Multiple regression with SAS

SAS Program:

data;

input Obs fat_index Age Weight Height Neck Chest Abdomen Hip Thigh Knee Ankle index2;

datalines;

1 11.5040 23 154.25 67.75 36.2 93.1 85.2 94.5 59.0 37.3 21.9 90.195

2 8.4765 22 173.25 72.25 38.5 93.6 83.0 98.7 58.7 37.3 23.4 91.392

3 17.8570 22 154.00 66.25 34.0 95.8 87.9 99.2 59.6 38.9 24.0 94.299

4 10.5755 26 184.75 72.25 37.4 101.8 86.4 101.2 60.1 37.3 22.8 94.348

5 19.5200 24 184.25 71.25 34.4 97.3 100.0 101.9 63.2 42.2 24.0 101.765

6 15.7010 24 210.25 74.75 39.0 104.5 94.4 107.8 66.0 42.0 25.6 101.434

7 14.8745 26 181.00 69.75 36.4 105.1 90.7 100.3 58.4 38.3 22.9 96.348

8 11.5520 25 176.00 72.50 37.8 99.6 88.5 97.1 60.0 39.4 23.2 93.216

9 7.5000 25 191.00 74.00 38.1 100.9 82.5 99.9 62.9 38.3 23.8 91.775

10 11.2110 23 198.25 73.50 42.1 99.6 88.6 104.1 63.1 41.7 25.0 96.702

11 8.9650 26 186.25 74.50 38.5 101.5 83.6 98.2 59.7 39.7 25.2 90.896

12 9.3060 27 216.00 76.00 39.4 103.6 90.9 107.7 66.2 39.2 25.9 98.961

13 15.6565 32 180.50 69.50 38.4 102.0 91.6 103.9 63.4 38.3 21.5 98.513

14 15.8525 30 205.25 71.25 39.4 104.1 101.8 108.6 66.0 41.5 23.7 106.450

15 16.2920 35 187.75 69.50 40.5 101.3 96.4 100.1 69.0 39.0 23.1 98.868

16 15.7060 35 162.75 66.00 36.4 99.1 92.8 99.2 63.1 38.7 21.7 97.484

17 19.6665 34 195.75 71.00 38.9 101.9 96.4 105.2 64.8 40.8 23.1 102.216

18 16.6840 32 209.25 71.00 42.1 107.6 97.5 107.0 66.9 40.0 24.4 103.605

19 13.3110 28 183.75 67.75 38.0 106.8 89.6 102.4 64.2 38.7 22.9 96.656

20 13.5550 33 211.75 73.50 40.0 106.2 100.5 109.0 65.8 40.6 24.0 105.594

21 14.8255 28 179.00 68.00 39.1 103.3 95.9 104.9 63.5 38.0 22.1 100.391

22 12.9200 28 200.50 69.75 41.3 111.4 98.8 104.8 63.4 40.6 24.6 102.472

23 13.1155 31 140.25 68.25 33.9 86.0 76.4 94.6 57.4 35.3 22.2 85.835

24 14.1420 32 148.75 70.00 35.5 86.7 80.0 93.4 54.9 36.2 22.1 87.549

25 12.3340 28 151.25 67.75 34.5 90.2 76.3 95.8 58.4 35.5 22.9 86.490

26 7.3055 27 159.25 71.50 35.7 89.6 79.7 96.5 55.0 36.7 22.5 88.685

27 9.3555 34 131.50 67.50 36.2 88.6 74.6 85.3 51.7 34.7 21.4 80.359

28 16.6840 31 148.00 67.50 38.8 97.4 88.7 94.7 57.5 36.0 21.0 92.328

29 7.3050 27 133.25 64.75 36.4 93.5 73.9 88.5 50.1 34.5 21.3 81.280

30 9.7950 29 160.75 69.00 36.7 97.4 83.5 98.7 58.9 35.3 22.6 91.753

SAS response variable is fat_index. It is determined fr underwater weighing plus percent body fat from iri's (1956) equation Age (years) Weight (lbs) Height (inches) Neck circumference (cm) Chest circumference (cm) Abdomen 2 circumference (cm) Hip circumference (cm) Thigh circumference () Knee circumference (cm) Ankle circumference (cm) Index2: a health index. A low value is better. ollow these guidelines for your report. the steps we covered in class. Note that obs stands for observation number. Do not use obs in any I. Check for any outliers or influence points. Any RStudent> 2.50 e investigated as a potential outlier. Use several of the influence Explain whether deleting any points will improve the model or Check the X's for any strong multicollinearity. Identify if y regressor variables should not be used in the same models. Use as cut- :VIF> 25 Run proc rsquare to obtain the adjusted R square, MSE and Mallow's Cp. 3 models that look promising to you, and also add the full model ay, you will have four models for consideration (making it 4 models) Explain what each statistic is measuring and what it means. Obtain the PRESS statistic for each candidate model. Explain what PRESS and why we need it. Obtain the "PRESS based adjusted R square" as 1-(PRESS/(SSTotal)) ith a calculator for the 4 candidate models. This is an R square that is n oriented. If PRESS is very large, this r square may be negative. I a case, say that this model is poor for prediction. Summarize your findings in a table. The table has columns for a) Model b) adj. R square c) PRESS based R square. d) MSE e) Cp PRESS g) The largest VIF in the model Briefly explain why you prefer one particular model. Give the model in Run proc stepwise for stepwise regression. Compare your "best model