. Gross state product (GSP) of 50 states are measured in 13 different areas of economic activity list below. In order to remove the influence of scale, the contribution of each area is measured as the proportion of the total GSP. The data can be found in file gsp.sav. Columns 2-14 in the data are the shares of GSP of the following areas: agriculture mining construction manufacturing (durable goods) manufacturing (nondurable goods) transportation communications utilities wholesale retail fiduciary, insurance, and real estate services government . . . . Conduct a principal component analysis of the data set. a. Check if the correlation in the data supports PCA. b. Extract the factors using PCA, use a scree plot to help determine the appropriate number of factors. c. Evaluate the goodness of the factor model using the proportion of variance explained and the communalities. d. Comment on the unrotated component loadings. B colt 1 Variable 2 Label 3 4 22.4 1.3 11.8 9 7 9 10 11 AL AK AZ AR CA CO CT DE FL GA HI ID IL IN LA 12.5 12 13 14 15 16 167 10 19 20 21 22 23 24 25 26 cola Coll cos col co Go agriculture mining constructor manufactur manufactur transportat communicaties 1.5 2.0 4.2 10.5 11.0 2.9 3.6 2.9 1.5 4.1 1.1 3.7 12.1 2.0 1.5 11.5 1.7 3.0 2.0 2.7 2.2 5.1 1.0 4.0 128 4.4 2.4 4.2 2.1 0.6 3.3 9.0 5.0 2.6 2.5 18 1.8 5.4 7.7 4.5 3.1 5.7 2.2 0.7 0.0 3.3 11.0 5.7 18 2.3 2.2 10 0.0 3.4 4.5 16.6 1.6 1.3 2.4 18 0.2 4.7 4.6 3.5 3.1 3.0 28 10 0.4 2.9 7.4 10.7 4.0 4.5 2.7 1.2 0.1 4.8 0.0 4.5 3.1 63 0.6 5.9 15.0 5.6 1.6 1.7 14 03 4.2 11.3 7.9 18 23 3.1 1.8 0.5 46 214 10.3 3.5 14 3.1 7.6 0.2 4.1 13.2 10.10 3.3 20 20 4.4 1.4 42 10.4 7.9 3.9 3.6 2.6 2.6 3.0 149 13.2 3.9 1.5 2.9 1.2 140 4.2 15.3 3.0 1.9 3.6 1.3 0.1 4,5 7.9 10.6 2.0 3.1 0.1 5.0 4.1 45 2.1 2.9 2.9 0.6 0.1 3.2 10.5 20 1.9 1.0 0.4 1.8 20.0 7.2 2.4 16 2.7 0.6 4.4 11.0 82 3.7 2.1 1.2 0.9 3.9 13.0 10.5 3.2 2.4 5.1 1.8 0.4 4.6 11.3 10.1 4,0 3.5 28 5.1 4.9 4.8 4.4 1.3 2.1 5.0 9.2 0.2 4.4 7.0 7.1 68 2.1 1.4 0.8 3.7 3.1 1.7 2.9 18 3.0 0.7 0.1 3.5 16.4 5.7 1,5 1.2 4.4 0.6 0.0 3.5 4.3 9,4 32 4,1 2.7 7.1 4.6 14.4 2.1 2.5 