Question
In: Statistics and Probability
Problem 1: The following data is in the following of Table. Education Expenditure data, Assuming there...
Problem 1: The following data is in the following of Table. Education Expenditure data, Assuming there is unique variance in each region, using two stage approach weighted least square approach to estimate X1, X2 and X3 effect on Y.
（sas programming）
STATE Y X1 X2 X3 Region
ME 189 2828 351 508 1
NH 169 3259 346 564 1
VT 230 3072 348 322 1
MA 168 3835 335 846 1
RI 180 3549 327 871 1
CT 193 4256 341 774 1
NY 261 4151 326 856 1
NJ 214 3954 333 889 1
PA 201 3419 326 715 1
OH 172 3509 354 753 2
IN 194 3412 359 649 2
IL 189 3981 349 830 2
MI 233 3675 369 738 2
WI 209 3363 361 659 2
MN 262 3341 365 664 2
IA 234 3265 344 572 2
MO 177 3257 336 701 2
ND 177 2730 369 443 2
SD 187 2876 369 446 2
NB 148 3239 350 615 2
KS 196 3303 340 661 2
DE 248 3795 376 722 3
MD 247 3742 364 766 3
VA 180 3068 353 631 3
WV 149 2470 329 390 3
NC 155 2664 354 450 3
SC 149 2380 377 476 3
GA 156 2781 371 603 3
FL 191 3191 336 805 3
KY 140 2645 349 523 3
TN 137 2579 343 588 3
AL 112 2337 362 584 3
MS 130 2081 385 445 3
AR 134 2322 352 500 3
LA 162 2634 390 661 3
OK 135 2880 330 680 3
TX 155 3029 369 797 3
MT 238 2942 369 534 4
ID 170 2668 368 541 4
WY 238 3190 366 605 4
CO 192 3340 358 785 4
NM 227 2651 421 698 4
AZ 207 3027 387 796 4
UT 201 2790 412 804 4
NV 225 3957 385 809 4
WA 215 3688 342 726 4
OR 233 3317 333 671 4
CA 273 3968 348 909 4
AK 372 4146 440 484 4
HI 212 3513 383 831 4
Solutions
Expert Solution
The output is:
| Regression Statistics | ||||||||
| Multiple R | 0.826129 | |||||||
| R Square | 0.682488 | |||||||
| Adjusted R Square | 0.661781 | |||||||
| Standard Error | 26.97031 | |||||||
| Observations | 50 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 3 | 71922.59 | 23974.2 | 32.95886 | 1.59E-11 | |||
| Residual | 46 | 33460.29 | 727.3976 | |||||
| Total | 49 | 105382.9 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | -289.179 | 66.16956 | -4.37028 | 7.01E-05 | -422.372 | -155.987 | -422.372 | -155.987 |
| X1 | 0.080886 | 0.009474 | 8.537784 | 4.83E-11 | 0.061816 | 0.099956 | 0.061816 | 0.099956 |
| X2 | 0.818411 | 0.161628 | 5.063534 | 7.1E-06 | 0.49307 | 1.143752 | 0.49307 | 1.143752 |
| X3 | -0.10377 | 0.035062 | -2.9595 | 0.004856 | -0.17434 | -0.03319 | -0.17434 | -0.03319 |
The least-square equation to estimate X1, X2 and X3 effect on Y using two-stage approach will be:
Y = -289.179 + 0.080886*X1 + 0.818411*X2 -0.10377*X3
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$)
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440
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6
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8
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10
11
12
13
14
15
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