SAS Output

Chapter 7 : Hubble example (expanded with data set 7.27)

Raw data listing

Obs	VELOCITY	DISTANCE	source
1	-220	0.2750	Original 24
2	-185	0.2750	Original 24
3	-130	0.2140	Original 24
4	-70	0.2630	Original 24
5	-30	0.9000	Original 24
6	150	0.9000	Original 24
7	170	0.0320	Original 24
8	200	0.4500	Original 24
9	200	0.6300	Original 24
10	270	0.5000	Original 24
11	290	0.0340	Original 24
12	290	0.5000	Original 24
13	300	0.8000	Original 24
14	450	1.1000	Original 24
15	500	0.9000	Original 24
16	500	1.1000	Original 24
17	500	1.4000	Original 24
18	500	2.0000	Original 24
19	630	2.1500	Added 10
20	650	0.9000	Original 24
21	800	2.0000	Original 24
22	850	2.0000	Original 24
23	890	1.8000	Added 10
24	920	1.0000	Original 24
25	960	1.7000	Original 24
26	1090	2.0000	Original 24
27	1200	.
28	2350	4.2000	Added 10
29	3810	7.2500	Added 10
30	4638	7.0000	Added 10
31	4820	9.0000	Added 10
32	5230	11.0000	Added 10
33	7500	13.8000	Added 10
34	11800	22.0000	Added 10
35	19600	32.0000	Added 10

Chapter 7 : Hubble example (expanded with data set 7.27)

Raw data listing

                        Plot of DISTANCE*VELOCITY.  Legend: A = 1 obs, B = 2 obs, etc.                         
                                                                                                               
DISTANCE |                                                                                                     
         |                                                                                                     
      35 +                                                                                                     
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         |                                                                                                 A   
         |                                                                                                     
      30 +                                                                                                     
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      25 +                                                                                                     
         |                                                                                                     
         |                                                                                                     
         |                                                              A                                      
         |                                                                                                     
      20 +                                                                                                     
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         |                                                                                                     
         |                                                                                                     
         |                                                                                                     
      15 +                                                                                                     
         |                                           A                                                         
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         |                                 A                                                                   
      10 +                                                                                                     
         |                               A                                                                     
         |                                                                                                     
         |                          A   A                                                                      
         |                                                                                                     
       5 +                                                                                                     
         |                    A                                                                                
         |                                                                                                     
         |           AADA                                                                                      
         |         AEDAA                                                                                       
       0 +        CAC                                                                                          
         |                                                                                                     
         -+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+-
        -2000      0      2000     4000     6000     8000     10000    12000    14000    16000    18000   20000
                                                                                                               
                                                        VELOCITY                                               
                                                                                                               
NOTE: 1 obs had missing values.

Chapter 7 : Hubble example (expanded with data set 7.27)

Regression without labels and with output statement

The REG Procedure

Model: MODEL1

Dependent Variable: DISTANCE

Number of Observations Read	35
Number of Observations Used	34
Number of Observations with Missing Values	1

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	1	1528.60195	1528.60195	3179.77	<.0001
Error	32	15.38328	0.48073
Corrected Total	33	1543.98523

Root MSE	0.69335	R-Square	0.9900
Dependent Mean	3.88450	Adj R-Sq	0.9897
Coeff Var	17.84902

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|	99% Confidence Limits
Intercept	1	0.39153	0.13407	2.92	0.0064	0.02437	0.75869
VELOCITY	1	0.00169	0.00002999	56.39	<.0001	0.00161	0.00177

Chapter 7 : Hubble example (expanded with data set 7.27)

Regression without labels and with output statement

Test of value from the first 24 observations

The REG Procedure

Model: MODEL1

Test Old_Model_Slope_Value Results for Dependent Variable DISTANCE
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	54.14688	112.64	<.0001
Denominator	32	0.48073

Chapter 7 : Hubble example (expanded with data set 7.27)

