"MODEL" 100 * (LOG (DEATHS) - 2) = CONSTANT + TELEPHONES * TEL + F CAL * FAT CAL + AP CAL * ANIMAL PROTEIN CAL; "INPUT" 21 * [ OBSNO, TELEPHONES, FAT CAL, ANIMAL PROTEIN CAL, DEATHS ]; "OPTIONS" TRANSFORMED DATA MATRIX, CORRELATION MATRIX, RESIDUAL ANALYSIS, NO INPUT DATA REWIND; Transformed data matrix ======================= obs.no. CONSTANT TEL F CAL AP CAL dep.var. 1 1.000 124.000 33.000 8.000 81.023 2 1.000 49.000 31.000 6.000 55.023 3 1.000 181.000 38.000 8.000 80.003 4 1.000 4.000 17.000 2.000 24.055 5 1.000 22.000 20.000 4.000 78.032 6 1.000 152.000 39.000 6.000 51.983 7 1.000 75.000 30.000 7.000 88.024 8 1.000 54.000 29.000 7.000 45.025 9 1.000 43.000 35.000 6.000 49.969 10 1.000 41.000 31.000 5.000 69.020 11 1.000 17.000 23.000 4.000 65.992 12 1.000 22.000 21.000 3.000 45.025 13 1.000 16.000 8.000 3.000 24.055 14 1.000 10.000 23.000 3.000 42.975 15 1.000 63.000 37.000 6.000 38.021 16 1.000 170.000 40.000 8.000 72.016 17 1.000 125.000 38.000 6.000 40.993 18 1.000 15.000 25.000 4.000 38.021 19 1.000 221.000 39.000 7.000 51.983 20 1.000 171.000 33.000 7.000 51.983 21 1.000 97.000 38.000 6.000 65.992 Control information =================== transformed variable denoted by parameter mean standard deviation minimum maximum CONSTANT 1.000000 0.000000 1.000000 1.000000 TEL 79.619048 67.241710 4.000000 221.000000 F CAL 29.904762 8.677008 8.000000 40.000000 AP CAL 5.523810 1.833550 2.000000 8.000000 dep.var. 55.200537 18.350018 24.054925 88.024178 Number of observations : 21 Correlation matrix of the variables =================================== CONSTANT TEL F CAL AP CAL dep.var. CONSTANT 1.000000 TEL * 1.000000 F CAL * 0.765373 1.000000 AP CAL * 0.794133 0.820403 1.000000 dep.var. * 0.352227 0.400646 0.578991 1.000000 Multiple correlation coefficient 0.610225 (adjusted 0.511486) ================================ Proportion of variation explained 0.372375 (adjusted 0.261617) ================================= Standard deviation of the error term 15.768022 ==================================== Regression parameters ===================== right tail parameter estimate standard deviation F - ratio probability CONSTANT 20.2254131503 15.8475377537 1.628813 0.219028 TEL -0.0676015740 0.0913200444 0.548001 0.469237 F CAL -0.2985412292 0.7521792489 0.157531 0.696378 AP CAL 8.9223390010 3.7695192402 5.602547 0.030066 Correlation matrix of the estimates =================================== CONSTANT TEL F CAL AP CAL CONSTANT 1.000000 TEL 0.599763 1.000000 F CAL -0.554905 -0.327665 1.000000 AP CAL -0.335187 -0.451691 -0.543531 1.000000 Analysis of variance ==================== source of right tail variation df sum of squares mean square F - ratio probability --------------------------------------------------------------------------------------------------------------- total 21 70723.548495 --------------------------------------------------------------------------------------------------------------- mean 1 63989.084941 63989.084941 257.366170 0.000000 regression 3 2507.744689 835.914896 3.362077 0.043260 residual 17 4226.718865 248.630521 --------------------------------------------------------------------------------------------------------------- regression null hypothesis : TEL = F CAL = AP CAL = 0 Residual analysis ================= standardized studentized obs.no. observation fitted value standard deviation residual residual residual 1 81.023252 73.369669 7.538479 7.653582 0.539477 0.552635 2 55.022835 61.192192 5.291015 -6.169357 -0.434858 -0.415338 3 80.002936 68.023674 6.705223 11.979262 0.844380 0.839394 4 24.054925 32.724484 7.952029 -8.669559 -0.611090 -0.636718 5 78.031731 48.456710 5.339626 29.575021 2.084649 1.993409 6 51.982799 51.840900 