$*$I really only need help with parts A$,$B and C$.$ I added the rest incase the table is needed at all!! thanks!!!

Consider an experiment with a fractional factorial design and $7$ factors, each with two levels.

The generators for this experiment are $-$BCDE,$-$ACDF, and ABCG.

a$.$ Determine the complete defining relation for the design of this experiment. Make sure

to write the letters for each effect in alphabetical order. HINT: This defining

relation will include all generators and all effects corresponding to possible two$-$way and

three$-$way interactions between generators. There should be seven "words" $($i$.$e$.,$ effects$)$

in the defining relation.

b$.$ What is the resolution of this design? Justify your answer.

c$.$ What type of design was implemented in this experiment? Be as specific as possible $($for

example: a $2_{\text{I}\text{I}\text{I}}^{5-2}$ fractional factorial$).$

d$.$ Determine all seven aliases of the $F$ effect. Make sure to write the letters for each

effect in alphabetical order.

e$.$ Below are the observations from each treatment with a run in this experiment. Deter$-$

mine the estimates of the $D$ and AFG effects $($confounded with their aliases$).$ Round all

final answers to $3$ decimals, if necessary.

f$.$ Determine the sums of squares for the $D$ and AFG effects $($confounded with their aliases$).$

Round all final answers to $3$ decimals, if necessary.