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Hubble01
Course: STAT 3201, Fall 2005School: LSU
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Hubble01 Page EXST3201 1 1 /* 2 The Big Bang 3 Edwin Hubble discovered a relationship between a nebula's distance 4 from earth and the velocity with which it was moving away from earth. 5 The data in this analysis is for the first 24 nebulae Hubble measured. 6 */ 7 8 dm'log;clear;output;clear'; 9 options nodate nocenter nonumber ps=512 ls=132; 10 ODS HTML style=minimal rs=none...
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Hubble01
Page EXST3201 1
1 /* 2 The Big Bang 3 Edwin Hubble discovered a relationship between a nebula's distance 4 from earth and the velocity with which it was moving away from earth. 5 The data in this analysis is for the first 24 nebulae Hubble measured. 6 */ 7 8 dm'log;clear;output;clear'; 9 options nodate nocenter nonumber ps=512 ls=132; 10 ODS HTML style=minimal rs=none body='C:\Geaghan\Current\EXST3201\Fall2005\SAS\Hubble01.html' ; NOTE: Writing HTML Body file: C:\Geaghan\Current\EXST3201\Fall2005\SAS\Hubble01.html 11 12 Title1 'Chapter 6 : Hubble example'; 13 filename input 'C:\Geaghan\Current\EXST3201\Datasets\ASCII\case0701.csv'; 14 15 data Hubble; infile input missover DSD dlm="," firstobs=2; 16 input VELOCITY DISTANCE; 17 label velocity = 'Velocity in km/sec' 18 distance = 'Distance in megaparsecs'; 19 datalines; NOTE: The infile INPUT is: File Name=C:\Geaghan\Current\EXST3201\Datasets\ASCII\case0701.csv, RECFM=V,LRECL=256 NOTE: 24 records were read from the infile INPUT. The minimum record length was 5. The maximum record length was 23. NOTE: The data set WORK.HUBBLE has 24 observations and 2 variables. NOTE: DATA statement used (Total process time): real time 0.15 seconds cpu time 0.00 seconds 20 run; 21 22 data madeup; VELOCITY=1200; DISTANCE=.; output; run; NOTE: The data set WORK.MADEUP has 1 observations and 2 variables. NOTE: DATA statement used (Total process time): real time 0.01 seconds cpu time 0.01 seconds 23 24 data hubble; set hubble madeup; 25 NOTE: There were 24 observations read from the data set WORK.HUBBLE. NOTE: There were 1 observations read from the data set WORK.MADEUP. NOTE: The data set WORK.HUBBLE has 25 observations and 2 variables. NOTE: DATA statement used (Total process time): real time 0.01 seconds cpu time 0.01 seconds 26 proc sort data=Hubble; by velocity; run; NOTE: There were 25 observations read from the data set WORK.HUBBLE. NOTE: The data set WORK.HUBBLE has 25 observations and 2 variables. NOTE: PROCEDURE SORT used (Total process time): real time 0.07 seconds cpu time 0.00 seconds 27 Title2 'Raw data listing'; 28 proc print data=Hubble; run; NOTE: There were 25 observations read from the data set WORK.HUBBLE. NOTE: The PROCEDURE PRINT printed page 1. NOTE: PROCEDURE PRINT used (Total process time): real time 0.13 seconds
EXST3201 Hubble01
Page 2
Chapter 6 : Hubble example Raw data listing Obs 1 2 3 4 5 6 7 8 9 10 11 VELOCITY -220 -185 -130 -70 -30 150 170 200 200 270 290 DISTANCE 0.27500 0.27500 0.21400 0.26300 0.90000 0.90000 0.03200 0.45000 0.63000 0.50000 0.03400
12 13 14 15 16 17 18 19 20 21 22 23 24 25
290 300 450 500 500 500 500 650 800 850 920 960 1090 1200
0.50000 0.80000 1.10000 0.90000 1.10000 1.40000 2.00000 0.90000 2.00000 2.00000 1.00000 1.70000 2.00000 .
