FIRST BROWNLEE 4 3 E1 1 12161 3111 EX1 0010 ( A6, I4, I2, 2F6.3, F5.2, F1.0, F6.3, 2F1.0 ) EX1 0011 22 EX1 0012 23 4 EX1 0013 1 2 3 4 2 61 8 -2. 71 6 100. 7 EX1 0020 EXAMPLE OF SAVING COEFFICIENTS FOR CROSS VERIFICATION OF EQUATION, EX1 0030 REDUCING PRINTOUT (CENTRAL RESIDUALS AND OBSERVATIONS 10-12), E FORMAT, EX1 0040 DELETED OBSERVATION, INDICATOR-VARIABLE-OBSERVATION, AND CP FACTORIAL EX1 0041 SEARCH WITH GIVEN ESTIMATE OF VARIANCE. EX1 0050 OBSERVATION 22 DELETED FROM FIRST SET OF DATA, INCLUDED IN NEXT SET. EX1 0060 Y = B(0) + B(1)X1 + B(2)X2 + B(3)X3 + B(4)X4 EX1 0070 Y = 100( LOG(NUMBER OF DEATHS FROM HEART DISEASE PER 100,000 FOR MALES EX1 0080 IN THE 55 TO 59 AGE GROUP) - 2 ) EX1 0090 X1 = 1000(TELEPHONES PER PERSON) EX1 0100 X2 = FAT CALORIES AS PER CENT OF TOTAL CALORIES EX1 0110 X3 = ANIMAL PROTEIN CALORIES AS PER CENT TOTAL CALORIES EX1 0120 X4 = INDICATOR VARIABLE, 1 FOR OBSERVATION 23 (U.N.), 0 OTHERWISE. EX1 0121 TELEPH F. CAL AP.CAL UN IND DEATHS EX1 0130 1 2 3 EX1 0131 AUSTRL 1 124 33 8 646 EX1 0140 ASTRIA 2 49 31 6 355 EX1 0150 CANADA 3 181 38 8 631 EX1 0160 CEYLON 4 4 17 2 174 EX1 0170 CHILE 5 22 20 4 603 EX1 0180 DENMK 6 152 39 6 331 EX1 0190 FINLND 7 75 30 7 759 EX1 0200 FRANCE 8 54 29 7 282 EX1 0210 GMANY 9 43 35 6 316 EX1 0220 IRELND 10 41 31 5 490 EX1 0230 ISRAEL 11 17 23 4 457 EX1 0240 ITALY 12 22 21 3 282 EX1 0250 JAPAN 13 16 8 3 174 EX1 0260 MEXICO 14 10 23 3 269 EX1 0270 NTHLDS 15 63 37 6 240 EX1 0280 NWZEAL 16 170 40 8 525 EX1 0290 NORWAY 17 125 38 6 257 EX1 0300 PORTGL 18 15 25 4 240 EX1 0310 SWEDEN 19 221 39 7 331 EX1 0320 SWITZD 20 171 33 7 331 EX1 0330 UNKING 21 97 38 6 457 EX1 0340 U.S.A. 22 254 39 8 776 EX1 0341 U.N. 23 87 30 5 776 EX1 0342 END EX1 0350 235. EX1 0351 NEXT BROWNLEE 4 3 1 1 101 2 1 EX1 0360 ( A6, I4, I2, 2F6.3, F5.2, F1.0, F6.3, 2F1.0 ) EX1 0361 23 4 EX1 0362 1 2 3 4 2 61 8 -2. 71 6 100. 7 EX1 0370 EXAMPLE OF CROSS VERIFICATION WITH SAVED COEFFICIENTS FROM FIT WITH EX1 0371 FIRST SET OF DATA. THIS SECOND SET OF DATA CONTAINS USA, OBSERVATION EX1 0372 22, DELETED FROM FIRST SET OF DATA. EX1 0373 Y = B(0) + B(1)X1 + B(2)X2 + B(3)X3 + B(4)X4 EX1 0380 Y = 100( LOG(NUMBER OF DEATHS FROM HEART DISEASE PER 100,000 FOR MALES EX1 0390 IN THE 55 TO 59 AGE GROUP) - 2 ) EX1 0400 X1 = 1000(TELEPHONES PER PERSON) EX1 0410 X2 = FAT CALORIES AS PER CENT OF TOTAL CALORIES EX1 0420 X3 = ANIMAL PROTEIN CALORIES AS PER CENT TOTAL CALORIES EX1 0430 X4 = INDICATOR VARIABLE, 1 FOR OBSERVATION 23 (U.N.), 0 OTHERWISE. EX1 0431 TELEPH F. CAL AP.CAL UN IND DEATHS EX1 0440 AUSTRL 1 124 33 8 646 EX1 0450 ASTRIA 2 49 31 6 355 EX1 0460 CANADA 3 181 38 8 631 EX1 0470 CEYLON 