1.7 3.5 0.5 0.1 2.9 5.9 5.9 2.1 3.6 2.4 23 0.1 4.2 10.2 16.7 28 2.0 3.0 10.6 1.1 4.9 4.6 4.9 1.9 40 1.1 0.6 3.9 17.9 9.3 1.9 3,0 2.1 5.3 1.2 10.2 7.1 37 2.8 3.0 0.1 5.4 16.0 45 1.4 1.9 2.5 1.0 0.5 3.3 9.4 3.0 2.2 1.6 08 0.1 11.1 5.6 1.5 2.5 1,1 wholesale retall fiduciary servkes Fovernment 6.3 9.9 12.8 16.1 15.5 2.9 6.5 10.7 119 19.6 6.3 10.5 18.9 20.2 13.0 6.1 11.4 14.8 11.8 6.8 8.9 22.7 23.1 11.5 6.3 9.7 17.0 21.6 13.1 6.6 7.4 28.2 21.8 9.0 4.0 6.0 35.4 14.3 9.4 7.3 11.2 218 23.4 12.4 8.8 8.9 16.4 18.0 4.0 11.5 214 22.2 21.3 6.1 9.9 123 163 132 7.7 11 19.2 20.7 10.0 60 9.1 13.1 15.3 9.8 6.8 8.3 14.3 15.3 11.4 7.8 9.6 12.7 14.1 5.8 11.2 15.0 13.6 5.3 7.0 12.1 15.7 10. 6.0 111 18.5 18.7 13.5 8.7 21.4 23.2 17.8 7.1 78 25.8 9.2 7.2 8.9 15.8 18.5 10.5 13 8.7 17.9 10.9 5.6 10.0 11.5 16.0 14.9 7.3 9.1 14,7 19.1 11.2 6.4 13.4 19.2 15.9 7.4 8.3 14.8 17.1 14.1 4.6 9.4 18.4 12.3 9.9 62 9.1 22:2 19.4 9.1 9.1 7.3 21.2 10.8 8.9 18,9 17.5 17.7 6.2 6.9 29.7 111 6.4 8.9 14.6 15.4 11.2 9.1 12.7 17.5 15.1 7.1 9.2 15.3 17.7 10.5 10.0 12.5 17.4 16.2 30 8.2 163 11.9 3.6 19.0 212 10.5 8.7 226 22.7 12.1 SA KY LA ME MD MA MI MN MS MO MT NE NV NH NI NM NY NC ND OH OK OR PA RI 24.4 > 31 33 34 35 36 17 18 30 40 41 6'5 Rawdata List Variables + D c co 10 wholesale retall o 12 fiduciary cots services governme coll 10. 1 Variable 2 Label cala agriculture mining 8.2 83 5.6 7.3 6.4 7.4 4.6 6.2 17.9 11.5 14.7 13.4 14.8 18.4 25 26 27 28 29 30 11 32 33 34 8.7 10.0 9.1 9.9 8.3 9.4 9.1 7.3 8.9 22.2 2.9 12 13 5.1 9.2 08 0.7 0.6 1.9 0.5 2.3 10.6 23.2 13.9 29.7 14.6 12.7 15.3 35 35 E cold cols col col col constructior manufactur manufactur transportati communicattles Ti 1.9 3.7 2.1 11.0 0.6 4.4 3.9 13.0 0.9 10.5 2.4 3.2 5.1 3.5 11.3 4.6 4.0 0.4 10.1 2.8 4.8 4.4 4.9 3.3 2.1 5.4 5.0 4.4 7.0 0.2 7.1 2.1 6.8 1.4 3.7 8.4 3.1 1.7 2.9 1.8 3.0 3.5 0.1 16.4 5.7 1.5 4.4 1.7 0.0 3.5 4.3 9.4 4.1 3.2 2.7 7.1 4.6 14.4 2.1 2.5 1.7 3.5 0.1 2.9 5.9 5.9 21 3.6 2.4 0.1 4.2 10.2 16.7 2.8 2.0 3.0 3.1 4.6 2.9 4.9 1.9 4.0 0.4 3.9 17.9 9.3 2.9 1.9 3.0 5.3 3.2 7.1 3.7 2.8 3.5 0.1 5.4 16.0 4.5 3.4 1.9 2.5 0.5 3.8 113 9.4 