (0.001323, 0.020290) 2.34 Time 0.09464 0.05455 Model Summary S R-sq R-sq(adj) 72.92%Explanation / Answer
a)
WRS=-0.7560+0.15453Conc+0.21705Ratio+0.010806Temp+0.09464Time
R^adj=1-(1-R^2)(n-1)/n-k-1)=1-(1-0.7292)(31)/32-4-1=1-0.31=0.69
b)
Adj MS=47.9096/4=11.9774, DF=27, F-value=11.9774/0.6591=18.17
FCRIT=2.7277. Hence, reject null hypothesis.
c)
WRS=-0.7560+0.15453(0.8)+0.21705(2)+0.010806(40)+0.09464(21)
=2.22, it is not a good fabric
d)
LCL=0.09464-(2.04)(0.05455)=-0.016642
UCL=0.09464+(2.04)(0.05455)=0.205922
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