brain wt - body wt data/* file: mreg-dino-27jan04.doc directory: Classes\Spring ‘04 purpose: multiple regression with indicator variables*/Multiple Regression with indicator variablesLog(Brain Weight)i = 0 +1 Log(Body Weight)i + i Log(Brain Weight)i = 0 +1 Log(Body Weight)i +2 Idinoi + i Log(Brain Weight)i = 0 +1 Log(Body Weight)i +2 Idinoi + 3 Idinoi ×Log(Body Weight)i +idata mrexample;* Lunneborg (1994);* body weight brain example; input species $ bodywt brainwt @@; logbody = log10(bodywt); logbrain = log10(brainwt); idino = 0; if (species="diplodoc" or species="tricerat" or species="brachios") then idino=1; idinobod = idino*logbody; cards;beaver 1.35 8.10 cow 465.00 423.00 wolf 36.33 119.50 goat 27.66 115.00guipig 1.04 5.50 diplodocus 11700.00 50.00 asielephant 2547.00 4603.00donkey 187.10 419.00 horse 521.00 655.00 potarmonkey 10.00 115.00cat 3.30 25.60 giraffe 529.000 680.00 gorilla 207.00 406.00human 62.00 1320.00 afrelephant 6654.00 5712.00 triceratops 9400.00 70.00rhemonkey 6.80 179.00 kangaroo 35.00 56.00 hamster 0.12 1.00mouse 0.023 0.40 rabbit 2.50 12.10 sheep 55.50 175.00 jaguar 100.00 157.00 chimp 52.16 440.00 brachiosaurus 87000.00 154.50rat 0.28 1.90 mole 0.122 3.00 pig 192.00 180;ODS RTF file='D:\baileraj\Classes\Fall 2003\sta402\SAS-programs\mreg-output.rtf’;proc print;title ‘brain wt - body wt data’;run;proc univariate; var bodywt brainwt; id species; run;proc reg;07:04 Monday, January 14, 2019 1brain wt - body wt datatitle2 ‘allometric scaling - brain and body wt.’;title3 ‘[All Species combined]’; model logbrain=logbody; plot logbrain*logbody="o" p.*logbody="+" / overlay; plot r.*logbody;run;proc reg;title2 ‘Dinosaurs fitted with potentially different line’; model logbrain=logbody idino idinobod; plot logbrain*logbody="o" p.*logbody="+" / overlay; plot r.*logbody;run;proc reg;title2 ‘Dinosaurs fitted with potentially different INTERCEPTS’; model logbrain=logbody idino; plot logbrain*logbody="o" p.*logbody="+" / overlay; plot r.*logbody;run;ODS RTF CLOSE;Obs species bodywt brainwt logbody logbrain idino idinobod1beaver 1.35 8.1 0.13033 0.90849 0 0.000002cow 465.00 423.0 2.66745 2.62634 0 0.000003wolf 36.33 119.5 1.56027 2.07737 0 0.000004goat 27.66 115.0 1.44185 2.06070 0 0.000005guipig 1.04 5.5 0.01703 0.74036 0 0.000006diplodoc 11700.00 50.0 4.06819 1.69897 1 4.068197asieleph 2547.00 4603.0 3.40603 3.66304 0 0.000008donkey 187.10 419.0 2.27207 2.62221 0 0.000009horse 521.00 655.0 2.71684 2.81624 0 0.0000010potarmon 10.00 115.0 1.00000 2.06070 0 0.0000011cat 3.30 25.6 0.51851 1.40824 0 0.0000012giraffe 529.00 680.0 2.72346 2.83251 0 0.0000013gorilla 207.00 406.0 2.31597 2.60853 0 0.0000014human 62.00 1320.0 1.79239 3.12057 0 0.0000015afreleph 6654.00 5712.0 3.82308 3.75679 0 0.0000007:04 Monday, January 14, 2019 2brain wt - body wt dataObs species bodywt brainwt logbody logbrain idino idinobod16tricerat 9400.00 70.0 3.97313 1.84510 1 3.9731317rhemonke 6.80 179.0 0.83251 2.25285 0 0.0000018kangaroo 35.00 56.0 1.54407 1.74819 0 0.0000019hamster 0.12 1.0 -0.92082 0.00000 0 0.0000020mouse 0.02 0.4 -1.63827 -0.39794 0 0.0000021rabbit 2.50 12.1 0.39794 1.08279 0 0.0000022sheep 55.50 175.0 1.74429 2.24304 0 