The following data is given regarding! the effect of reaction temperature on the

Question

The following data is given regarding! the effect of reaction temperature on the molecular weight of resulting poly polyols. Perform a linear regression on y as a function of x. What change in the average molecular weight accompanies a 1 degreeC change in temperature within the range of the data? What molecular weight would you predict for an additional reaction ran at 200 degreeC? Would you use this equation to predict a molecular weight for a temperature of 70 degreeC? Why or why not? The experimenter managed the temperature variable while running this experiment. Assuming the range of temperatures is adequate, what additional runs would you like to have performed so that you will feel more confident about your statistical analysis? Find S_LF for this data. Find 95 % confidence intervals for the mean average molecular weight at 212 degree C and 250 degree C. For which value of Pot Temperature will we be able to find the narrowest confidence interval? Using the answers from part g and confidence intervals for the mean average molecular weight at other (choose them yourself) Pot Temperatures, draw a graph of the linear fit equation and the confidence bands for the mean average molecular weight in this model.

Explanation / Answer

Sol)

The Regression equation is

y=a+bx

a)

From Excel

The Fitted Regression is y= -3174.57 +23.498(Temp)

b) If we change 1 centigrade in temp then there will be 23.498 points change in weight

c) When Temp=200

Then y hat= -3174.57 +23.498(Temp)

y hat=-3174.57 +23.498(200) =1525.03

d) When Temp=70

Then y hat= -3174.57 +23.498(Temp)

y hat=-3174.57 +23.498(70) = -1529.71

SUMMARY OUTPUT Regression Statistics Multiple R 0.997132 R Square 0.994272 Adjusted R Square 0.993318 Standard Error 67.00832 Observations 8 ANOVA df SS MS F Significance F Regression 1 4676798 4676798 1041.576 5.88E-08 Residual 6 26940.69 4490.116 Total 7 4703739 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -3174.57 156.4343 -20.2933 9.3E-07 -3557.35 -2791.79 Temp 23.49827 0.728099 32.27346 5.88E-08 21.71667 25.27986

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