7. An experiment was conducted to determine the effect of four factors on the re- sistivity of a semiconductor wafer. The data is found in wafer where each of the four factors is coded as or + depending on whether the low or the high setting for that factor was used. Fit the linear model resist x1 + x2 + x3 + x4.

(a)Extract the X matrix using the model.matrix function. Examine this to deter- mine how the low and high levels have been coded in the model.

(b)Compute the correlation in the X matrix. Why are there some missing values in the matrix?

(c)What difference in resistance is expected when moving from the low to the high level of x1?

(d)Refit the model without x4 and examine the regression coefficients and stan- dard errors? What stayed the the same as the original fit and what changed?

(e)Explain how the change in the regression coefficients is related to the correla- tion matrix of X.

Thank you so much for answering this!!!