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. e. Perform Varimax factor rotation, comment on the loading structure. A col6 1 5.9 15.3 coli AL AK AZ AR CA co DE 0 FL 1 GA 2 HI 13 ID 14 IL 15 IN 15 IA 17 KS 18 KY 19 LA 20 ME 21 MD 22 MA 23 MI 24 MN 25 MS 26 MO 27 MT 28 NE 29 90 NH 31 NU 32 NM 33 NY 34 NC 35 ND 36 OH 37 OK 38 OR 39 PA 40 RI 41 SC 42 5D 43 TN 44 TX 45 UT 46 VT 47 VA 48 WA 49 WV 50 W 51 WY B D E Icol2 cols col4 cols 20 15 42 105 15 224 41 11 17 13 58 115 5.1 1.0 40 128 21 06 3.3 9.0 1.8 17 5.4 7.7 0.7 0.0 3.3 110 10 0.0 34 45 18 0.2 47 46 18 04 39 7.4 1.2 0.1 4.8 08 6.3 0.6 15.0 14 0.3 4.2 113 1.8 0.5 46 214 7.6 0.2 13.2 4.4 14 4.2 10.4 2.6 26 3.9 149 12 14.8 4.2 3.7 1.8 45 79 0.9 0.1 5.0 0.6 01 32 105 1.0 0.4 3.8 20.0 29 0.6 4.4 110 3.2 0.9 3.9 13.0 18 0.4 46 113 5.1 4.8 92 0.2 4.4 08 3.7 8.4 3.1 07 0.1 3.5 164 0.6 0.0 3.5 19 7.1 4.6 05 0.1 2.9 5.9 2.3 0.1 42 102 10.6 3.1 46 1.1 0.4 3.9 17.9 21 53 3.2 10.2 3.0 01 5.4 16.0 1.0 0.5 3.8 0.8 0.1 3.5 14 02 4.7 10.4 99 12 3.7 111 1.2 03 3.9 124 13 75 86 1.2 5.7 91 23 4,3 123 10 05 44 60 2.9 02 8.5 0.6 80 4.6 72 22 0.3 43 16.5 2.1 316 3.7 14 H G K M N col7 col8 co19 col 10 col11 col12 col13 col14 29 118 29 3.6 63 99 128 16.1 15.5 3.7 121 20 15 29 6.5 10.7 119 19,6 30 28 22 2.7 6.3 105 189 20.2 13.0 118 24 42 61 102 11.4 14.8 118 5.0 26 25 18 68 8.9 22.7 23.1 11.5 45 5.7 22 6.3 9.7 170 21.6 13.1 5.7 18 23 22 6.6 7.4 28.2. 21.8 9.0 16.6 13 24 40 6.0 35.4 14.3 9.4 3.5 30 3.0 2.8 7.3 112 21.8 23.4 124 107 45 2.7 8.8 8.9 164 18.0 12.5 23 45 31 2.7 40 11.5 21.4 222 21.3 5.6 16 3.7 6.1 99 12.3 16.3 13.2 7.9 3.8 23 3.1 7.7 8.1 19.2 20.7 10.0 10.3 35 14 3.1 6.0 9.1 13.1 15,3 9.8 10.8 3.3 20 2.8 6.8 8,3 14.3 11.4 7.9 3.9 36 34 7.8 9.6 12.7 16.7 14.1 13.2 39 15 2.9 5.8 8.9 11.2 15.0 13.6 153 3.3 19 3.6 53 7.8 121 15.7 10.9 10.6 23 20 3.1 6.0 111 18.5 18.7 135 45 21 29 29 6.3 8.7 21.4 23.2 17.8 49 2.0 19 2.5 7.1 7.8 24.4 25.8 9.2 7.2 24 16 2.7 7.2 89 15.8 18.5 10.5 82 3.7 19 21 83 8.7 179 19.5 10.9 10.5 24 5.1 5.6 10.0 115 16.0 14.9 10.1 4.0 35 28 73 9.1 14.7 19.1 11.2 33 5.4 21 5.0 6.4 99 13.4 19.2 15.9 7.1 68 14 7.4 8.3 14.8 171 14.1 17 18 30 9.4 18.4 32.3 9.9 5.7 15 17 6.2 9.1 22.2 19.4 9.1 32 27 9.1 7.3 232 218 10,8 21 25 1.7 3.5 43 8.9 13.9 17.5 17.7 5.9 21 36 2.4 6.2 6.9 29.7 22.9 111 16.7 2B 20 3.0 8.9 14.6 15.4 13.2 49 19 40 8.8 9.1 12.7 17.5 15.1 29 19 3.0 9.2 15.3 17.7 10.5 3.7 28 3.5 6.1 10.0 12.5 17.4 16.2 45 3.4 19 25 80 8.7 16.3 18.3 119 9.4 3.0 22 3.6 59 8.6 190 21.2 10.5 5.6 15 25 3.1 5.6 8.7 22.6 22.7 12.1 16.1 20 3.6 5.8 10.3 13.3 15.1 14.8 3.4 3.1 16 3.1 6.1 8.8 20.6 15.6 11.7 105 43 20 10 7.4 10.9 13.8 19.6 12.1 77 3.7 3.7 73 8.7 143 18.0 11.7 41 20 2.6 61 10.3 165 19.6 14.7 5.8 22 3,6 61 9.7 17.8 20.8 121 28 24 56 82 17.8 19.9 44 3.2 16 74 9.7 18 3 20.7 14.9 10.9 23 7.5 5.3 8.7 112 16.5 13.8 113 32 15 2.4 6.3 8.6 16.1 16.6 10.9 6.4 3.2 65 10.4 9.6 12.9 32 49 7.0 29 94 MONS 104 