3.0 2.2 3.6 0.1 3.5 11.1 5.6 1.5 2.5 3.1 0.2 4.7 10.4 2.4 2.0 3.6 12 3.7 11.1 3.1 1.6 3.1 0.3 3.9 12.4 10.5 4.8 2.0 1.0 7.5 4.4 8.6 7.7 3.7 3.2 3.7 3.2 5.7 9.1 4.9 4.1 2.0 2.6 0.3 4.3 12.3 5.8 2.2 2.6 3.6 0.5 4.4 6.0 9.2 2.8 3.4 2.4 0.2 4.8 8.8 4.4 3.2 3.2 1.6 8.0 4.6 7.2 10.9 3.3 23 7.5 0.3 4.3 16.5 11.3 3.2 1.5 2.4 31.6 3.7 1.4 4.3 6.4 1.4 6.4 12.5 MN MS MO MT NE NV NH NU NM NY NC ND OH OK OR PA RI SC SD TN TX UT VT VA WA WV WI WY 10.2 19.5 16.0 19.1 19.2 17.1 32.3 19.4 21.8 17.5 22.9 15.4 17.5 17.7 17.4 18.3 21.2 22.7 15.1 15.6 19.6 18.0 19.6 20.8 19.9 20.7 16.5 16.6 9.6 38 39 2.1 3.0 1.0 14. 11. 15. 14. 9. 9. 10. 17. 11. 13. 15. 10. 16. 11. 10. 12 14. 11. 12 11. 14. 12. 18. 14. 13. 10. 12. 4.3 6.2 6.4 8.8 7.1 6.1 8.0 5.9 5.6 5.8 6.1 7.4 7.3 6.1 6.1 5.6 7.4 5.3 6.3 3.2 40 0.8 8.9 9.1 9.2 10.0 8.7 8.6 8.7 10.3 8.8 10.9 8.7 10.3 9.7 8.2 9.7 8.7 8.6 6.5 14 42 43 LA 45 A6 16.3 19.0 22.6 13.3 20.6 138 14.3 16.5 17.8 17.8 18.3 11.2 16.1 10.4 1.2 1.3 1.2 2.3 LO 2.9 0.6 2.2 2.1 48 49 50 53 52 53 56 52 50 60 61 62 Rawdata ListVariables + . Gross state product (GSP) of 50 states are measured in 13 different areas of economic activity list below. In order to remove the influence of scale, the contribution of each area is measured as the proportion of the total GSP. The data can be found in file gsp.sav. Columns 2-14 in the data are the shares of GSP of the following areas: agriculture mining construction manufacturing (durable goods) manufacturing (nondurable goods) transportation communications utilities wholesale retail fiduciary, insurance, and real estate services government . . . . Conduct a principal component analysis of the data set. a. Check if the correlation in the data supports PCA. b. Extract the factors using PCA, use a scree plot to help determine the appropriate number of factors. c. Evaluate the goodness of the factor model using the proportion of variance explained and the communalities. d. Comment on the unrotated component loadings. B colt 1 Variable 2 Label 3 4 22.4 1.3 11.8 9 7 9 10 11 AL AK AZ AR CA CO CT DE FL GA HI ID IL IN LA 12.5 12 13 14 