[Solved] 1. Fit a model with all the independent v

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Sep 14, 2024

1. Fit a model with all the independent variables other than Density. (a) Determine how many different groups of variables are involved in multicollinearity. Only

1. Fit a model with all the independent variables other than Density. (a) Determine how many different groups of variables are involved in multicollinearity. Only identify the groups with condition indices bigger than or equal to 100. Just state the number of multicollinear sets and the MODEL Statement you used to obtain these collinearity diagnostics. You need not copy and paste the whole computer program or the output. Just provide the Model Statement and the number of multicollinear sets. (b) For each of the multicollinear sets, identify the variables belonging to that set. Please use the table below to present your answer and list the sets in increasing order of the condition index. Leave blank any rows in the table below that are not needed to list all multicollinear sets with condition indices 2 100. The REG Procedure Model: MODEL 1 Dependent Variable: percentfat Collinearity Diagnostics Proportion of Variation Condition Number Eigenvalue Index Intercept age weight height neck chest abdomen hip 1 13.88925 1.00000 0.00000126 0.00015659 0.00000100 0.00000834 0.00000486 0.00000378 0.0000058 0.00000178 2 0.07317 13.77789 3.6866345-7 0.39879 0.00033750 0.00007353 0.00001915 0.00001025 0.00000475 0.00003852 3 0.02065 25.93541 0.00190 0.01261 0.01525 0.01186 0.00015635 0.00065454 0.00793 0.00003586 0.00382 60.30830 0.00013165 0.00053597 0.00313 0.01070 0.0004 0.00010548 0.00491 0.00185 5 0.00311 66.84493 0.00859 0.05580 0.02626 0.00001740 0.00067 121 0.01068 0.06135 0.00636 6 0.00260 73.07606 0.00108 0.00497 0.03940 0.28380 0.00054 0.00124 0.00054977 0.00241 7 0.00204 82.50599 0.00000298 0.07907 0.00197 0.05611 0.00365 0.04035 0.03778 0.00178 8 0.00158 93.72593 0.00732 0.10132 0.01633 0.00187 0.01377 0.06216 0.03803 0.00278 9 0.00121 107.35581 0.00000654 0.01050 0.00282 0.13850 0.40644 0.00586 0.05758 0.00000130 10 0.00076993 134.31206 0.00287 0.10163 0.00224 0.15721 0.07538 0.14066 0.00269 0.00038568 11 0.00062913 148.58247 0.00001679 0.04008 0.00009666 0.00067447 0.23788 0.13189 0.13583 0.02766 12 0.00057795 15502202 0.00385 0.17166 0.03334 0.00382 0.13094 0.30685 0.50665 001962 13 0.00046753 172.35980 0.06153 0.02094 0.01994 0.05281 0.02335 0.08982 0.05964 0.35273 14 0.00013859316.57414 0.93769 0.00193 0.80889 0.09 496 0.20973 0.00706 0.58435 Collinearity Diagnostics Proportion of Variation Number thigh knee anke biceps forearm 1 0.00000513 0.00000035 0.00001443 0.00001225 0.00001161 0.00000399 2 0.00031627 0.00004319 0.00028192 0.00035553 0.000 19964 0.00000112 3 0.00035821 0.00021358 0.00440 0.00060587 0.00281 0.00119 4 0.00014001 0.00649 0.17513 0.22335 0.16258 0.00000114 5 0.01748 0.00015937 0.31830 0.04652 0.01778 0.00324 6 0.05709 0.00273 0.16009 0.03426 0.00004492 0.00249 7 0.05465 0.01542 0.06139 0.25527 0.33592 0.00091551 8 0.07363 0.08274 0.09273 0.27524 0.30024 0.00003212 9 0.00991 0.0099 0.02079 0.07060 0.091025 0.11411 10 0.19368 035367 0.1205 0.0103 0.06263 011014 11 0.00747 0.14217 0.01907 0.00832 0.00085338 0.59119 12 0.18699 0.32533 