Question

# Use the Manufacturing database from “Excel Databases.xls” on Blackboard. Use Excel to develop a multiple regression...

Use the Manufacturing database from “Excel Databases.xls” on Blackboard. Use Excel to develop a multiple regression model to predict Cost of Materials by Number of Employees, New Capital Expenditures, Value Added by Manufacture, and End-of-Year Inventories.

Locate the observed value that is in Industrial Group 12 and has 7 employees. Based on the model and the multiple regression output, what is the corresponding residual of this observation? Write your answer as a number, round to 2 decimal places.

 SIC Code No. Emp. No. Prod. Wkrs. Value Added by Mfg. Cost of Materials Value of Indus. Shipmnts New Cap. Exp. End Yr. Inven. Indus. Grp. 201 433 370 23518 78713 4 1833 3630 1 202 131 83 15724 42774 4 1056 3157 1 203 204 169 24506 27222 4 1405 8732 1 204 100 70 21667 37040 4 1912 3407 1 205 220 137 20712 12030 4 1006 1155 1 206 89 69 12640 13674 3 873 3613 1 207 26 18 4258 19130 3 487 1946 1 208 143 72 35210 33521 4 2011 7199 1 209 171 126 20548 19612 4 1135 3135 1 211 21 15 23442 5557 3 605 5506 2 212 3 2 287 163 1 2 42 2 213 2 2 1508 314 1 15 155 2 214 6 4 624 2622 1 27 554 2 221 52 47 2471 4219 2 292 929 3 222 74 63 4307 5357 2 454 1427 3 223 13 12 673 1061 1 20 325 3 224 17 13 817 707 1 84 267 3 225 169 147 8986 10421 3 534 2083 3 226 51 41 3145 4140 2 220 697 3 227 55 44 4076 7125 2 176 1446 3 228 84 76 3806 8994 2 423 1014 3 229 61 47 4276 5504 2 464 1291 3 231 27 22 1239 716 1 22 356 4 232 200 178 9423 8926 3 200 2314 4 233 294 250 11045 11121 3 189 2727 4 234 38 32 1916 2283 1 29 682 4 235 17 14 599 364 1 21 197 4 236 34 28 2063 1813 1 20 450 4 237 1 1 34 71 1 2 17 4 238 31 25 1445 1321 1 16 526 4 239 224 179 10603 12376 3 465 2747 4 241 83 68 5775 9661 3 539 578 5 242 172 147 10404 19285 4 1071 3979 5 243 257 209 13274 18632 4 711 3329 5 244 51 43 1909 2170 1 88 355 5 245 82 68 4606 7290 2 182 580 5 249 94 78 5518 8135 2 715 1604 5 251 273 233 12464 12980 3 481 3535 6 252 70 53 5447 4011 2 358 829 6 253 37 29 2290 5101 2 128 447 6 254 81 61 4182 3755 2 177 956 6 259 54 39 2818 2694 2 109 718 6 261 15 11 2201 3279 2 698 725 7 262 116 90 18848 20596 4 3143 4257 7 263 55 42 9655 10604 3 2360 1502 7 265 212 163 15668 24634 4 1352 3976 7 267 232 182 25918 28963 4 1750 5427 7 271 403 136 30692 8483 4 1277 894 8 272 121 16 17982 6940 3 311 1216 8 273 136 57 17857 8863 3 618 3736 8 274 69 25 9699 2823 2 144 874 8 275 604 437 38407 29572 4 2959 4300 8 276 41 28 3878 3811 2 198 688 8 277 21 12 3989 1047 2 66 577 8 278 65 50 4388 2055 2 130 504 8 279 55 39 4055 1098 2 210 236 8 281 80 45 16567 11298 3 2002 2644 9 282 115 79 25025 34596 4 3731 6192 9 283 213 106 59813 27187 4 4301 11533 9 284 126 75 31801 19932 4 1304 4535 9 285 51 28 8497 9849 3 404 2178 9 286 126 75 28886 46935 4 6269 8577 9 287 37 24 12277 11130 3 1025 2354 9 289 76 45 11547 13085 3 1006 2749 9 291 67 43 26006 132880 4 5197 10718 10 295 25 18 3464 6182 2 251 658 10 299 14 8 2187 4446 2 124 670 10 301 65 54 7079 7091 3 579 1067 11 302 8 7 442 496 1 9 175 11 305 61 46 4528 3805 2 341 1057 11 306 122 95 7275 7195 3 435 1411 11 308 763 598 55621 57264 4 5658 11874 11 311 15 12 1313 1865 1 52 404 12 313 3 2 162 163 1 1 35 12 314 37 31 1907 1682 1 35 716 12 315 2 2 53 85 1 12 62 12 316 6 4 747 395 1 18 199 12 317 8 7 