7.200893 0.141899 0.010002 0.010116 7 88.024178 68.655431 6.685317 19.368746 1.365241 1.356293 8 45.024911 70.373606 7.973323 -25.348695 -1.786749 -1.863388 9 49.968708 60.403636 6.875734 -10.434928 -0.735525 -0.735374 10 69.019608 52.810666 5.122108 16.208942 1.142517 1.086908 11 65.991620 47.899094 4.789749 18.092526 1.275285 1.204326 12 45.024911 39.235830 6.108147 5.789081 0.408054 0.398234 13 24.054925 43.522475 11.158540 -19.467550 -1.372206 -1.747410 14 42.975228 39.449966 6.304806 3.525262 0.248485 0.243918 15 38.021124 58.454523 6.572849 -20.433398 -1.440285 -1.425642 16 72.015930 68.170208 6.085242 3.845722 0.271073 0.264375 17 40.993312 53.964684 5.845876 -12.971371 -0.914311 -0.885761 18 38.021124 47.437215 5.034123 -9.416091 -0.663710 -0.630141 19 51.982799 56.098730 9.598451 -4.115931 -0.290119 -0.329011 20 51.982799 61.270056 7.006951 -9.287257 -0.654629 -0.657476 21 65.991620 55.857528 5.819685 10.134092 0.714320 0.691523 sum of residuals : 0.000000 Upper bound for the right tail probability of the largest absolute studentized residual (no. 5) : 0.883762 End of job : 1 "MODEL" 100 * (LOG (DEATHS) - 2) = CONSTANT + TELEPHONES * TEL + F CAL * FAT CAL + AP CAL * ANIMAL PROTEIN CAL; "INPUT" 22 * [ OBSNO, TELEPHONES, FAT CAL, ANIMAL PROTEIN CAL, DEATHS ]; "OPTIONS" TRANSFORMED DATA MATRIX, CORRELATION MATRIX, RESIDUAL ANALYSIS, NO INPUT DATA REWIND; Transformed data matrix ======================= obs.no. CONSTANT TEL F CAL AP CAL dep.var. 1 1.000 124.000 33.000 8.000 81.023 2 1.000 49.000 31.000 6.000 55.023 3 1.000 181.000 38.000 8.000 80.003 4 1.000 4.000 17.000 2.000 24.055 5 1.000 22.000 20.000 4.000 78.032 6 1.000 152.000 39.000 6.000 51.983 7 1.000 75.000 30.000 7.000 88.024 8 1.000 54.000 29.000 7.000 45.025 9 1.000 43.000 35.000 6.000 49.969 10 1.000 41.000 31.000 5.000 69.020 11 1.000 17.000 23.000 4.000 65.992 12 1.000 22.000 21.000 3.000 45.025 13 1.000 16.000 8.000 3.000 24.055 14 1.000 10.000 23.000 3.000 42.975 15 1.000 63.000 37.000 6.000 38.021 16 1.000 170.000 40.000 8.000 72.016 17 1.000 125.000 38.000 6.000 40.993 18 1.000 15.000 25.000 4.000 38.021 19 1.000 221.000 39.000 7.000 51.983 20 1.000 171.000 33.000 7.000 51.983 21 1.000 97.000 38.000 6.000 65.992 22 1.000 254.000 39.000 8.000 88.986 Control information =================== transformed variable denoted by parameter mean standard deviation minimum maximum CONSTANT 1.000000 0.000000 1.000000 1.000000 TEL 87.545455 75.421184 4.000000 254.000000 F CAL 30.318182 8.687081 8.000000 40.000000 AP CAL 5.636364 1.865615 2.000000 8.000000 dep.var. 56.736248 19.302168 24.054925 88.986172 Number of observations : 22 Correlation matrix of the variables =================================== CONSTANT TEL F CAL AP CAL dep.var. CONSTANT 1.000000 TEL * 1.000000 F CAL * 0.759153 1.000000 AP CAL * 0.802196 0.830182 1.000000 dep.var. * 0.468275 0.445625 0.620810 1.000000 Multiple correlation coefficient 0.633482 (adjusted 0.549105) ================================ Proportion of variation explained 0.401299 (adjusted 0.301516) ================================= Standard deviation of the error term 16.131858 ==================================== Regression parameters ===================== right tail parameter estimate standard deviation F - ratio probability CONSTANT 23.9806255432 15.9639459467 2.256527 0.150393 TEL -0.0068705367 0.0814301787 0.007119 0.933691 F CAL -0.4808401312 0.7571543310 0.403304 0.533378 AP CAL 8.5046508708 3.8436114905 4.895917 0.040082 Correlation matrix of the estimates =================================== CONSTANT TEL F CAL AP CAL CONSTANT 1.000000 TEL 0.599087 1.000000 F CAL -0.540572 -0.279955 1.000000 AP CAL -0.327023 -0.473879 -0.569153 