SAS Output

Data from Intel Corporation

Increasing power of Intel computer processor chips over years

Raw data Listing

Obs	CHIP	YEAR	TRANS	logTRANS	MIPS
1	4004	1971	2.3	0.8329	0.042
2	8008	1972	2.5	0.9163	0.045
3	8080	1974	4.5	1.5041	0.082
4	8086	1978	29.0	3.3673	0.527
5	80286	1982	134.0	4.8978	2.436
6	80386	1985	275.0	5.6168	5.000
7	80486	1989	1200.0	7.0901	21.818
8	Pentium (5)	1993	3100.0	8.0392	56.364
9	Pentium Pro (6)	1995	5500.0	8.6125	100.000
10	Pentium II	1997	7500.0	8.9227	136.364
11	Pentium III	1999	9500.0	9.1590	172.727
12	Pentium 4	2000	42000.0	10.6454	763.636

Data from Intel Corporation

Increasing power of Intel computer processor chips over years

Plot of the raw data

                            Plot of TRANS*YEAR.  Legend: A = 1 obs, B = 2 obs, etc.                            
                                                                                                               
       TRANS |                                                                                                 
             |                                                                                                 
       50000 +                                                                                                 
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             |                                                                                      A          
       40000 +                                                                                                 
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       30000 +                                                                                                 
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       20000 +                                                                                                 
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       10000 +                                                                                   A             
             |                                                                                                 
             |                                                                              A                  
             |                                                                        A                        
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             |                                                                  A                              
             |                                                       A                                         
           0 +     A  A    A          A           A       A                                                    
             |                                                                                                 
             ---+-------------+-------------+-------------+-------------+-------------+-------------+--        
              1970          1975          1980          1985          1990          1995          2000         
                                                                                                               
                                                        YEAR

Data from Intel Corporation

Increasing power of Intel computer processor chips over years

Plot of the log transformed data

                          Plot of logTRANS*YEAR.  Legend: A = 1 obs, B = 2 obs, etc.                           
                                                                                                               
      logTRANS |                                                                                               
               |                                                                                               
            12 +                                                                                               
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               |                                                                                      A        
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            10 +                                                                                               
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               |                                                                              A    A           
               |                                                                        A                      
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             8 +                                                                  A                            
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             6 +                                                                                               
               |                                            A                                                  
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               |                                    A                                                          
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             4 +                                                                                               
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               |                        A                                                                      
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             2 +                                                                                               
               |             A                                                                                 
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               |        A                                                                                      
               |     A                                                                                         
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             0 +                                                                                               
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               ---+-------------+-------------+-------------+-------------+-------------+-------------+--      
                1970          1975          1980          1985          1990          1995          2000       
                                                                                                               
                                                          YEAR

Data from Intel Corporation

Increasing power of Intel computer processor chips over years

Computer Chip example using REG with CLM

The REG Procedure

Model: MODEL1

Dependent Variable: logTRANS

Number of Observations Read	12
Number of Observations Used	12

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	1	131.29985	131.29985	850.47	<.0001
Error	10	1.54386	0.15439
Corrected Total	11	132.84371

Root MSE	0.39292	R-Square	0.9884
Dependent Mean	5.80034	Adj R-Sq	0.9872
Coeff Var	6.77408

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|	95% Confidence Limits
Intercept	1	-632.78864	21.89772	-28.90	<.0001	-681.57980	-583.99749
YEAR	1	0.32150	0.01102	29.16	<.0001	0.29694	0.34607

Data from Intel Corporation

Increasing power of Intel computer processor chips over years

Computer Chip example using REG with CLM

The REG Procedure

Model: MODEL1

Dependent Variable: logTRANS

Output Statistics
Obs	YEAR	Dependent Variable	Predicted Value	Std Error Mean Predict	95% CL Mean		95% CL Predict		Residual
1	1971	0.8329	0.8974	0.2028	0.4455	1.3493	-0.0878	1.8826	-0.0645
2	1972	0.9163	1.2189	0.1938	0.7872	1.6506	0.2427	2.1950	-0.3026
3	1974	1.5041	1.8619	0.1764	1.4689	2.2549	0.9023	2.8215	-0.3578
4	1978	3.3673	3.1479	0.1454	2.8240	3.4719	2.2144	4.0814	0.2194
5	1982	4.8978	4.4339	0.1227	4.1605	4.7074	3.5168	5.3511	0.4639
6	1985	5.6168	5.3985	0.1143	5.1439	5.6530	4.4867	6.3102	0.2183
7	1989	7.0901	6.6845	0.1174	6.4229	6.9461	5.7707	7.5982	0.4056
8	1993	8.0392	7.9705	0.1357	7.6682	8.2728	7.0443	8.8967	0.0687
9	1995	8.6125	8.6135	0.1489	8.2817	8.9453	7.6773	9.5497	-0.001002
10	1997	8.9227	9.2565	0.1640	8.8910	9.6220	8.3078	10.2052	-0.3339
11	1999	9.1590	9.8995	0.1806	9.4971	10.3020	8.9360	10.8631	-0.7405
12	2000	10.6454	10.2210	0.1893	9.7992	10.6429	9.2492	11.1928	0.4244