4 4 17 2 174 EX1 0480 CHILE 5 22 20 4 603 EX1 0490 DENMK 6 152 39 6 331 EX1 0500 FINLND 7 75 30 7 759 EX1 0510 FRANCE 8 54 29 7 282 EX1 0520 GMANY 9 43 35 6 316 EX1 0530 IRELND 10 41 31 5 490 EX1 0540 ISRAEL 11 17 23 4 457 EX1 0550 ITALY 12 22 21 3 282 EX1 0560 JAPAN 13 16 8 3 174 EX1 0570 MEXICO 14 10 23 3 269 EX1 0580 NTHLDS 15 63 37 6 240 EX1 0590 NWZEAL 16 170 40 8 525 EX1 0600 NORWAY 17 125 38 6 257 EX1 0610 PORTGL 18 15 25 4 240 EX1 0620 SWEDEN 19 221 39 7 331 EX1 0630 SWITZD 20 171 33 7 331 EX1 0640 UNKING 21 97 38 6 457 EX1 0650 U.S.A. 22 254 39 8 776 EX1 0660 U.N. 23 87 30 5 776 EX1 0661 END EX1 0670 MANDEL WEIGHT OBSV 1 1 1 1 51 EX2 0010 SAMPLE LEVEL OF X WEIGHT OF OBSERVATION EX2 0020 1 10 1 EX2 0030 2 20 4 EX2 0040 3 30 1 EX2 0050 4 40 1 EX2 0060 LEVEL EX2 0070 1 10. 33.8 1. EX2 0080 2 20. 62.2 4. EX2 0090 3 30. 92.0 1. EX2 0100 4 40. 122.4 1. EX2 0110 END EX2 0120 PRECISION - EMPLOY 6 8 1 1111 1 11 812 2 EX3 0010 ( A6,I4,I2, F6.1,9F6.0/ 12X, 4F6.0 ) EX3 0020 1 2 3 4 5 6 7 EX3 0030 81 91 101 111 121 131 141 EX3 0040 Y = B(0) + B(1)X1 + B(2)X2 + B(3)X3 + B(4)X4 + B(5)X5 + B(6)X6 EX3 0050 Y = EMPLOYMENT EX3 0060 X1 = PRICE INDEX EX3 0070 X2 = GROSS NATIONAL PRODUCT EX3 0080 X3 = UNEMPLOYMENT EX3 0090 X4 = SIZE OF ARMED FORCES EX3 0100 X5 = NONINSTITIONAL POPULATION EX3 0110 X6 = TIME IN YEARS EX3 0120 PRICE GNP UNEMPY ARMY NONIST TIME TOTAL EX3 0130 FARM SELF UNPAID HOUSE PRIVAT FED GOV LOCALG EX3 0140 JASA P1947 1 83.0234289 2356 1590107608 1947 60323 8256 6045 427EX3 0150 JASA 1947 2 1714 38407 1892 3582 EX3 0160 JASA R1948 1 88.5259426 2325 1456108632 1948 61122 7960 6139 401EX3 0170 JASA 1948 2 1731 39241 1863 3787 EX3 0180 JASA E1949 1 88.2258054 3682 1616109773 1949 60171 8017 6208 396EX3 0190 JASA 1949 2 1772 37922 1908 3948 EX3 0200 JASA C1950 1 89.5284599 3351 1650110929 1950 61187 7497 6069 404EX3 0210 JASA 1950 2 1995 39196 1928 4098 EX3 0220 JASA I1951 1 96.2328975 2099 3099112075 1951 63221 7048 5869 400EX3 0230 JASA 1951 2 2055 41460 2302 4087 EX3 0240 JASA S1952 1 98.1346999 1932 3594113270 1952 63639 6792 5670 431EX3 0250 JASA 1952 2 1922 42216 2420 4188 EX3 0260 JASA I1953 1 99.0365385 1870 3547115094 1953 64989 6555 5794 423EX3 0270 JASA 1953 2 1985 43587 2305 4340 EX3 0280 JASA O1954 1 100.0363112 3578 3350116219 1954 63761 6495 5880 445EX3 0290 JASA 1954 2 1919 42271 2188 4563 EX3 0300 JASA N1955 1 101.2397469 2904 3048117388 1955 66019 6718 5886 524EX3 0310 JASA 1955 2 2216 43761 2187 4727 EX3 0320 JASA 1956 1 104.6419180 2822 2857118734 1956 67857 6572 5936 581EX3 0330 JASA 1956 2 2359 45131 2209 5069 EX3 0340 JASA T1957 1 108.4442769 2936 2798120445 1957 