1.000000 Analysis of variance ==================== source of right tail variation df sum of squares mean square F - ratio probability --------------------------------------------------------------------------------------------------------------- total 22 78642.087325 --------------------------------------------------------------------------------------------------------------- mean 1 70818.039589 70818.039589 272.129182 0.000000 regression 3 3139.784535 1046.594845 4.021701 0.023613 residual 18 4684.263201 260.236845 --------------------------------------------------------------------------------------------------------------- regression null hypothesis : TEL = F CAL = AP CAL = 0 Residual analysis ================= standardized studentized obs.no. observation fitted value standard deviation residual residual residual 1 81.023252 75.298162 7.574047 5.725090 0.392349 0.401951 2 55.022835 59.765830 5.305139 -4.742995 -0.325045 -0.311331 3 80.002936 72.502340 5.970777 7.500596 0.514028 0.500500 4 24.054925 32.788163 8.135375 -8.733238 -0.598503 -0.626925 5 78.031731 48.231275 5.460188 29.800457 2.042272 1.963179 6 51.982799 55.211444 6.914612 -3.228645 -0.221264 -0.221522 7 88.024178 68.572687 6.839291 19.451490 1.333041 1.331354 8 45.024911 69.197809 8.108961 -24.172898 -1.656607 -1.733363 9 49.968708 57.883693 6.772802 -7.914985 -0.542426 -0.540595 10 69.019608 51.316144 5.117648 17.703464 1.213246 1.157197 11 65.991620 46.823107 4.832613 19.168513 1.313648 1.245437 12 45.024911 39.245784 6.249083 5.779127 0.396053 0.388583 13 24.054925 45.537929 11.314373 -21.483004 -1.472264 -1.868286 14 42.975228 38.366550 6.398324 4.608678 0.315840 0.311214 15 38.021124 56.784602 6.605527 -18.763478 -1.285891 -1.274912 16 72.015930 71.616236 5.657260 0.399694 0.027392 0.026457 17 40.993312 55.877789 5.804126 -14.884476 -1.020057 -0.988900 18 38.021124 45.875168 5.013742 -7.854044 -0.538250 -0.512233 19 51.982799 63.242028 8.210275 -11.259229 -0.771613 -0.810818 20 51.982799 66.470596 6.000549 -14.487796 -0.992871 -0.967509 21 65.991620 56.070164 5.951810 9.921456 0.679933 0.661706 22 88.986172 71.519951 9.312532 17.466221 1.196988 1.325965 sum of residuals : 0.000000 Upper bound for the right tail probability of the largest absolute studentized residual (no. 5) : 1.000000 End of job : 2 "MODEL" Y & W = A + B * X; "INPUT" 4 * [O, X, Y, W]; "OPTIONS" TRANSFORMED DATA MATRIX, CORRELATION MATRIX, RESIDUAL ANALYSIS, NO INPUT DATA REWIND; Transformed data matrix ======================= obs.no. A B dep.var. weight 1 1.000 10.000 33.800 1.000 2 1.000 20.000 62.200 4.000 3 1.000 30.000 92.000 1.000 4 1.000 40.000 122.400 1.000 Control information =================== transformed variable denoted by parameter mean standard deviation minimum maximum A 1.000000 0.000000 1.000000 1.000000 B 22.857143 9.511897 10.000000 40.000000 dep.var. 71.000000 28.215126 33.800000 122.400000 Number of observations : 4 Correlation matrix of the variables =================================== A B dep.var. A 1.000000 B * 1.000000 dep.var. * 0.999828 1.000000 Multiple correlation coefficient 0.999828 (adjusted 0.999743) ================================ Proportion of variation explained 0.999657 (adjusted 0.999485) ================================= Standard deviation of the error term 0.905248 ==================================== Regression parameters ===================== right tail parameter estimate standard deviation F - ratio probability A 3.2105263158 0.9517006210 11.380249 0.077760 B 2.9657894737 0.0388530152 5826.814387 0.000172 Correlation matrix of the estimates =================================== A B A 1.000000 B -0.933139 1.000000 Analysis of variance ==================== source