EXST7034 : Regression Techniques Geaghan Polynomial Regression Page 1 1 ***************************************************************; 2 *** EXST7034 Homework Example ***; 3 *** Problem from Neter, Wasserman & Kuttner 1989, Table 9.1 ***; 4 ***************************************************************; 5 6 OPTIONS LS=133 PS=256 NOCENTER NODATE NONUMBER; 7 8 DATA ONE; INFILE CARDS MISSOVER; 9 TITLE1 'EXST7034 - Example NWK Table 9.1 : Cafeteria Coffee sales'; 10 INPUT Cafteria X1 Y LINE QUAD CUBE QUAR QUIN SEST; 11 X2=X1*X1; X3=X1*X2; X4=X1*X3; X5=X1*X4; X6=X1*X5; ANOTHERX=X1; 12 D1 = X1 - 3; 13 D2=D1*D1; D3=D1*D2; D4=D1*D3; D5=D1*D4; D6=D1*D5; ANOTHERD=D1; 14 LABEL X1 = 'X : Number of Dispensers'; 15 LABEL D1 = 'X - Xmean : Deviation units'; 16 LABEL Y = 'Coffee sales (x 100 gals)'; 17 LABEL X2 = 'X Squared'; LABEL X3 = 'X Cubed'; 18 LABEL X4 = 'X**4'; LABEL X5 = 'X**5'; LABEL X6 = 'X**6'; 19 LABEL D2 = 'D Squared'; LABEL D3 = 'D Cubed'; 20 LABEL D4 = 'D**4'; LABEL D5 = 'D**5'; LABEL D6 = 'D**6'; 21 CARDS; NOTE: The data set WORK.ONE has 14 observations and 22 variables. NOTE: DATA statement used: real time 0.10 seconds 21 ! RUN; 36 ; 37 PROC IML; NOTE: IML Ready 37 ! RESET PRINT; 38 X={0, 1 , 2 , 3 , 4 , 5, 6}; 39 O=ORPOL(X,3); 39 ! RUN; NOTE: Module MAIN is undefined in IML; cannot be RUN. 40 QUIT; NOTE: Exiting IML. NOTE: The PROCEDURE IML printed page 1. NOTE: PROCEDURE IML used: real time 0.17 seconds EXST7034 - Example NWK Table 9.1 : Cafeteria Coffee sales X 7 rows 1 col (numeric) 0 1 2 3 4 5 6 O 7 rows 4 cols (numeric) 0.3779645 -0.566947 0.5455447 -0.408248 0.3779645 -0.377964 2.165E-16 0.4082483 0.3779645 -0.188982 -0.327327 0.4082483 0.3779645 -6.97E-17 -0.436436 -3.42E-17 0.3779645 0.1889822 -0.327327 -0.408248 0.3779645 0.3779645 -8.18E-17 -0.408248 0.3779645 0.5669467 0.5455447 0.4082483 The numbers in each column can be multiplied by the value: 2.645751122 5.291502711 9.16515182 2.449489686 To yield more integer like values in each column: 1 -3.00000159 5.00000000 -0.99999927 1 -1.99999753 0.00000000 1.00000000 1 -0.99999877 -3.00000165 1.00000000 1 0.00000000 -4.00000220 0.00000000 1 0.99999982 -3.00000165 -0.99999927 1 2.00000018 0.00000000 -0.99999927 1 3.00000000 5.00000000 1.00000000EXST7034 : Regression Techniques Geaghan Polynomial Regression Page 2 42 PROC PRINT DATA=ONE; VAR X1 Y D1 D2 D3 LINE QUAD CUBE QUAR QUIN SEST; 43 TITLE2 'Raw Data Listing'; RUN; NOTE: There were 14 observations read from the data set WORK.ONE. NOTE: The PROCEDURE PRINT printed page 2. NOTE: PROCEDURE PRINT used: real time 0.04 seconds EXST7034 - Example NWK Table 9.1 : Cafeteria Coffee sales Raw Data Listing Obs X1 Y D1 D2 D3 LINE QUAD CUBE QUAR QUIN SEST 1 0 508.1 -3 9 -27 -3 5 1 3 -1 1 2 0 498.4 -3 9 -27 -3 5 1 3 -1 1 3 1 568.2 -2 4 -8 -2 0 -1 -7 4 -6 4 1 577.3 -2 4 -8 -2 0 -1 -7 4 -6 5 2 651.7 -1 1 -1 -1 -3 -1 1 -5 15 6 2 657.0 -1 1 -1 -1 -3 -1 1 -5 15 7 3 713.4 0 0 0 0 -4 0 6 0 -20 8 3 697.5 0 0 0 0 -4 0 6 0 -20 9 4 755.3 1 1 1 1 -3 1 1 5 15 10 4 758.9 1 1 1 1 -3 1 1 5 15 11 5 787.6 2 4 8 2 0 1 -7 -4 -6 12 5 792.1 2 4 8 2 0 1 -7 -4 -6 13 6 841.4 3 9 27 3 5 -1 3 1 1 14 6 831.8 3 9 27 3 5 -1 3 1 1 44 OPTIONS PS=55; PROC PLOT DATA=ONE; PLOT Y*X1; RUN; OPTIONS PS=256; NOTE: There were 14 observations read from the data set WORK.ONE. NOTE: The PROCEDURE PLOT printed page 3. NOTE: PROCEDURE PLOT used: real time 0.00 seconds EXST7034 - Example NWK Table 9.1 : Cafeteria Coffee sales Raw Data Listing Plot of Y*X1. Legend: A = 1 obs, B = 2 obs, etc. | 850 + | A | A | | | 800 + | B C | o | f | f | B e 750 + e | | s | a | A l | e 700 + A s | | ( | x | | A 1 650 + A 0 | 0 | | g | a | l 600 + s | ) | | A | A | 550 + | | | | | A 500 + A ---+----------------+----------------+----------------+----------------+----------------+----------------+-- 0 1 2 3 4 5 6 X : Number of DispensersEXST7034 : Regression Techniques Geaghan Polynomial Regression Page 3 45 PROC REG DATA=ONE; TITLE2 'Fits of levels of Deviation units as a polynomial'; 46 Quadratc:MODEL Y= D1 D2 / SS1 SS2; 47 Sestic:MODEL Y = D1 D2 D3 D4