Question 5 10 pts The table shows a 32 factorial design. Both factors A and B have 3 different levels each and the table shows the response variable Y. Which factors or two-way interaction are statistically significant to the 0.05 level? m 1 ' Only interaction AB is significant. ) Only factor B is significant. (O Factors A, B and AB are all significant. O Only factor A iis significant. Question 7 10 pts If you have a response variable y and two factors x1 and x2, what is a suitable R command to fit a second order regression model to a set of data. y = Bo + BIX, + B2-x2 + BI1 *1 + 22 x2 + $12*1 *2 + E O Im(y ~ x1*x2 + [(x1^2) + 1(x2^2), data = table) O Im(y ~ x1*x2 + x1^2+ x2^2, data = table) O Im(y ~ x1*x2 + x1^2*x2^2, data = table) O Im(y ~ x1+x2 + I(x1^2) + I(x2^2), data = table)Question 8 10 pts After analysing the available data, the path of steepest ascentis y =20+ 8x1 + 4x2. The experimenter would like to follow the line of steepest ascent to reach an optimal point. From the equation, if he moves 4 units in the x2 direction, how many units must he move in the x1 direction? O He must move 4x4 units in the x1 direction. () He can move any units he chooses. @ He must move 8 units in the x1 direction. (O He must move 4 units in the x1 direction. Question @ 10 pts To generate the response surface, second-order model need to be fitted. If one of the natural variable E1 has 3 levels: 70, 80 and 90, how shoud it be coded as x1 for the central composite design? ) It should coded as x1 = (E1-80)/20. () It should coded as x1 =0, 1, 2. O It should coded as x1 = (E1-80)/10. O It should coded as x1 = -1, 0 +1. Question 10 10 pts The table shows two factors x1 and x2 and the response variable v. It comprise a 22 factorial, 4 axial points and 5 centre points. Fit a second-order central composite design to the data. Is the second- order a good fit for the data? (O False - The data does not fit a response surface quadratic model. @ True, the data fits a response surface quadratic model significantly