of right tail variation df sum of squares mean square F - ratio probability --------------------------------------------------------------------------------------------------------------- total 4 40063.560000 --------------------------------------------------------------------------------------------------------------- mean 1 35287.000000 35287.000000 43060.565189 0.000000 regression 1 4774.921053 4774.921053 5826.814387 0.000172 residual 2 1.638947 0.819474 --------------------------------------------------------------------------------------------------------------- regression null hypothesis : B = 0 Residual analysis ================= standardized studentized obs.no. observation fitted value standard deviation residual residual residual 1 33.800000 32.868421 0.605481 0.931579 1.455349 1.384313 2 62.200000 62.526316 0.359709 -0.326316 -0.509783 -0.392814 3 92.000000 92.184211 0.440552 -0.184211 -0.287781 -0.232938 4 122.400000 121.842105 0.748794 0.557895 0.871565 1.096695 sum of residuals : 0.000000 Upper bound for the right tail probability of the largest absolute studentized residual (no. 1) : 0.524572 End of job : 3 "MODEL" TOTAL = PRICE * X1 + GNP * X2 + UNEMPY * X3 + ARMY * X4 + NONIST * X5 + TIME * X6 + CONSTANT; "INPUT" 16 * [X1, X2, X3, X4, X5, X6, TOTAL]; "OPTIONS" TRANSFORMED DATA MATRIX, CORRELATION MATRIX, RESIDUAL ANALYSIS, PROCESS SUBMODELS (1), NO INPUT DATA REWIND; Transformed data matrix ======================= obs.no. PRICE GNP UNEMPY ARMY NONIST TIME CONSTANT dep.var. 1 83.000 234289.000 2356.000 1590.000 107608.000 1947.000 1.000 60323.000 2 88.500 259426.000 2325.000 1456.000 108632.000 1948.000 1.000 61122.000 3 88.200 258054.000 3682.000 1616.000 109773.000 1949.000 1.000 60171.000 4 89.500 284599.000 3351.000 1650.000 110929.000 1950.000 1.000 61187.000 5 96.200 328975.000 2099.000 3099.000 112075.000 1951.000 1.000 63221.000 6 98.100 346999.000 1932.000 3594.000 113270.000 1952.000 1.000 63639.000 7 99.000 365385.000 1870.000 3547.000 115094.000 1953.000 1.000 64989.000 8 100.000 363112.000 3578.000 3350.000 116219.000 1954.000 1.000 63761.000 9 101.200 397469.000 2904.000 3048.000 117388.000 1955.000 1.000 66019.000 10 104.600 419180.000 2822.000 2857.000 118734.000 1956.000 1.000 67857.000 11 108.400 442769.000 2936.000 2798.000 120445.000 1957.000 1.000 68169.000 12 110.800 444546.000 4681.000 2637.000 121950.000 1958.000 1.000 66513.000 13 112.600 482704.000 3813.000 2552.000 123366.000 1959.000 1.000 68655.000 14 114.200 502601.000 3931.000 2514.000 125368.000 1960.000 1.000 69564.000 15 115.700 518173.000 4806.000 2572.000 127852.000 1961.000 1.000 69331.000 16 116.900 554894.000 4007.000 2827.000 130081.000 1962.000 1.000 70551.000 Control information =================== transformed variable denoted by parameter mean standard deviation minimum maximum PRICE 101.681250 10.791553 83.000000 116.900000 GNP 387698.437500 99394.937795 234289.000000 554894.000000 UNEMPY 3193.312500 934.464247 1870.000000 4806.000000 ARMY 2606.687500 695.919604 1456.000000 3594.000000 NONIST 117424.000000 6956.101561 107608.000000 130081.000000 TIME 1954.500000 4.760952 1947.000000 1962.000000 CONSTANT 1.000000 0.000000 1.000000 1.000000 dep.var. 65317.000000 3511.968356 60171.000000 70551.000000 Number of observations : 16 Correlation matrix of the variables =================================== PRICE GNP UNEMPY ARMY NONIST TIME CONSTANT dep.var. PRICE 1.000000 GNP 0.991589 1.000000 UNEMPY 0.620633 0.604261 1.000000 ARMY 0.464744 0.446437 -0.177421 1.000000 NONIST 0.979163 0.991090 0.686552 0.364416 1.000000 TIME 0.991149 0.995273 0.668257 0.417245 0.993953 1.000000 CONSTANT * * * * * * 1.000000 dep.var. 0.970899 