Week_7_Practice_Problems

Week_7_Practice_Problems - Week 7 Practice Problems 1. In...

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Week 7 Practice Problems 1. In the production of a certain chemical, the yield (y) of the process (measured as %) is approximately a linear function of the amount of catalyst (x) used. In a laboratory experiment, 10 levels of catalyst were used with two replicates at each level. The data are Catalyst (x) Yield (y) Catalyst (x) Yield (y) 0.3 46.9 0.8 53.9 0.3 50.6 0.8 52.8 0.4 50 0.9 55.3 0.4 48.6 0.9 53.8 0.5 50.1 1 58.9 0.5 50.1 1 60.9 0.6 52.2 1.2 58.7 0.6 50 1.2 61.8 0.7 52.4 1.4 63.4 0.7 57.9 1.4 62.1 To save you calculation time, we provide the following summaries: 22 ˆ 0.78, 54.42, ( ) 2.238, ( ) 30.458, 65.220 ii i i x y xx y r == = = = ∑∑ catalyst yield 1.4 1.2 1.0 0.8 0.6 0.4 0.2 65 60 55 50 45 Yield vs Catalyst Level Consider the Gaussian response model to describe the experiment. ( ) , ~ (0, ), 1,. ..,20independent i i Yx x R R G i α βσ =+ − + = a) What do the parameters and β represent? b) Find the MLEs of and (you can do this from scratch for practice if you wish – otherwise use the formulas given in class). Add the fitted line to the scatterplot. c) Find the estimate of σ . What are the degrees of freedom in this case?
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d) Find a 95% confidence interval for β . How would you interpret this interval formally?
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Week_7_Practice_Problems - Week 7 Practice Problems 1. In...

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