0.0000023jaguar 100.00 157.0 2.00000 2.19590 0 0.0000024chimp 52.16 440.0 1.71734 2.64345 0 0.0000025brachios 87000.00 154.5 4.93952 2.18893 1 4.9395226rat 0.28 1.9 -0.55284 0.27875 0 0.0000027mole 0.12 3.0 -0.91364 0.47712 0 0.0000028pig 192.00 180.0 2.28330 2.25527 0 0.0000007:04 Monday, January 14, 2019 3brain wt - body wt dataThe UNIVARIATE ProcedureVariable: bodywtBODY WEIGHTMomentsN28Sum Weights28Mean4278.43875Sum Observations119796.285Std Deviation16480.4904Variance271606563Skewness5.03388585Kurtosis26.0100719Uncorrected SS7845918273Corrected SS7333377205Coeff Variation385.198698Std Error Mean3114.51993Basic Statistical MeasuresLocation VariabilityMean4278.439Std Deviation16480Median53.830Variance271606563Mode.Range87000Interquartile Range490.10000Tests for Location: Mu0=0Test Statistic p ValueStudent's t t1.373707Pr > |t|0.1808Sign M14Pr >= |M|<.0001Signed Rank S203Pr >= |S|<.0001Quantiles (Definition 5)Quantile Estimate100% Max87000.00099%87000.00095%11700.00090%9400.00007:04 Monday, January 14, 2019 4brain wt - body wt dataThe UNIVARIATE ProcedureVariable: bodywtQuantiles (Definition 5)Quantile Estimate75% Q3493.00050% Median53.83025% Q12.90010%0.1225%0.1201%0.0230% Min0.023Extreme ObservationsLowest HighestValue species Obs Value species Obs0.023 mouse 20 2547 asieleph 70.120 hamster 19 6654 afreleph 150.122 mole 27 9400 tricerat 160.280 rat 26 11700 diplodoc 61.040 guipig 5 87000 brachios 2507:04 Monday, January 14, 2019 5brain wt - body wt dataThe UNIVARIATE ProcedureVariable: brainwtBRAIN WEIGHTMomentsN28Sum Weights28Mean574.521429Sum Observations16086.6Std Deviation1334.92919Variance1782035.94Skewness3.33453913Kurtosis10.6457044Uncorrected SS57357066.9Corrected SS48114970.5Coeff Variation232.354987Std Error Mean252.277904Basic Statistical MeasuresLocation VariabilityMean574.5214Std Deviation1335Median137.0000Variance1782036Mode115.0000Range5712Interquartile Range402.15000Tests for Location: Mu0=0Test Statistic p ValueStudent's t t2.277336Pr > |t|0.0309Sign M14Pr >= |M|<.0001Signed Rank S203Pr >= |S|<.0001Quantiles (Definition 5)Quantile Estimate100% Max5712.0099%5712.0095%4603.0090%1320.0007:04 Monday, January 14, 2019 6brain wt - body wt dataThe UNIVARIATE ProcedureVariable: brainwtQuantiles (Definition 5)Quantile Estimate75% Q3421.0050% Median137.0025% Q118.8510%1.905%1.001%0.400% Min0.40Extreme ObservationsLowest HighestValue species Obs Value species Obs0.4 mouse 20 655 horse 91.0 hamster 19 680 giraffe 121.9 rat 26 1320 human 143.0 mole 27 4603 asieleph 75.5 guipig 5 5712 afreleph1507:04 Monday, January 14, 2019 7brain wt - body wt dataallometric scaling - brain and body wt.[All Species combined]The REG ProcedureModel: MODEL1Dependent Variable: logbrainAnalysis of VarianceSource DFSum ofSquaresMeanSquare F Value Pr > FModel1 17.81230 17.81230 40.26 <.0001Error26 11.50305 0.44242Corrected Total27 29.31535Root MSE0.66515R-Square0.6076Dependent Mean1.92195Adj R-Sq0.5925Coeff Var34.60816Parameter EstimatesVariable DFParameterEstimateStandardError t Value Pr > |t|Intercept1 1.10958 0.17942 6.18 <.0001logbody1 0.49599 0.07817 6.35 <.000107:04 Monday, January 14, 2019 807:04 Monday, January 14, 2019 907:04 Monday, January