0.983552 0.502498 0.457307 0.960391 0.971329 * 1.000000 Multiple correlation coefficient 0.997737 (adjusted 0.996225) ================================ Proportion of variation explained 0.995479 (adjusted 0.992465) ================================= Standard deviation of the error term 304.854074 ==================================== Regression parameters ===================== right tail parameter estimate standard deviation F - ratio probability PRICE 15.0618722714 84.9149257749 0.031462 0.863141 GNP -0.0358191793 0.0334910078 1.143865 0.312681 UNEMPY -2.0202298038 0.4883996817 17.110031 0.002535 ARMY -1.0332268672 0.2142741632 23.251542 0.000944 NONIST -0.0511041057 0.2260732001 0.051099 0.826212 TIME 1829.1514646136 455.4784991427 16.127371 0.003037 CONSTANT -3482258.6345958211 890420.3836083020 15.294379 0.003560 Correlation matrix of the estimates =================================== PRICE GNP UNEMPY ARMY NONIST TIME CONSTANT PRICE 1.000000 GNP -0.649419 1.000000 UNEMPY -0.555000 0.945607 1.000000 ARMY -0.348815 0.468605 0.618566 1.000000 NONIST 0.659178 -0.833206 -0.758256 -0.188914 1.000000 TIME 0.186285 -0.801681 -0.824101 -0.549367 0.388160 1.000000 CONSTANT -0.204933 0.816117 0.835987 0.549722 -0.410687 -0.999690 1.000000 Analysis of variance ==================== source of right tail variation df sum of squares mean square F - ratio probability --------------------------------------------------------------------------------------------------------------- total 16 68445976650.000000 --------------------------------------------------------------------------------------------------------------- mean 1 68260967824.000000 68260967824.000000 734494.311074 0.000000 regression 6 184172401.944492 30695400.324082 330.285339 0.000000 residual 9 836424.055508 92936.006168 --------------------------------------------------------------------------------------------------------------- regression null hypothesis : PRICE = GNP = UNEMPY = ARMY = NONIST = TIME = 0 Residual analysis ================= standardized studentized obs.no. observation fitted value standard deviation residual residual residual 1 60323.000000 60055.659970 198.632240 267.340030 1.169259 1.156014 2 61122.000000 61216.013942 229.143681 -94.013942 -0.411187 -0.467568 3 60171.000000 60124.712832 183.438757 46.287168 0.202445 0.190101 4 61187.000000 61597.114622 185.992913 -410.114622 -1.793709 -1.697900 5 63221.000000 62911.285409 239.171785 309.714591 1.354592 1.638429 6 63639.000000 63888.311215 185.328620 -249.311215 -1.090407 -1.029989 7 64989.000000 65153.048956 213.731089 -164.048956 -0.717497 -0.754657 8 63761.000000 63774.180357 216.565758 -13.180357 -0.057647 -0.061430 9 66019.000000 66004.695227 206.113154 14.304773 0.062564 0.063685 10 67857.000000 67401.605905 175.288498 455.394095 1.991747 1.825818 11 68169.000000 68186.268927 182.882356 -17.268927 -0.075529 -0.070802 12 66513.000000 66552.055043 211.895321 -39.055043 -0.170814 -0.178194 13 68655.000000 68810.549974 186.512006 -155.549974 -0.680325 -0.645057 14 69564.000000 69649.671308 145.686592 -85.671308 -0.374699 -0.319920 15 69331.000000 68989.068486 186.153396 341.931514 1.495498 1.416343 16 70551.000000 70757.757825 252.976463 -206.757825 -0.904292 -1.215404 sum of residuals : 0.000000 Upper bound for the right tail probability of the largest absolute studentized residual (no. 10) : 0.989947 Control information - submodel 1 =================== transformed variable denoted by parameter mean standard deviation minimum maximum CONSTANT omitted PRICE 101.681250 10.791553 83.000000 116.900000 GNP 387698.437500 99394.937795 234289.000000 554894.000000 UNEMPY 3193.312500 934.464247 1870.000000 4806.000000 ARMY 