Now restrict the data set in Exercise 11.15 to eight, then six, then five cases, and record the changing values of R. Remember that these are only random data.

Exercise 11.15

Use the table of random numbers (Table E.9 in the Appendix) to generate data for 10 cases on six variables, and label the first variable Y and the following variables X₁, X₂, X₃, X₄, and X₅.

Now use any regression program to predict Y from all five predictors using the complete data set with 10 cases. Are you surprised at the magnitude of R?

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Table E.9 Table of Uniform Random Numbers 68204 38787 73304 44886 92836 43877 61049 49249 66105 61010 78345 75444 91680 33003 24128 97817 77562 62045 04604 93468 78459 27541 19672 14220 25102 42021 19252 36021 25507 64060 72923 58848 10374 63102 41534 92884 28129 43470 94097 16753 56425 75299 93688 75569 52067 09406 06584 46324 13981 06449 42604 13372 69040 95955 86423 81835 64226 20398 65772 91052 73496 14451 95967 13249 58525 81893 32894 68627 75644 45848 61511 90232 75454 17352 56548 39618 86705 50783 48388 82047 14660 06260 46176 99237 69874 84180 32005 66130 18055 99748 38507 92795 80672 00102 22980 69115 95653 05231 94996 03917 26795 59832 19014 96206 45413 76624 71219 65855 17927 32368 08177 31236 45401 26731 92256 99530 43998 26811 88937 37187 39762 29942 40091 65731 95955 23368 18480 28160 81908 30456 22462 15677 55642 67383 86884 37589 91842. 76351 90585 45588 42858 37806 67969 50621 79903 34187 26952 75820 96335 90281 04269 85202 94965 46155 30200 75000 28570 47516 06744 72193 01258 85047 60916 73212 15853 28398 04721 69363 47071 65568 88519 34419 82840 88235 61966 86517 23966 45764 42177 17269 08692 26667 12941 14813 30815 26633 68184 80721 80505 92851 44185 90848 18341 77915 00177 64014 35490 02937 97909 07280 72167 10002 27374 92880 60055 94168 30742 28437 22027 07739 30905 33151 73567 82960 50104 67005 48165 28174 17909 11230 00929 54604 32435 54120 85199 99891 30913 06315 30201 72073 39589 62868 66339 15850 98022 13010 67970 99203 12536 88149 44387 20250 50798 91292 54688 47029 38970 77880 77295 11887 17628 93802 89081 34643 12988 12971 87742 57720 24438 64088 49496 32527 74239 20056 46668 94561 70111 92537 83562 11306 01870 21584 48574 09871 74453 24812 45770 95667 52377 84011 87542 96564 64256 64653 90025 61613 94168 83254 01568 29682 67489 62984 51901 30716 24513 46678 67991 40360 19206 40321 16004 64481 16130 03904 15811 19369 09392 39926 79590 23991 82492 13032 67337 54322 06058 77323 20500 52466 33008 84211 26357 79006 41178 35169 47590 01007 65376 18189 84040 39476 25383 45398 64917 29321 65783 71403 32894 32627 39067 47985 51485 27415 09530 05358 58722 31912 73356 65884 12583 36242 29646 65612 06843 72233 73352 66600 23237 71759 76881 19652 40355 85067 40788 40148 46099 48056 27858 58365 30202 24963 49571 82377 08687 73448 95484 15155 41780 71951 87273 44050 71961 48464 84084 65225 62846 11634 04853 31643 44756 12493 09024 74204 69949 67842 36141 08477