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. e. Perform Varimax factor rotation, comment on the loading structure. A col6 1 5.9 15.3 coli AL AK AZ AR CA co DE 0 FL 1 GA 2 HI 13 ID 14 IL 15 IN 15 IA 17 KS 18 KY 19 LA 20 ME 21 MD 22 MA 23 MI 24 MN 25 MS 26 MO 27 MT 28 NE 29 90 NH 31 NU 32 NM 33 NY 34 NC 35 ND 36 OH 37 OK 38 OR 39 PA 40 RI 41 SC 42 5D 43 TN 44 TX 45 UT 46 VT 47 VA 48 WA 49 WV 50 W 51 WY B D E Icol2 cols col4 cols 20 15 42 105 15 224 41 11 17 13 58 115 5.1 1.0 40 128 21 06 3.3 9.0 1.8 17 5.4 7.7 0.7 0.0 3.3 110 10 0.0 34 45 18 0.2 47 46 18 04 39 7.4 1.2 0.1 4.8 08 6.3 0.6 15.0 14 0.3 4.2 113 1.8 0.5 46 214 7.6 0.2 13.2 4.4 14 4.2 10.4 2.6 26 3.9 149 12 14.8 4.2 3.7 1.8 45 79 0.9 0.1 5.0 0.6 01 32 105 1.0 0.4 3.8 20.0 29 0.6 4.4 110 3.2 0.9 3.9 13.0 18 0.4 46 113 5.1 4.8 92 0.2 4.4 08 3.7 8.4 3.1 07 0.1 3.5 164 0.6 0.0 3.5 19 7.1 4.6 05 0.1 2.9 5.9 2.3 0.1 42 102 10.6 3.1 46 1.1 0.4 3.9 17.9 21 53 3.2 10.2 3.0 01 5.4 16.0 1.0 0.5 3.8 0.8 0.1 3.5 14 02 4.7 10.4 99 12 3.7 111 1.2 03 3.9 124 13 75 86 1.2 5.7 91 23 4,3 123 10 05 44 60 2.9 02 8.5 0.6 80 4.6 72 22 0.3 43 16.5 2.1 316 3.7 14 H G K M N col7 col8 co19 col 10 col11 col12 col13 col14 29 118 29 3.6 63 99 128 16.1 15.5 3.7 121 20 15 29 6.5 10.7 119 19,6 30 28 22 2.7 6.3 105 189 20.2 13.0 118 24 42 61 102 11.4 14.8 118 5.0 26 25 18 68 8.9 22.7 23.1 11.5 45 5.7 22 6.3 9.7 170 21.6 13.1 5.7 18 23 22 6.6 7.4 28.2. 21.8 9.0 16.6 13 24 40 6.0 35.4 14.3 9.4 3.5 30 3.0 2.8 7.3 112 21.8 23.4 124 107 45 2.7 8.8 8.9 164 18.0 12.5 23 45 31 2.7 40 11.5 21.4 222 21.3 5.6 16 3.7 6.1 99 12.3 16.3 13.2 7.9 3.8 23 3.1 7.7 8.1 19.2 20.7 10.0 10.3 35 14 3.1 6.0 9.1 13.1 15,3 9.8 10.8 3.3 20 2.8 6.8 8,3 14.3 11.4 7.9 3.9 36 34 7.8 9.6 12.7 16.7 14.1 13.2 39 15 2.9 5.8 8.9 11.2 15.0 13.6 153 3.3 19 3.6 53 7.8 121 15.7 10.9 10.6 23 20 3.1 6.0 111 18.5 18.7 135 45 21 29 29 6.3 8.7 21.4 23.2 17.8 49 2.0 19 2.5 7.1 7.8 24.4 25.8 9.2 7.2 24 16 2.7 7.2 89 15.8 18.5 10.5 82 3.7 19 21 83 8.7 179 19.5 10.9 10.5 24 5.1 5.6 10.0 115 16.0 14.9 10.1 4.0 35 28 73 9.1 14.7 19.1 11.2 33 5.4 21 5.0 6.4 99 13.4 19.2 15.9 7.1 68 14 7.4 8.3 14.8 171 14.1 17 18 30 9.4 18.4 32.3 9.9 5.7 15 17 6.2 9.1 22.2 19.4 9.1 32 27 9.1 7.3 232 218 10,8 21 25 1.7 3.5 43 8.9 13.9 17.5 17.7 5.9 21 36 2.4 6.2 6.9 29.7 22.9 111 16.7 2B 20 3.0 8.9 14.6 15.4 13.2 49 19 40 8.8 9.1 12.7 17.5 15.1 29 19 3.0 9.2 15.3 17.7 10.5 3.7 28 3.5 6.1 10.0 12.5 17.4 16.2 45 3.4 19 25 80 8.7 16.3 18.3 119 9.4 3.0 22 3.6 59 8.6 190 21.2 10.5 5.6 15 25 3.1 5.6 8.7 22.6 22.7 12.1 16.1 20 3.6 5.8 10.3 13.3 15.1 14.8 3.4 3.1 16 3.1 6.1 8.8 20.6 15.6 11.7 105 43 20 10 7.4 10.9 13.8 19.6 12.1 77 3.7 3.7 73 8.7 143 18.0 11.7 41 20 2.6 61 10.3 165 19.6 14.7 5.8 22 3,6 61 9.7 17.8 20.8 121 28 24 56 82 17.8 19.9 44 3.2 16 74 9.7 18 3 20.7 14.9 10.9 23 7.5 5.3 8.7 112 16.5 13.8 113 32 15 2.4 6.3 8.6 16.1 16.6 10.9 6.4 3.2 65 10.4 9.6 12.9 32 49 7.0 29 94 MONS 104