This has to be done by hand, not excel or any other software. Thank you!

TABLE E3.1 The 22 Design for Exercise 3.1 \begin{tabular}{ccccccc} \hline & & & \multicolumn{4}{c}{ Replicate } \\ \cline { 4 - 7 }A & B & Treatment Combination & I & II & III & IV \\ \hline & & (1) & 18.2 & 18.9 & 12.9 & 14.4 \\ + & & a & 27.2 & 24.0 & 22.4 & 22.5 \\ & + & b & 15.9 & 14.5 & 15.1 & 14.2 \\ + & + & ab & 41.0 & 43.9 & 36.3 & 39.9 \\ \hline \end{tabular} Using the data from Exercise 3.1 in Myers, Montgomery, and Anderson-Cook (MMA-C), comple the following analysis by hand. a) Calculate an ANOVA and indentify the significant effects. b) Draw the AB interaction plot. Interpret the plot. What levels of of the factors would you recommend? c) Fit a regression model to the data using the effect estimates and coded variables. d) Assuming that the regression model is adequate, at what rpm must the drill run to maintain vibration less than 25 for the 1/8 inch bit? TABLE E3.1 The 22 Design for Exercise 3.1 \begin{tabular}{ccccccc} \hline & & & \multicolumn{4}{c}{ Replicate } \\ \cline { 4 - 7 }A & B & Treatment Combination & I & II & III & IV \\ \hline & & (1) & 18.2 & 18.9 & 12.9 & 14.4 \\ + & & a & 27.2 & 24.0 & 22.4 & 22.5 \\ & + & b & 15.9 & 14.5 & 15.1 & 14.2 \\ + & + & ab & 41.0 & 43.9 & 36.3 & 39.9 \\ \hline \end{tabular} Using the data from Exercise 3.1 in Myers, Montgomery, and Anderson-Cook (MMA-C), comple the following analysis by hand. a) Calculate an ANOVA and indentify the significant effects. b) Draw the AB interaction plot. Interpret the plot. What levels of of the factors would you recommend? c) Fit a regression model to the data using the effect estimates and coded variables. d) Assuming that the regression model is adequate, at what rpm must the drill run to maintain vibration less than 25 for the 1/8 inch bit