An experiment was performed to investigate the surface finish of a metal part. The experiment is a $23$ factorial design in the factors feed rate $($A$),$ depth of cut $($B$),$ and tool angle $($C$)$ each having two levels, i$.$e$.$ High $($H$)$ and Low $($L$),$ with n $=2$ replicates. Table below presents the observed surface$-$finish data for this experiment. Analyze and interpret the data from this experiment at $12\%$ significance level.

Treatment Observations Total

$12$

LLL $9716$

HLL $101222$

LHL $91120$

HHL $121527$

LLH $111021$

HLH $101323$

LHH $10818$

HHH $161430$

a$)$ Fill the following Table,

Source of variation SS Degree of freedom MS Fcomputed p Fcritical Regression coefficient

A $45\mathrm{.}56251\mathrm{.}6875$

B $10\mathrm{.}56250\mathrm{.}8125$

C $3\mathrm{.}06250\mathrm{.}4375$

AB $7\mathrm{.}56250\mathrm{.}6875$

AC $0\mathrm{.}06250\mathrm{.}0625$

BC $1\mathrm{.}56250\mathrm{.}3125$

ABC $5\mathrm{.}06250\mathrm{.}5625$

Error $19\mathrm{.}5$

Total $92\mathrm{.}9375$

b$)$ Find the significant effects

c$)$ Given the regression coefficients, develop the regression model.

d$)$ If all the factors are set at low level, what will be the predicted value of surface finish?An experiment was performed to investigate the surface finish of a metal part. The

experiment is a $2^3$ factorial design in the factors feed rate $($A$),$ depth of cut $($B$),$ and tool

angle $($C$)$ each having two levels, i$.$e$.$ High $(H)$ and Low $($L$),$ with $n=2$ replicates. Table

below presents the observed surface$-$finish data for this experiment. Analyze and

interpret the data from this experiment at $12\%$ significance level.

a$)$ Fill the following Table,

b$)$ Find the significant effects

c$)$ Given the regression coefficients, develop the regression model.

d$)$ If all the factors are set at low level, what will be the predicted value of surface

finish?