328 255 1 6 75 12 319 7 6 233 177 1 4 40 12 321 12 9 1717 943 1 248 282 13 322 60 51 6532 3527 2 853 1505 13 323 64 50 4850 4254 2 493 883 13 324 17 13 3509 2282 2 495 828 13 325 31 25 2176 1387 1 201 700 13 326 45 36 2696 1183 1 154 600 13 327 205 152 15739 17010 4 1200 1966 13 328 17 13 999 565 1 50 263 13 329 72 53 7838 5432 2 464 1652 13 331 221 174 29180 45696 4 3433 12198 14 332 128 106 9061 6913 3 651 1543 14 333 35 26 4200 11184 3 635 1834 14 334 15 11 1410 5735 2 90 694 14 335 162 123 16670 31892 4 1761 6377 14 336 94 79 5856 4696 2 459 938 14 339 32 23 3164 2790 2 271 800 14 341 33 27 3999 9364 2 526 1453 15 342 140 107 11750 8720 3 620 3124 15 343 45 32 4412 3527 2 178 1121 15 344 432 315 27974 31527 4 1139 7204 15 345 104 81 6936 4909 2 421 1768 15 346 259 211 19880 21531 4 1908 3997 15 347 129 99 7793 6232 3 724 1181 15 348 40 24 3528 1689 2 85 1077 15 349 300 219 21718 19273 4 1273 6460 15 351 79 55 10513 12954 3 678 3679 16 352 94 70 9545 11858 3 414 3339 16 353 205 133 18178 23474 4 889 7344 16 354 295 211 22673 14343 4 1485 6730 16 355 192 110 19221 16515 4 1334 6823 16 356 265 172 23110 18543 4 1260 7898 16 357 259 96 41135 60857 4 2917 10277 16 358 201 147 17521 21819 4 907 4857 16 359 392 293 25322 13897 4 1568 4964 16 361 74 51 6700 5523 2 308 1495 17 362 171 120 14278 12657 3 784 3887 17 363 108 87 9466 12578 3 721 2299 17 364 157 117 13428 11065 3 671 3076 17 365 49 37 3459 7621 2 485 1070 17 366 258 120 38705 29591 4 2268 9467 17 367 588 368 84059 44486 4 14345 13145 17 369 151 106 13920 13398 3 1286 3514 17 371 772 634 105899 223639 4 10264 15852 18 372 377 190 45220 42367 4 2023 36814 18 373 141 108 7903 7760 3 351 2165 18 374 31 23 2590 4363 2 97 1233 18 375 18 14 1435 1674 1 131 412 18 376 81 29 9986 8120 3 490 4770 18 379 47 35 3564 5476 2 142 1102 18 381 186 68 21071 8760 4 1223 6183 19 382 272 141 29028 18028 4 1466 7681 19 384 268 157 31051 16787 4 1648 7761 19 385 27 17 2390 1020 1 197 426 19 386 61 36 14032 8114 3 724 2290 19 387 6 4 415 382 1 17 177 19 391 43 30 2761 3646 2 119 1451 20 393 13 10 685 506 1 15 328 20 394 103 76 8327 6604 3 396 2608 20 395 35 26 2643 1789 1 197 799 20 396 24 19 1406 997 1 51 415 20 399 179 123 11199 8530 3 595 2861 20

Solution:

We can use the excel regression data analysis tool to find the equation of the multiple regression line. The excel output is given below:

 SUMMARY OUTPUT Regression Statistics Multiple R 0.780602653 R Square 0.609340503 Adjusted R Square 0.597765406 Standard Error 15582.72237 Observations 140 ANOVA df SS MS F Significance F Regression 4 51130741892 12782685473 52.64237039 0.0000 Residual 135 32780866936 242821236.6 Total 139 83911608829 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -587.8061303 1806.693072 -0.325349191 0.745420499 -4160.889015 2985.276754 No. Emp. 1.696715833 18.21382118 0.093155402 0.925918211 -34.32461713 37.7180488 New Cap. Exp. 3.655194027 1.57594828 2.319361666 0.02187642 0.53845333 6.771934725 Value Added by Mfg. 0.769808992 0.2824569 2.725403391 0.007273847 0.211196171 1.328421814 End Yr. Inven. 0.402806454 0.493417774 0.816359839 0.415732535 -0.573022052 1.378634961

Therefore, the regression equation is:

The predicted value is:

Therefore, the residual is:

Residual = Actual value - Predicted value

=177 - (-365.83059)

=542.83

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