29 30 31 32 33
Title2 'Regression with labels and simple output'; proc reg data=Hubble; model distance = velocity / p; run;
Chapter 6 : Hubble example Regression with labels and simple output The REG Procedure Model: MODEL1 Dependent Variable: DISTANCE Distance in megaparsecs Number of Observations Read Number of Observations Used Number of Observations with Missing Values 25 24 1
Source Model Error Corrected Total Root MSE Dependent Mean Coeff Var
DF 1 22 23
Analysis of Variance Sum of Mean Squares Square 5.97547 5.97547 3.60782 0.16399 9.58329 R-Square Adj R-Sq 0.6235 0.6064
F Value 36.44
Pr > F <.0001
0.40496 0.91137 44.43383
Variable Intercept VELOCITY
Label Intercept Velocity in km/sec
Parameter Estimates Parameter DF Estimate 1 0.39910 1 0.00137
Standard Error 0.11847 0.00022744
t Value 3.37 6.04
Pr > |t| 0.0028 <.0001
EXST3201 Hubble01 Chapter 6 : Hubble example Regression with labels and simple output The REG Procedure Model: MODEL1 Dependent Variable: DISTANCE Distance in megaparsecs OutputStatistics Dependent Predicted Variable Value 0.2750 0.0971 0.2750 0.1451 0.2140 0.2206 0.2630 0.3030 0.9000 0.3579 0.9000 0.6050 0.0320 0.6325 0.4500 0.6737 0.6300 0.6737 0.5000 0.7698 0.0340 0.7972 0.5000 0.7972 0.8000 0.8110 1.1000 1.0169 0.9000 1.0856 1.1000 1.0856 1.4000 1.0856 2.0000 1.0856 0.9000 1.2915 2.0000 1.4974 2.0000 1.5661 1.0000 1.6622 1.7000 1.7171 2.0000 1.8956 . 2.0466
Page 3
Obs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Residual 0.1779 0.1299 -0.006617 -0.0400 0.5421 0.2950 -0.6005 -0.2237 -0.0437 -0.2698 -0.7632 -0.2972 -0.0110 0.0831 -0.1856 0.0144 0.3144 0.9144 -0.3915 0.5026 0.4339 -0.6622 -0.0171 0.1044 . 0 3.60782 4.20513
Sum of Residuals Sum of Squared Residuals Predicted Residual SS (PRESS)
35 options nolabel; 36 Title2 'Regression without labels and with output statement'; NOTE: The PROCEDURE REG printed pages 2-3. NOTE: PROCEDURE REG used (Total process time): real time 0.28 seconds cpu time 0.04 seconds 37 proc reg data=Hubble; 38 model distance = velocity / clb; 39 test velocity = 0.0015; 40 output out=next1 r=resid p=yhat lclm=lclm uclm=uclm lcl=lcli ucl=ucli stdp=stdp stdi=stdi; 41 run;
EXST3201 Hubble01 Chapter 6 : Hubble example Regression without labels and with output statement The REG Procedure Model: MODEL1 Dependent Variable: DISTANCE Number of Observations Read Number of Observations Used Number of Observations with Missing Values 25 24 1
Page 4
Source Model Error Corrected Total Root MSE Dependent Mean Coeff Var
DF 1 22 23
Analysis of Variance Sum of Mean Squares Square 5.97547 5.97547 3.60782 0.16399 9.58329 R-Square Adj R-Sq 0.6235 0.6064
F Value 36.44
Pr > F <.0001
0.40496 0.91137 44.43383
Parameter Estimate 0.39910 0.00137
Variable Intercept VELOCITY
DF 1 1
Parameter Estimates Standard Error t Value 0.11847 3.37 0.00022744 6.04
Pr > |t| 0.0028 <.0001
95% Confidence Limits 0.15341 0.64479 0.00090125 0.00184
Model: MODEL1 Test 1 Results for Dependent Variable DISTANCE Mean Source DF Square F Value Pr > F Numerator 1 0.05118 0.31 0.5820 Denominator 22 0.16399
42 43 Title3 'Listing of results from the regression output statement'; NOTE: The data set WORK.NEXT1 has 25 observations and 10 variables. NOTE: The PROCEDURE REG printed pages 4-5. NOTE: PROCEDURE REG used (Total process time): real time 0.03 seconds cpu time 0.03 seconds 44 proc print data=next1; run; NOTE: There were 25 observations read from the data set WORK.NEXT1. NOTE: The PROCEDURE PRINT printed page 6. NOTE: PROCEDURE PRINT used (Total process time): real time 0.03 seconds cpu time 0.03 seconds
EXST3201 Hubble01
Page 5
Chapter 6 : Hubble example Regression without labels and with output statement Listing of results from the regression output statement Obs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 VELOCITY -220 -185 -130 -70 -30 150 170 200 270 200 290 290 300 450 500 500 500 500 650 800 850 920 960 1090 1200 DISTANCE 0.27500 0.27500 0.21400 0.26300 0.90000 0.90000 0.03200 0.45000 0.63000 0.50000 0.03400 0.50000 0.80000 1.10000 0.90000 1.10000 1.40000 2.00000 0.90000 2.00000 2.00000 1.00000 1.70000 2.00000 . yhat 0.09705 0.14511 0.22062 0.30299 0.35791 0.60504 0.63250 0.67369 0.67369 0.76979 0.79725 0.79725 0.81098 1.01692 1.08557 1.08557 1.08557 1.08557 1.29151 1.49745 1.56609 1.66220 1.71712 1.89560 2.04662 stdp 0.15821 0.15148 0.14117 0.13035 0.12345 0.09700 0.09470 0.09156 0.09156 0.08593 0.08480 0.08480 0.08432 0.08449 0.08755 0.08755 0.08755 