15 16 167 10 19 20 21 22 23 24 25 26 cola Coll cos col co Go agriculture mining constructor manufactur manufactur transportat communicaties 1.5 2.0 4.2 10.5 11.0 2.9 3.6 2.9 1.5 4.1 1.1 3.7 12.1 2.0 1.5 11.5 1.7 3.0 2.0 2.7 2.2 5.1 1.0 4.0 128 4.4 2.4 4.2 2.1 0.6 3.3 9.0 5.0 2.6 2.5 18 1.8 5.4 7.7 4.5 3.1 5.7 2.2 0.7 0.0 3.3 11.0 5.7 18 2.3 2.2 10 0.0 3.4 4.5 16.6 1.6 1.3 2.4 18 0.2 4.7 4.6 3.5 3.1 3.0 28 10 0.4 2.9 7.4 10.7 4.0 4.5 2.7 1.2 0.1 4.8 0.0 4.5 3.1 63 0.6 5.9 15.0 5.6 1.6 1.7 14 03 4.2 11.3 7.9 18 23 3.1 1.8 0.5 46 214 10.3 3.5 14 3.1 7.6 0.2 4.1 13.2 10.10 3.3 20 20 4.4 1.4 42 10.4 7.9 3.9 3.6 2.6 2.6 3.0 149 13.2 3.9 1.5 2.9 1.2 140 4.2 15.3 3.0 1.9 3.6 1.3 0.1 4,5 7.9 10.6 2.0 3.1 0.1 5.0 4.1 45 2.1 2.9 2.9 0.6 0.1 3.2 10.5 20 1.9 1.0 0.4 1.8 20.0 7.2 2.4 16 2.7 0.6 4.4 11.0 82 3.7 2.1 1.2 0.9 3.9 13.0 10.5 3.2 2.4 5.1 1.8 0.4 4.6 11.3 10.1 4,0 3.5 28 5.1 4.9 4.8 4.4 1.3 2.1 5.0 9.2 0.2 4.4 7.0 7.1 68 2.1 1.4 0.8 3.7 3.1 1.7 2.9 18 3.0 0.7 0.1 3.5 16.4 5.7 1,5 1.2 4.4 0.6 0.0 3.5 4.3 9,4 32 4,1 2.7 7.1 4.6 14.4 2.1 2.5 1.7 3.5 0.5 0.1 2.9 5.9 5.9 2.1 3.6 2.4 23 0.1 4.2 10.2 16.7 28 2.0 3.0 10.6 1.1 4.9 4.6 4.9 1.9 40 1.1 0.6 3.9 17.9 9.3 1.9 3,0 2.1 5.3 1.2 10.2 7.1 37 2.8 3.0 0.1 5.4 16.0 45 1.4 1.9 2.5 1.0 0.5 3.3 9.4 3.0 2.2 1.6 08 0.1 11.1 5.6 1.5 2.5 1,1 wholesale retall fiduciary servkes Fovernment 6.3 9.9 12.8 16.1 15.5 2.9 6.5 10.7 119 19.6 6.3 10.5 18.9 20.2 13.0 6.1 11.4 14.8 11.8 6.8 8.9 22.7 23.1 11.5 6.3 9.7 17.0 21.6 13.1 6.6 7.4 28.2 21.8 9.0 4.0 6.0 35.4 14.3 9.4 7.3 11.2 218 23.4 12.4 8.8 8.9 16.4 18.0 4.0 11.5 214 22.2 21.3 6.1 9.9 123 163 132 7.7 11 19.2 20.7 10.0 60 9.1 13.1 15.3 9.8 6.8 8.3 14.3 15.3 11.4 7.8 9.6 12.7 14.1 5.8 11.2 15.0 13.6 5.3 7.0 12.1 15.7 10. 6.0 111 18.5 18.7 13.5 8.7 21.4 23.2 17.8 7.1 78 25.8 9.2 7.2 8.9 15.8 18.5 10.5 13 8.7 17.9 10.9 5.6 10.0 11.5 16.0 14.9 7.3 9.1 14,7 19.1 11.2 6.4 13.4 19.2 15.9 7.4 8.3 14.8 17.1 14.1 4.6 9.4 18.4 12.3 9.9 62 9.1 22:2 19.4 9.1 9.1 7.3 21.2 10.8 8.9 18,9 17.5 17.7 6.2 6.9 29.7 111 6.4 8.9 14.6 15.4 11.2 9.1 12.7 17.5 15.1 7.1 9.2 15.3 17.7 10.5 10.0 12.5 17.4 16.2 30 8.2 163 11.9 3.6 19.0 212 10.5 8.7 226 22.7 12.1 SA KY LA ME MD MA MI MN MS MO MT NE NV NH NI NM NY NC ND OH OK OR PA RI 24.4 > 31 33 34 35 36 17 18 30 40 41 6'5 Rawdata List Variables + D c co 10 wholesale retall o 12 fiduciary cots services governme coll 10. 