3:22 canopy.uc.edu C 1. Using the attached data (assignment3_1.Rdata), answer the following questions: a. Create a plot matrix using plot() command. What can you say about the relation between Y and the predictor variables (X1-X3) in the dataset? b. Fit the following model and create a summary: Yi = Bo + BiXi + B2Xiz + B3Xi3 + B5Xi2 + BeXia + ByXi1Xiz + BeXizXis + BgXuXi3 + ; Which regression coefficients appear to be significant? c. Compute the VIF for each variables. Which variables appear to cause multicollinearity issues? Based on the computed VIFs, is it a good idea to use only the significant variables found in part b for regression? d. Fit a linear regression model using only the variables that were significant in part b. Is it a good idea to use this model? Why? e. Now center the quantitative predictor variables X2 and X3 using the following code: dataset$X2=dataset$X2-mean(dataset$X2) dataset$X3=dataset$X3-mean(dataset$X3) dataset$X2.2=dataset$X2^2 dataset$X3.2=dataset$X3^2 Fit the same model as in part b. Which variables appear to be significant now? Re-do the model fitting using only the significant predictor variables and show the summary. Do we have a better fit now? f. Apply the best subset variable selection method using the following code: bestsubset=regsubsets(Y~X1+X2+X3+X2.2+X3.2+X1:X2+X2:X3+X1:X3,data=dataset) bestsummary=summary(bestsubset) bestsummary Choose the best subset model based on Mallow's Cp. g. Fit a linear regression model based on the best subset selected in part f. Show the model summary and compare it to the summary results in part e. Can we find any differences