68169 6222 6089 626EX3 0350 JASA 1957 2 2328 45278 2217 5409 EX3 0360 JASA E1958 1 110.8444546 4681 2637121950 1958 66513 5844 6185 605EX3 0370 JASA 1958 2 2456 43530 2191 5702 EX3 0380 JASA S1959 1 112.6482704 3813 2552123366 1959 68655 5836 6298 597EX3 0390 JASA 1959 2 2520 45214 2233 5957 EX3 0400 JASA T1960 1 114.2502601 3931 2514125368 1960 69564 5723 6367 615EX3 0410 JASA 1960 2 2489 45850 2270 6250 EX3 0420 JASA 1961 1 115.7518173 4806 2572127852 1961 69331 5463 6388 662EX3 0430 JASA 1961 2 2594 45397 2279 6548 EX3 0440 JASA 1962 1 116.9554894 4007 2827130081 1962 70551 5190 6271 623EX3 0450 JASA 1962 2 2626 46652 2340 6849 EX3 0460 END EX3 0470 END EX3 0480 B0=0 BRNLEE BLOOD 1 1 1 11 51 EX4 0010 (A3,2I2,F5.0,F7.0) EX4 0020 PROBLEM FROM STATISTICAL THEORY AND METHODOLOGY BY BROWNLEE, EX4 0030 2ND EDITION, SECTION 11.4 . EX4 0040 Y = B(1)X1 EX4 0050 Y = RATES OF BLOOD FLOW EX4 0060 X = MEASUREMENTS BY AN INSTRUMENT EX4 0070 A B C D EX4 0080 1 1190. 1115. EX4 0090 2 1455. 1425. EX4 0100 3 1550. 1515. EX4 0110 4 1730. 1795. EX4 0120 5 1745. 1715. EX4 0130 6 1770. 1710. EX4 0140 7 1900. 1830. EX4 0150 8 1920. 1920. EX4 0160 9 1960. 1970. EX4 0170 10 2295. 2300. EX4 0180 11 2335. 2280. EX4 0190 12 2490. 2520. EX4 0200 13 2720. 2630. EX4 0210 14 2710. 2740. EX4 0220 15 2530. 2390. EX4 0230 16 2900. 2800. EX4 0240 17 2760. 2630. EX4 0250 18 3010. 2970. EX4 0260 END EX4 0270 B0=0 BB,SWITCHES=1 1 1 1 111111111 2 2 EX5 0010 Y IS CONSTANT 1 1 EX6 0010 1. 3. EX6 0020 2. 3. EX6 0030 3. 3. EX6 0040 3. 3. EX6 0040 4. 3. EX6 0050 5. 3. EX6 0060 6. 3. EX6 0070 7. 3. EX6 0080 8. 3. EX6 0090 9. 3. EX6 0100 END EX6 0110 VAR3 = VAR4 4 1 1 EX7 0010 (A6,I4,I2,3F6.3, T25, 2F6.3 ) EX7 0020 AUSTRL 1 124 33 8 646 EX7 0030 ASTRIA 2 49 31 6 355 EX7 0040 CANADA 3 181 38 8 631 EX7 0050 CEYLON 4 4 17 2 174 EX7 0060 CHILE 5 22 20 4 603 EX7 0070 DENMK 6 152 39 6 331 EX7 0080 FINLND 7 75 30 7 759 EX7 0090 FRANCE 8 54 29 7 282 EX7 0100 GMANY 9 43 35 6 316 EX7 0110 IRELND 10 41 31 5 490 EX7 0120 ISRAEL 11 17 23 4 457 EX7 0130 ITALY 12 22 21 3 282 EX7 0140 JAPAN 13 16 8 3 174 EX7 0150 MEXICO 14 10 23 3 269 EX7 0160 NTHLDS 15 63 37 6 240 EX7 0170 NWZEAL 16 170 40 8 525 EX7 0180 NORWAY 17 125 38 6 257 EX7 0190 PORTGL 18 15 25 4 240 EX7 0200 SWEDEN 19 221 39 7 331 EX7 0210 SWITZD 20 171 33 7 331 EX7 0220 UNKING 21 97 38 6 457 EX7 0230 U.S.A. 22 254 39 8 776 EX7 0240 END EX7 0250 2 VARIABLES PASS 1 3 1 1 1 211 121 1 EX8 0010 (6X, A4, I2, I1, F5.2, F6.2, F1.0, F10.4 ) EX8 0020 1 2 31 4 EX8 0030 EQUATION: Y = 20 + 20X1 - 3X2 - 1X1SQRD + ERROR(0,1) EX8 0040 FITTED WITH Y = B0 + B1X1 + B2X2 EX8 0050 ERROR FROM "A MILLION RANDOM