1 Variable 2 Label cala agriculture mining 8.2 83 5.6 7.3 6.4 7.4 4.6 6.2 17.9 11.5 14.7 13.4 14.8 18.4 25 26 27 28 29 30 11 32 33 34 8.7 10.0 9.1 9.9 8.3 9.4 9.1 7.3 8.9 22.2 2.9 12 13 5.1 9.2 08 0.7 0.6 1.9 0.5 2.3 10.6 23.2 13.9 29.7 14.6 12.7 15.3 35 35 E cold cols col col col constructior manufactur manufactur transportati communicattles Ti 1.9 3.7 2.1 11.0 0.6 4.4 3.9 13.0 0.9 10.5 2.4 3.2 5.1 3.5 11.3 4.6 4.0 0.4 10.1 2.8 4.8 4.4 4.9 3.3 2.1 5.4 5.0 4.4 7.0 0.2 7.1 2.1 6.8 1.4 3.7 8.4 3.1 1.7 2.9 1.8 3.0 3.5 0.1 16.4 5.7 1.5 4.4 1.7 0.0 3.5 4.3 9.4 4.1 3.2 2.7 7.1 4.6 14.4 2.1 2.5 1.7 3.5 0.1 2.9 5.9 5.9 21 3.6 2.4 0.1 4.2 10.2 16.7 2.8 2.0 3.0 3.1 4.6 2.9 4.9 1.9 4.0 0.4 3.9 17.9 9.3 2.9 1.9 3.0 5.3 3.2 7.1 3.7 2.8 3.5 0.1 5.4 16.0 4.5 3.4 1.9 2.5 0.5 3.8 113 9.4 3.0 2.2 3.6 0.1 3.5 11.1 5.6 1.5 2.5 3.1 0.2 4.7 10.4 2.4 2.0 3.6 12 3.7 11.1 3.1 1.6 3.1 0.3 3.9 12.4 10.5 4.8 2.0 1.0 7.5 4.4 8.6 7.7 3.7 3.2 3.7 3.2 5.7 9.1 4.9 4.1 2.0 2.6 0.3 4.3 12.3 5.8 2.2 2.6 3.6 0.5 4.4 6.0 9.2 2.8 3.4 2.4 0.2 4.8 8.8 4.4 3.2 3.2 1.6 8.0 4.6 7.2 10.9 3.3 23 7.5 0.3 4.3 16.5 11.3 3.2 1.5 2.4 31.6 3.7 1.4 4.3 6.4 1.4 6.4 12.5 MN MS MO MT NE NV NH NU NM NY NC ND OH OK OR PA RI SC SD TN TX UT VT VA WA WV WI WY 10.2 19.5 16.0 19.1 19.2 17.1 32.3 19.4 21.8 17.5 22.9 15.4 17.5 17.7 17.4 18.3 21.2 22.7 15.1 15.6 19.6 18.0 19.6 20.8 19.9 20.7 16.5 16.6 9.6 38 39 2.1 3.0 1.0 14. 11. 15. 14. 9. 9. 10. 17. 11. 13. 15. 10. 16. 11. 10. 12 14. 11. 12 11. 14. 12. 18. 14. 13. 10. 12. 4.3 6.2 6.4 8.8 7.1 6.1 8.0 5.9 5.6 5.8 6.1 7.4 7.3 6.1 6.1 5.6 7.4 5.3 6.3 3.2 40 0.8 8.9 9.1 9.2 10.0 8.7 8.6 8.7 10.3 8.8 10.9 8.7 10.3 9.7 8.2 9.7 8.7 8.6 6.5 14 42 43 LA 45 A6 16.3 19.0 22.6 13.3 20.6 138 14.3 16.5 17.8 17.8 18.3 11.2 16.1 10.4 1.2 1.3 1.2 2.3 LO 2.9 0.6 2.2 2.1 48 49 50 53 52 53 56 52 50 60 61 62 Rawdata ListVariables +