0.00096381 0.05297 0.00010786 0.00221 13 0.39626 0.02269 0.0001 1955 0.01061 0.01535 0.16163 14 0.00202 0.03846 0.02247 0.00767 0.00321 0.01284 1. Fit a model with all the independent variables other than Density. (a) Determine how many different groups of variables are involved in multicollinearity. Only identify the groups with condition indices bigger than or equal to 100. Just state the number of multicollinear sets and the MODEL Statement you used to obtain these collinearity diagnostics. You need not copy and paste the whole computer program or the output. Just provide the Model Statement and the number of multicollinear sets. (b) For each of the multicollinear sets, identify the variables belonging to that set. Please use the table below to present your answer and list the sets in increasing order of the condition index. Leave blank any rows in the table below that are not needed to list all multicollinear sets with condition indices 2 100. The REG Procedure Model: MODEL 1 Dependent Variable: percentfat Collinearity Diagnostics Proportion of Variation Condition Number Eigenvalue Index Intercept age weight height neck chest abdomen hip 1 13.88925 1.00000 0.00000126 0.00015659 0.00000100 0.00000834 0.00000486 0.00000378 0.0000058 0.00000178 2 0.07317 13.77789 3.6866345-7 0.39879 0.00033750 0.00007353 0.00001915 0.00001025 0.00000475 0.00003852 3 0.02065 25.93541 0.00190 0.01261 0.01525 0.01186 0.00015635 0.00065454 0.00793 0.00003586 0.00382 60.30830 0.00013165 0.00053597 0.00313 0.01070 0.0004 0.00010548 0.00491 0.00185 5 0.00311 66.84493 0.00859 0.05580 0.02626 0.00001740 0.00067 121 0.01068 0.06135 0.00636 6 0.00260 73.07606 0.00108 0.00497 0.03940 0.28380 0.00054 0.00124 0.00054977 0.00241 7 0.00204 82.50599 0.00000298 0.07907 0.00197 0.05611 0.00365 0.04035 0.03778 0.00178 8 0.00158 93.72593 0.00732 0.10132 0.01633 0.00187 0.01377 0.06216 0.03803 0.00278 9 0.00121 107.35581 0.00000654 0.01050 0.00282 0.13850 0.40644 0.00586 0.05758 0.00000130 10 0.00076993 134.31206 0.00287 0.10163 0.00224 0.15721 0.07538 0.14066 0.00269 0.00038568 11 0.00062913 148.58247 0.00001679 0.04008 0.00009666 0.00067447 0.23788 0.13189 0.13583 0.02766 12 0.00057795 15502202 0.00385 0.17166 0.03334 0.00382 0.13094 0.30685 0.50665 001962 13 0.00046753 172.35980 0.06153 0.02094 0.01994 0.05281 0.02335 0.08982 0.05964 0.35273 14 0.00013859316.57414 0.93769 0.00193 0.80889 0.09 496 0.20973 0.00706 0.58435 Collinearity Diagnostics Proportion of Variation Number thigh knee anke biceps forearm 1 0.00000513 0.00000035 0.00001443 0.00001225 0.00001161 0.00000399 2 0.00031627 0.00004319 0.00028192 0.00035553 0.000 19964 0.00000112 3 0.00035821 0.00021358 0.00440 0.00060587 0.00281 0.00119 4 0.00014001 0.00649 0.17513 0.22335 0.16258 0.00000114 5 0.01748 0.00015937 0.31830 0.04652 0.01778 0.00324 6 0.05709 0.00273 0.16009 0.03426 0.00004492 0.00249 7 0.05465 0.01542 0.06139 0.25527 0.33592 0.00091551 8 0.07363 0.08274 0.09273 0.27524 0.30024 0.00003212 9 0.00991 0.0099 0.02079 0.07060 0.091025 0.11411 10 0.19368 035367 0.1205 0.0103 0.06263 011014 11 0.00747 0.14217 0.01907 0.00832 0.00085338 0.59119 12 0.18699 0.32533 0.00096381 0.05297 0.00010786 0.00221 13 0.39626 0.02269 0.0001 1955 0.01061 0.01535 0.16163 14 0.00202 0.03846 0.02247 0.00767 0.00321 0.01284