A company that stamps gaskets out of sheets of rubber, plastic and cork wants to

Question

A company that stamps gaskets out of sheets of rubber, plastic and cork wants to compare the mean number of gaskets produced per hour for two different types of stamping machines. In practical terms, the manufacturer wants to determine whether one machine is more productive than the other and, even more importantly, whether one machine is more productive in producing rubber gaskets while the other is more productive in producing plastic or cork gaskets. To answer these questions, the manufacturer decides to conduct an experiment using the three types of gasket material (cork, rubber, and plastic) with each of the two stamping machines. Each machine is operated for three one-hour time periods for each of the gasket materials, with the 18 one-hour time periods assigned to the six machine- material combinations in a random order. The data from the experiment, the number of gaskets (in thousands) produced per hour, are shown below. (a) Write down the classical model for this data. Clearly define and estimate all parameters used.

Explanation / Answer

We used multiple linear regression to model the production using dummy variables:

SUMMARY OUTPUT Regression Statistics Multiple R 0.725708 R Square 0.526652 Adjusted R Square 0.425221 Standard Error 0.242128 Observations 18 ANOVA df SS MS F Significance F Regression 3 0.913194 0.304398 5.192187 0.012792 Residual 14 0.820767 0.058626 Total 17 1.733961 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 3.636667 0.11414 31.86133 1.82E-14 3.39186 3.881474 3.39186 3.881474 Stamping machine-1 0.15 0.11414 1.31417 0.209915 -0.09481 0.394807 -0.09481 0.394807 Cork 0.408333 0.139793 2.920987 0.011169 0.108507 0.708159 0.108507 0.708159 Rubber -0.075 0.139793 -0.53651 0.60003 -0.37483 0.224826 -0.37483 0.224826

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