Sum of Residuals	-5.6503E-13
Sum of Squared Residuals	1.54386
Predicted Residual SS (PRESS)	2.30901

Data from Intel Corporation

Increasing power of Intel computer processor chips over years

Computer Chip example using REG with CLM

The REG Procedure

Model: MODEL1

Test 1 Results for Dependent Variable logTRANS
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	25.07333	162.41	<.0001
Denominator	10	0.15439

Data from Intel Corporation

Increasing power of Intel computer processor chips over years

Plot of residuals

                            Plot of resid*YEAR.  Legend: A = 1 obs, B = 2 obs, etc.                            
                                                                                                               
       resid |                                                                                                 
             |                                                                                                 
         0.6 +                                                                                                 
             |                                                                                                 
             |                                                                                                 
             |                                    A                                                            
         0.4 +                                                       A                              A          
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         0.2 +                        A                   A                                                    
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             |                                                                  A                              
         0.0 +------------------------------------------------------------------------A----------------        
             |     A                                                                                           
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        -0.2 +                                                                                                 
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             |        A                                                                                        
             |             A                                                                A                  
        -0.4 +                                                                                                 
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        -0.6 +                                                                                                 
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             |                                                                                   A             
        -0.8 +                                                                                                 
             |                                                                                                 
             ---+-------------+-------------+-------------+-------------+-------------+-------------+--        
              1970          1975          1980          1985          1990          1995          2000         
                                                                                                               
                                                        YEAR

Data from Intel Corporation

Increasing power of Intel computer processor chips over years

Plot of residuals

The UNIVARIATE Procedure

Variable: resid

Moments
N	12	Sum Weights	12
Mean	0	Sum Observations	0
Std Deviation	0.37463418	Variance	0.14035077
Skewness	-0.5243539	Kurtosis	-0.4472994
Uncorrected SS	1.54385842	Corrected SS	1.54385842
Coeff Variation	.	Std Error Mean	0.10814757

Basic Statistical Measures
Location		Variability
Mean	0.000000	Std Deviation	0.37463
Median	0.033830	Variance	0.14035
Mode	.	Range	1.20437
		Interquartile Range	0.63072

Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	0	Pr > \|t\|	1.0000
Sign	M	0	Pr >= \|M\|	1.0000
Signed Rank	S	3	Pr >= \|S\|	0.8501

Tests for Normality
Test	Statistic		p Value
Shapiro-Wilk	W	0.939064	Pr < W	0.4860
Kolmogorov-Smirnov	D	0.136633	Pr > D	>0.1500
Cramer-von Mises	W-Sq	0.040599	Pr > W-Sq	>0.2500
Anderson-Darling	A-Sq	0.292949	Pr > A-Sq	>0.2500

Quantiles (Definition 5)
Quantile	Estimate
100% Max	0.4638977
99%	0.4638977
95%	0.4638977
90%	0.4243957
75% Q3	0.3124870
50% Median	0.0338302
25% Q1	-0.3182297
10%	-0.3578260
5%	-0.7404772
1%	-0.7404772
0% Min	-0.7404772

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
-0.7404772	11	0.218314	6
-0.3578260	3	0.219373	4
-0.3338563	10	0.405601	7
-0.3026030	2	0.424396	12
-0.0644798	1	0.463898	5

Data from Intel Corporation

Increasing power of Intel computer processor chips over years

Plot of residuals

The UNIVARIATE Procedure

Variable: resid

   Stem Leaf                     #  Boxplot                        Normal Probability Plot                     
      4 126                      3     |         0.5+                                 *  *++++*                
      2 22                       2  +-----+         |                            * *+++++                      
      0 7                        1  *--+--*         |                         +*++++                           
     -0 60                       2  |     |     -0.1+                    ++*+*                                 
     -2 630                      3  +-----+         |              *++*++*                                     
     -4                                |            |         ++++++                                           
     -6 4                        1     |        -0.7+    +++++*                                                
        ----+----+----+----+                         +----+----+----+----+----+----+----+----+----+----+       
    Multiply Stem.Leaf by 10**-1                         -2        -1         0        +1        +2