Question: The following three scenarios are each based on the IQ scores and the SAT Math scores for 26 12^th-graders. For each scenario I have regressed SATM scores on IQ and have provided the relevant scatterplot, the studentized deleted residuals, the leverages and the Cook’s distances. In each of the three scenarios, there is one observation that stands apart from the others in some way.

For each of the three scenarios:

(a) Identify (in terms of IQ and SATM scores) from the scatterplot, the way in which the observation differs from the others.

(b Indicate which 12^th-grader you identified in part (a) and how the values of these three diagnostic measures for the observations you identified in part (a) correspond to the descriptions you gave there.

(c) Predict how the slope of the least-squares regression line would change (increase in value, stay roughly the same, or decrease in value) if the observation you identified in part (a) was not included in the data set

Scenario 1

12G IQ SATM SDR Lev COOK

1 107 518 0.18085 0.040589 0.00072

2 107 538 0.70446 0.040589 0.01072

3 94 494 0.29742 0.050173 0.00243

4 107 506 -0.12908 0.040589 0.00037

5 106 504 -0.12416 0.039634 0.00033

6 104 550 1.21185 0.038572 0.02890

7 120 599 1.66020 0.078645 0.10961

8 92 503 0.65173 0.055876 0.01288

9 87 432 -0.94432 0.075067 0.03635

10 127 581 0.71474 0.118871 0.03518

11 110 530 0.32255 0.045142 0.00255

12 78 417 -0.83953 0.127371 0.05208

13 97 482 -0.18425 0.043733 0.00081

14 115 538 0.24784 0.058370 0.00198

15 98 494 0.06953 0.042150 0.00011

16 93 437 -1.15919 0.052884 0.03698

17 75 382 -1.71832 0.149880 0.24070

18 155 500 -6.43111 0.417904 5.53636

19 105 480 -0.69379 0.038962 0.00997

20 108 544 0.80709 0.041825 0.01443

21 93 488 0.19840 0.052884 0.00114

22 95 495 0.26610 0.047745 0.00185

23 129 588 0.79458 0.132901 0.04914

24 98 520 0.75022 0.042150 0.01261

25 86 422 -1.16795 0.079751 0.05823

26 95 523 1.01304 0.047745 0.02570

Scenario 2

12G IQ SATM SDR Lev COOK

1 95 495 0.62038 0.047745 0.009902

2 75 382 -1.29107 0.149880 0.142965

3 107 506 -0.77280 0.040589 0.012849

4 110 530 -0.19177 0.045142 0.000906

5 95 523 1.97531 0.047745 0.087265

6 104 550 1.69014 0.038572 0.053188

7 97 482 -0.25639 0.043733 0.001564

8 107 518 -0.24614 0.040589 0.001334

9 155 690 -0.30010 0.417904 0.033603

10 87 432 -0.90023 0.075067 0.033148

11 108 544 0.72925 0.041825 0.011838

12 92 503 1.50006 0.055876 0.063290

13 93 488 0.62897 0.052884 0.011330

14 86 422 -1.20606 0.079751 0.061857

15 115 538 -0.62835 0.058370 0.012554

16 127 581 -0.64659 0.118871 0.028902

17 105 480 -1.66604 0.038962 0.052389

18 106 504 -0.70205 0.039634 0.010390

19 107 538 0.62124 0.040589 0.008378

20 129 588 -0.65910 0.132901 0.034095

21 98 520 1.27129 0.042150 0.034670

22 93 437 -1.68347 0.052884 0.073506

23 98 494 0.10749 0.042150 0.000265

24 78 417 -0.13394 0.127371 0.001365

25 94 494 0.73619 0.050173 0.014593

26 120 599 1.31271 0.078645 0.071394

Scenario 3

12G IQ SATM SDR Lev COOK

1 104 550 0.62918 0.040764 0.008629

2 127 581 -0.42118 0.196823 0.022507

3 115 538 -0.43888 0.084841 0.009239

4 107 518 -0.27316 0.047229 0.001924

5 105 480 -0.95170 0.042456 0.020159

6 87 432 -0.66839 0.082847 0.020653

7 95 523 0.71272 0.046374 0.012610

8 129 588 -0.42391 0.221969 0.026541

9 95 495 0.10961 0.046374 0.000305

10 108 544 0.20829 0.050310 0.001197

11 75 382 -0.93154 0.193119 0.104421

12 110 530 -0.23696 0.057861 0.001795

13 98 494 -0.12913 0.040337 0.000365

14 78 417 -0.33602 0.159300 0.011108

15 106 504 -0.49992 0.044611 0.006023

16 107 538 0.15283 0.047229 0.000603

17 96 690 8.50980 0.043899 0.418161

18 93 437 -1.00303 0.052714 0.027985

19 120 599 0.53091 0.123397 0.020451

20 94 494 0.16127 0.049313 0.000703

21 93 488 0.10633 0.052714 0.000328

22 107 506 -0.53123 0.047229 0.007210

23 98 520 0.42368 0.040337 0.003906

24 97 482 -0.31198 0.041886 0.002211

25 92 503 0.50294 0.056579 0.007828

26 86 422 -0.81942 0.089489 0.033454