0.08755 0.10392 0.12751 0.13637 0.14935 0.15700 0.18281 0.20543 lclm -0.23106 -0.16905 -0.07214 0.03267 0.10189 0.40388 0.43611 0.48380 0.48380 0.59159 0.62139 0.62139 0.63611 0.84170 0.90399 0.90399 0.90399 0.90399 1.07600 1.23300 1.28328 1.35247 1.39151 1.51648 1.62058 uclm 0.42517 0.45926 0.51338 0.57332 0.61393 0.80620 0.82889 0.86357 0.86357 0.94799 0.97311 0.97311 0.98584 1.19214 1.26714 1.26714 1.26714 1.26714 1.50702 1.76189 1.84891 1.97192 2.04272 2.27471 2.47266 lcli -0.80460 -0.75156 -0.66878 -0.57928 -0.52008 -0.25855 -0.22999 -0.18735 -0.18735 -0.08874 -0.06080 -0.06080 -0.04687 0.15900 0.22633 0.22633 0.22633 0.22633 0.42446 0.61696 0.67992 0.76707 0.81637 0.97416 1.10490 ucli 0.99871 1.04177 1.11001 1.18526 1.23590 1.46863 1.49499 1.53472 1.53472 1.62832 1.65530 1.65530 1.66882 1.87484 1.94480 1.94480 1.94480 1.94480 2.15855 2.37793 2.45227 2.55732 2.61786 2.81704 2.98834 resid 0.17795 0.12989 -0.00662 -0.03999 0.54209 0.29496 -0.60050 -0.22369 -0.04369 -0.26979 -0.76325 -0.29725 -0.01098 0.08308 -0.18557 0.01443 0.31443 0.91443 -0.39151 0.50255 0.43391 -0.66220 -0.01712 0.10440 . stdi 0.43477 0.43236 0.42886 0.42542 0.42336 0.41641 0.41588 0.41518 0.41518 0.41397 0.41374 0.41374 0.41364 0.41368 0.41432 0.41432 0.41432 0.41432 0.41808 0.42456 0.42730 0.43162 0.43433 0.44431 0.45409
46 Title2 'Regression forced through the origin'; 47 proc reg data=Hubble; 48 model distance = velocity / noint; 49 run; NOTE: The PROCEDURE REG printed page 7. NOTE: PROCEDURE REG used (Total process time): real time 0.01 seconds cpu time 0.01 seconds
EXST3201 Hubble01 Chapter 6 : Hubble example Regression forced through the origin The REG Procedure Model: MODEL1 Dependent Variable: DISTANCE Number of Observations Read Number of Observations Used Number of Observations with Missing Values NOTE: No intercept in model. R-Square is redefined. Analysis of Variance Sum of Mean Squares Square 24.04889 24.04889 5.46890 0.23778 29.51780 R-Square Adj R-Sq 0.8147 0.8067 25 24 1
Page 6
Source Model Error Uncorrected Total Root MSE Dependent Mean Coeff Var
DF 1 23 24
F Value 101.14
Pr > F <.0001
0.48763 0.91137 53.50434
Parameter Estimate 0.00192
Variable VELOCITY
DF 1
Parameter Estimates Standard Error t Value 0.00019109 10.06
Pr > |t| <.0001
95% Confidence Limits 0.00153 0.00232
One megaparsec = 979.8 billion years, estimate = 0.00192*979.8 = 1.88 billion years with a range of 1.50 to 2.27 billion years.
51 Title2 'Regression with PROC MIXED'; 52 proc mixed data=Hubble; 53 model distance = velocity; 54 run; NOTE: 1 observation is not included because of missing values. NOTE: The PROCEDURE MIXED printed page 8. NOTE: PROCEDURE MIXED used (Total process time): real time 0.10 seconds cpu time 0.01 seconds Chapter 6 : Hubble example Regression with PROC MIXED The Mixed Procedure Model Information Data Set WORK.HUBBLE Dependent Variable DISTANCE Covariance Structure Diagonal Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Residual Dimensions Covariance Parameters Columns in X Columns in Z Subjects Max Obs Per Subject
1 2 0 1 25
EXST3201 Hubble01
Page 7
Number of Observations Number of Observations Read Number of Observations Used Number of Observations Not Used Covariance Parameter Estimates Cov Parm Estimate Residual 0.1640 FitStatistics -2 Res Log Likelihood AIC (s...
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References G. Aigner and U. Hozle, Eliminating Virual Function Calls in C+ Programs, ECOOP96. L. O. Andersen. Program analysis and specialization for the C programming language. PhD thesis, DIKU, University of Copenhagen, 1994. Also availab
Virginia Tech - ETD - 05152008
Chapter 1: Rethinking the Concept of ShiLao Zi,8 the philosopher of ancient China and the central figure in Taoism, uses the word shi in his Dao de jing to refer to the environment. He writes, The Tao (Dao) engenders them, And its Te (de) cultivates
Virginia Tech - ETD - 05152008
Chapter 2: The Shi of Huizhou Merchants and Craftsmen around 1800 A.D.In this chapter, the Huizhou culture is briefly explored to establish the context for the later discussions of shi manifested in different house doors. Two groups of Huizhou peopl
Virginia Tech - ETD - 05152008
Chapter 3: The Door as a Clever Device with Crafty ConstructsThe advantageous shi generated by setting up cunning strategies in warfare as in Sun Zis The Art of War is also evident in the clever construction techniques of the traditional Chinese doo