Problem statement: Fly ash is used to remove phosphate in wastewater. Three factors including phosphate concentration (x1), initial pH value of solution (x2) and fly ash dosage (x3) affect the removal efficiency of phosphate (y). A 23 full factorial experimental design shown below was used to analyze the influence of three process factors on the removal efficiency of phosphate. -1 +1 Table 1 values of process variables in experiments Process variables X1 (phosphate concentration, mg/l) X2 (pH value) X3 (fly ash dosage, g/l) 25 50 2.9 5.5 0.5 2 Table 2 Experimental results in standard 23 full factorial design table Experiments X1 x2 x3 Y 1 -1 -1 -1 17.16 2 +1 - 1 -1 1.5 3 -1 +1 -1 99.41 4 +1 +1 -1 41.22 5 -1 -1 +1 26.4 6 +1 -1 +1 1.1 7 -1 +1 +1 99.6 8 +1 +1 +1 49.56 -1 -1 -1 16.95 Repeat 1 Repeat 8 +1 +1 +1 51.25 Questions: Q1: Please fill the Standard 23 full factorial design table 2 in Excel with the operating conditions given in Table 1 (1 pt) Q2: Please find the mean, maximum, minimum, mediation and standard deviation of the y values using Excel (1 pt) Q3: Please write a coutif function to the number of Y values bigger than 15 and smaller than 50 (1 pt) Q4: Please use the experimental data to find the model parameters of the following linear regression model (3 pt): Y = B. +B,X, +B2X2 +B,X, +B12X,X2 +313X,X2 + B23X,X, +B 123X,X,X; + 3 Q5: Please show the ANOVA (Analysis of Variance) Table and properly interpret the meanings of the parameters in the ANOVA table (2 pt) Q6: Please use the ANOVA table to determine the significance of regressor terms in the model. (2 pts) Problem statement: Fly ash is used to remove phosphate in wastewater. Three factors including phosphate concentration (x1), initial pH value of solution (x2) and fly ash dosage (x3) affect the removal efficiency of phosphate (y). A 23 full factorial experimental design shown below was used to analyze the influence of three process factors on the removal efficiency of phosphate. -1 +1 Table 1 values of process variables in experiments Process variables X1 (phosphate concentration, mg/l) X2 (pH value) X3 (fly ash dosage, g/l) 25 50 2.9 5.5 0.5 2 Table 2 Experimental results in standard 23 full factorial design table Experiments X1 x2 x3 Y 1 -1 -1 -1 17.16 2 +1 - 1 -1 1.5 3 -1 +1 -1 99.41 4 +1 +1 -1 41.22 5 -1 -1 +1 26.4 6 +1 -1 +1 1.1 7 -1 +1 +1 99.6 8 +1 +1 +1 49.56 -1 -1 -1 16.95 Repeat 1 Repeat 8 +1 +1 +1 51.25 Questions: Q1: Please fill the Standard 23 full factorial design table 2 in Excel with the operating conditions given in Table 1 (1 pt) Q2: Please find the mean, maximum, minimum, mediation and standard deviation of the y values using Excel (1 pt) Q3: Please write a coutif function to the number of Y values bigger than 15 and smaller than 50 (1 pt) Q4: Please use the experimental data to find the model parameters of the following linear regression model (3 pt): Y = B. +B,X, +B2X2 +B,X, +B12X,X2 +313X,X2 + B23X,X, +B 123X,X,X; + 3 Q5: Please show the ANOVA (Analysis of Variance) Table and properly interpret the meanings of the parameters in the ANOVA table (2 pt) Q6: Please use the ANOVA table to determine the significance of regressor terms in the model. (2 pts)