Regression without labels and with output statement

Listing of results from the regression output statement

Obs	VELOCITY	DISTANCE	source	yhat	stdp	lclm	uclm	lcli	ucli	resid	stdi
1	-220	0.2750	Original 24	0.0195	0.13725	-0.3564	0.3953	-1.9161	1.9550	0.25553	0.70680
2	-185	0.2750	Original 24	0.0787	0.13673	-0.2958	0.4531	-1.8566	2.0139	0.19634	0.70670
3	-130	0.2140	Original 24	0.1717	0.13592	-0.2005	0.5439	-1.7632	2.1065	0.04233	0.70654
4	-70	0.2630	Original 24	0.2731	0.13506	-0.0967	0.6430	-1.6613	2.2075	-0.01015	0.70638
5	-30	0.9000	Original 24	0.3408	0.13449	-0.0275	0.7091	-1.5933	2.2749	0.55921	0.70627
6	150	0.9000	Original 24	0.6452	0.13206	0.2836	1.0068	-1.2876	2.5781	0.25479	0.70581
7	170	0.0320	Original 24	0.6790	0.13180	0.3181	1.0400	-1.2537	2.6117	-0.64703	0.70576
8	200	0.4500	Original 24	0.7298	0.13141	0.3699	1.0896	-1.2027	2.6623	-0.27977	0.70569
9	200	0.6300	Original 24	0.7298	0.13141	0.3699	1.0896	-1.2027	2.6623	-0.09977	0.70569
10	270	0.5000	Original 24	0.8482	0.13053	0.4907	1.2056	-1.0839	2.7802	-0.34815	0.70553
11	290	0.0340	Original 24	0.8820	0.13029	0.5252	1.2388	-1.0500	2.8139	-0.84798	0.70548
12	290	0.5000	Original 24	0.8820	0.13029	0.5252	1.2388	-1.0500	2.8139	-0.38198	0.70548
13	300	0.8000	Original 24	0.8989	0.13016	0.5424	1.2553	-1.0330	2.8308	-0.09889	0.70546
14	450	1.1000	Original 24	1.1526	0.12840	0.8010	1.5042	-0.7784	3.0836	-0.05257	0.70513
15	500	0.9000	Original 24	1.2371	0.12784	0.8870	1.5872	-0.6936	3.1678	-0.33713	0.70503
16	500	1.1000	Original 24	1.2371	0.12784	0.8870	1.5872	-0.6936	3.1678	-0.13713	0.70503
17	500	1.4000	Original 24	1.2371	0.12784	0.8870	1.5872	-0.6936	3.1678	0.16287	0.70503
18	500	2.0000	Original 24	1.2371	0.12784	0.8870	1.5872	-0.6936	3.1678	0.76287	0.70503
19	630	2.1500	Added 10	1.4570	0.12646	1.1107	1.8033	-0.4731	3.3870	0.69302	0.70478
20	650	0.9000	Original 24	1.4908	0.12626	1.1451	1.8366	-0.4391	3.4207	-0.59081	0.70475
21	800	2.0000	Original 24	1.7445	0.12482	1.4027	2.0863	-0.1847	3.6737	0.25551	0.70449
22	850	2.0000	Original 24	1.8290	0.12437	1.4885	2.1696	-0.1000	3.7581	0.17095	0.70441
23	890	1.8000	Added 10	1.8967	0.12402	1.5571	2.2363	-0.0322	3.8255	-0.09670	0.70435
24	920	1.0000	Original 24	1.9474	0.12377	1.6085	2.2864	0.0187	3.8762	-0.94743	0.70431
25	960	1.7000	Original 24	2.0151	0.12344	1.6770	2.3531	0.0865	3.9437	-0.31508	0.70425
26	1090	2.0000	Original 24	2.2349	0.12245	1.8996	2.5703	0.3068	4.1630	-0.23494	0.70408
27	1200	.		2.4210	0.12171	2.0877	2.7543	0.4932	4.3487	.	0.70395
28	2350	4.2000	Added 10	4.3658	0.11921	4.0394	4.6923	2.4393	6.2924	-0.16584	0.70352
29	3810	7.2500	Added 10	6.8350	0.12991	6.4792	7.1908	4.9032	8.7667	0.41501	0.70541
30	4638	7.0000	Added 10	8.2353	0.14175	7.8471	8.6235	6.2973	10.1733	-1.23531	0.70769
31	4820	9.0000	Added 10	8.5431	0.14479	8.1466	8.9396	6.6034	10.4828	0.45690	0.70830
32	5230	11.0000	Added 10	9.2365	0.15214	8.8199	9.6531	7.2926	11.1804	1.76350	0.70984
33	7500	13.8000	Added 10	13.0755	0.20176	12.5230	13.6280	11.0980	15.0530	0.72449	0.72210
34	11800	22.0000	Added 10	20.3477	0.31524	19.4844	21.2109	18.2619	22.4334	1.65233	0.76165
35	19600	32.0000	Added 10	33.5390	0.53916	32.0625	35.0155	31.1338	35.9442	-1.53901	0.87831

Chapter 7 : Hubble example (expanded with data set 7.27)

Regression forced through the origin

The REG Procedure

Model: MODEL1

Dependent Variable: DISTANCE

Number of Observations Read	35
Number of Observations Used	34
Number of Observations with Missing Values	1

No intercept in model. R-Square is redefined.

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	1	2037.54000	2037.54000	3451.19	<.0001
Error	33	19.48280	0.59039
Uncorrected Total	34	2057.02280

Root MSE	0.76837	R-Square	0.9905
Dependent Mean	3.88450	Adj R-Sq	0.9902
Coeff Var	19.78033

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|	95% Confidence Limits
VELOCITY	1	0.00173	0.00002948	58.75	<.0001	0.00167	0.00179

Chapter 7 : Hubble example (expanded with data set 7.27)

Regression forced through the origin

Calculaton of the age of the universe (slope of velocity * 979.8)

Obs	_MODEL_	_TYPE_	_DEPVAR_	_RMSE_	VELOCITY	DISTANCE	UniverseAge
1	MODEL1	PARMS	DISTANCE	0.76837	.001731662	-1	1.69668