The Output of a Continuous Extruding Machine That Coats Steel $x _ { 0010 } = 8242 , x _ { 0020 } = 9732 \text {, and } x _ { 0030 } = 11,210$

question 33

Essay

The output of a continuous extruding machine that coats steel pipe with plastic was studied as a function of the thermostat temperature profile (A, at three levels), type of plastic (B, at three levels), and the speed of the rotating screw that forces the plastic through a tube-forming die (C, at three levels). There were two replications (L = 2) at each combination of levels of the factors, yielding a total of 54 observations on output. The sums of squares were SSA = 14,144.44, SSB = 5511.27, SSC = 244,696.39, SSAB = 1069.62, SSAC = 62.67, SSBC = 331.67, SSE = 3127.50, and SST = 270,024.33.
a. Construct the ANOVA table.
b. Use appropriate F tests to show that none of the F ratios for two- or three-factor interactions is
at level .05.
c. Which main effects appear significant?
d. With $x _ { 0010 } = 8242 , x _ { 0020 } = 9732 \text {, and } x _ { 0030 } = 11,210$
use Tukey's procedure to identify significant
differences among the levels of factor C.

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Definitions:

Alpha

In finance, a measure of performance on a risk-adjusted basis, calculating the excess return of an investment relative to the return of a benchmark index.

Regression Equation

An equation that describes the average relationship between a dependent variable and one or more explanatory variables.

Beta

A metric representing the instability or consistent risk involved in a security or portfolio relative to the entire market.

Adjustment Technique

A method or process applied to modify or correct data, parameters, or conditions for a specific purpose, such as statistical analysis or financial models.