DIGITS", RAND CORP., FREE PRESS, 1955. EX8 0060 1-20 OBSV. FROM TABLE PAGE 4, COL 4; 21-40 OBSV. FROM PAGE 12, COL 2. EX8 0070 OBSERVATIONS 21-40 ARE REPLICATES OF OBSERVATIONS 1-20. EX8 0080 STD. DEVIATION ESTIMATED FROM NEAR NEIGHBORS (1.0), IS MUCH LESS EX8 0090 THAN RRMS OF FIT, SUGGESTING A BETTER FORM OF EQUATION IS NEEDED. EX8 0100 NEED FOR SQUARED TERM CAN BE SEEN FROM RESIDUAL VS. INDEPENDENT EX8 0110 VARIABLE X1 PLOT. SLIGHT EFFECT ON CURVATURE CAN BE SEEN FROM EX8 0120 COMPONENT AND COMPONENT-PLUS-RESIDUAL VS. INDEPENDENT VARIABLE X1 EX8 0130 PLOT. FROM "THE USE OF INDIVIDUAL EFFECTS AND RESIDUALS IN FITTING EX8 0140 EQUATIONS TO DATA" BY F.S.WOOD, TECHNOMETRICS VOL.15, NO 4, NOV. 1973. EX8 0150 X1 X2 Y EX8 0160 1 1 0.0 0.0 20.1640 EX8 0170 2 2 0.20 2.00 18.8470 EX8 0180 3 3 0.50 7.00 6.6780 EX8 0190 4 4 1.00 10.00 8.7090 EX8 0200 5 5 1.50 4.00 36.9340 EX8 0210 6 6 2.00 16.00 8.3970 EX8 0220 7 7 2.50 22.00 -1.7780 EX8 0230 8 8 3.00 6.00 53.1360 EX8 0240 9 9 3.50 9.00 51.8830 EX8 0250 1010 4.00 18.00 31.5640 EX8 0260 1111 4.50 28.00 5.7390 EX8 0270 1212 5.00 34.00 -6.4660 EX8 0280 1313 5.30 14.00 56.4940 EX8 0290 1414 5.50 24.00 28.5230 EX8 0300 1515 6.00 19.00 47.4980 EX8 0310 1616 6.50 38.00 -4.5750 EX8 0320 1717 7.00 33.00 10.7300 EX8 0330 1818 7.50 35.00 8.2140 EX8 0340 1919 7.80 30.00 23.7900 EX8 0350 2020 8.00 40.00 -3.5180 EX8 0360 121 0.0 0.0 20.2830 EX8 0370 222 0.20 2.00 16.9700 EX8 0380 323 0.50 7.00 8.3790 EX8 0390 424 1.00 10.00 9.8760 EX8 0400 525 1.50 4.00 37.7190 EX8 0410 626 2.00 16.00 8.4450 EX8 0420 727 2.50 22.00 -1.8410 EX8 0430 828 3.00 6.00 54.3390 EX8 0440 929 3.50 9.00 51.6460 EX8 0450 1030 4.00 18.00 30.7380 EX8 0460 1131 4.50 28.00 5.3730 EX8 0470 1232 5.00 34.00 -7.5370 EX8 0480 1333 5.30 14.00 53.9740 EX8 0490 1434 5.50 24.00 28.6360 EX8 0500 1535 6.00 19.00 46.0650 EX8 0510 1636 6.50 38.00 -6.3270 EX8 0520 1737 7.00 33.00 13.0010 EX8 0530 1838 7.50 35.00 7.8550 EX8 0540 1939 7.80 30.00 26.8690 EX8 0550 2040 8.00 40.00 -3.6590 EX8 0560 END EX8 0570 2 VARIABLES PASS 2 3 1 1 1 212 81 EX8 0580 8-4.0 1 2 9 1 1 32 4 EX8 0590 EQUATION: Y = 20 + 20X1 - 3X2 - 1X1SQRD + ERROR(0,1) EX8 0600 FITTED WITH Y = B0 + B1(X1-4.0) + B2X2 + B3(X1-4.0)SQRD EX8 0610 ERROR FROM "A MILLION RANDOM DIGITS", RAND CORP., FREE PRESS, 1955. EX8 0620 1-20 OBSV. FROM TABLE PAGE 4, COL 4; 21-40 OBSV. FROM PAGE 12, COL 2. EX8 0630 OBSERVATIONS 21-40 ARE REPLICATES OF OBSERVATIONS 1-20. EX8 0640 STD. DEVIATION ESTIMATED FROM NEAR NEIGHBORS (1.0), IS CLOSE TO EX8 0650 RRMS OF FIT. EX8 0660 UNCODED FITTED EQUATION: Y = 20.006 + 20.310X1 - 3.007X2 - 1.038X1SQRD EX8 0670 X1-4.0 X2 X1SQRD Y EX8 0680