2606.687500 695.919604 1456.000000 3594.000000 NONIST 117424.000000 6956.101561 107608.000000 130081.000000 TIME 1954.500000 4.760952 1947.000000 1962.000000 dep.var. 65317.000000 3511.968356 60171.000000 70551.000000 Number of observations : 16 There is no constant independent variable in the transformed (sub)model (message) Multiple correlation coefficient 0.999984 (adjusted 0.999974) ================================ Proportion of variation explained 0.999967 (adjusted 0.999947) ================================= Standard deviation of the error term 475.165508 ==================================== Regression parameters ===================== right tail parameter estimate standard deviation F - ratio probability PRICE -52.9935701387 129.5448669312 0.167342 0.691108 GNP 0.0710731991 0.0301664000 5.550917 0.040224 UNEMPY -0.4234658557 0.4177365406 1.027618 0.334618 ARMY -0.5725686684 0.2789908747 4.211872 0.067251 NONIST -0.4142035888 0.3212849619 1.662061 0.226347 TIME 48.4178656200 17.6894873782 7.491707 0.020937 Correlation matrix of the estimates =================================== PRICE GNP UNEMPY ARMY NONIST TIME PRICE 1.000000 GNP -0.852459 1.000000 UNEMPY -0.714348 0.830438 1.000000 ARMY -0.288837 0.041363 0.346873 1.000000 NONIST 0.644329 -0.945216 -0.829296 0.048380 1.000000 TIME -0.762065 0.984993 0.850275 0.008842 -0.985941 1.000000 Analysis of variance ==================== source of right tail variation df sum of squares mean square F - ratio probability --------------------------------------------------------------------------------------------------------------- total 16 68445976650.000000 --------------------------------------------------------------------------------------------------------------- regression 6 68443718827.400242 11407286471.233374 50523.395737 0.000000 residual 10 2257822.599758 225782.259976 --------------------------------------------------------------------------------------------------------------- reduction 1 1421398.544250 1421398.544250 15.294379 0.003560 --------------------------------------------------------------------------------------------------------------- regression null hypothesis : PRICE = GNP = UNEMPY = ARMY = NONIST = TIME = 0 (in the reduced model) reduction null hypothesis : CONSTANT = 0 (in the original model) Residual analysis ================= standardized studentized obs.no. observation fitted value standard deviation residual residual residual 1 60323.000000 60043.097251 309.560718 279.902749 0.745113 0.776447 2 61122.000000 61252.324654 356.865023 -130.324654 -0.346930 -0.415397 3 60171.000000 60080.267713 285.370407 90.732287 0.241533 0.238814 4 61187.000000 61588.312522 289.879498 -401.312522 -1.068311 -1.065904 5 63221.000000 63661.467688 222.660402 -440.467688 -1.172544 -1.049314 6 63639.000000 64182.545129 263.991240 -543.545129 -1.446941 -1.375773 7 64989.000000 64787.678884 299.623135 201.321116 0.535925 0.545892 8 63761.000000 63545.091106 324.970636 215.908894 0.574759 0.622818 9 66019.000000 65945.906318 320.405881 73.093682 0.194579 0.208311 10 67857.000000 66943.783055 203.353946 913.216945 2.431023 2.126468 11 68169.000000 67744.175150 224.073833 424.824850 1.130902 1.013867 12 66513.000000 66521.564759 330.050279 -8.564759 -0.022800 -0.025055 13 68655.000000 69016.329746 278.901149 -361.329746 -0.961875 -0.939243 14 69564.000000 69536.654395 222.564387 27.345605 0.072795 0.065137 15 69331.000000 69179.710440 280.025712 151.289560 0.402739 0.394101 16 70551.000000 71043.499374 377.501703 -492.499374 -1.311055 -1.706668 sum of residuals : -0.408183 Upper bound for the right tail probability of the largest absolute studentized residual (no. 10) : 0.374272 End of job : 4