1          OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 NOTE: ODS statements in the SAS Studio environment may disable some output features.
 73         
 74         /********************* cars2.sas ***************************/
 75         title 'Regression on the Metric Cars Data';
 76         
 77         /* Read data directly from Excel spreadsheet */
 78         proc import datafile="/home/u1407221/441s24/data/mcars4.xlsx"
 79                     out=cars dbms=xlsx replace;
 80                     getnames=yes;
 81         /* Input data file is mcars4.xlsx
 82            Ouput data set is called cars
 83            dbms=xlsx      The input file is an Excel spreadsheet.
 84                           Necessary to read an Excel spreadsheet directly under unix/linux
 85                           Works in PC environment too except for Excel 4.0 spreadsheets
 86                           If there are multiple sheets, use sheet="sheet1" or something.
 87            replace      If the data set cars already exists, replace it.
 88            getnames=yes   Use column names as variable names.                  */
 89         
 
 NOTE: One or more variables were converted because the data type is not supported by the V9 engine. For more details, run with 
       options MSGLEVEL=I.
 NOTE: The import data set has 100 observations and 4 variables.
 NOTE: WORK.CARS data set was successfully created.
 NOTE: PROCEDURE IMPORT used (Total process time):
       real time           0.01 seconds
       user cpu time       0.01 seconds
       system cpu time     0.01 seconds
       memory              3348.31k
       OS Memory           35836.00k
       Timestamp           02/21/2024 06:18:32 PM
       Step Count                        87  Switch Count  4
       Page Faults                       0
       Page Reclaims                     781
       Page Swaps                        0
       Voluntary Context Switches        30
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           264
       
 
 90         proc print  data=cars(obs=10);
 91              title2 'Look at first 10 lines of input data set';
 92         
 
 NOTE: There were 10 observations read from the data set WORK.CARS.
 NOTE: PROCEDURE PRINT used (Total process time):
       real time           0.03 seconds
       user cpu time       0.03 seconds
       system cpu time     0.00 seconds
       memory              2524.75k
       OS Memory           33704.00k
       Timestamp           02/21/2024 06:18:32 PM
       Step Count                        88  Switch Count  1
       Page Faults                       0
       Page Reclaims                     149
       Page Swaps                        0
       Voluntary Context Switches        6
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           8
       
 
 93         proc contents;
 94              title2 'Contents of the default data set';
 95         
 
 NOTE: PROCEDURE CONTENTS used (Total process time):
       real time           0.04 seconds
       user cpu time       0.04 seconds
       system cpu time     0.00 seconds
       memory              1511.34k
       OS Memory           34476.00k
       Timestamp           02/21/2024 06:18:32 PM
       Step Count                        89  Switch Count  1
       Page Faults                       0
       Page Reclaims                     162
       Page Swaps                        0
       Voluntary Context Switches        13
       Involuntary Context Switches      1
       Block Input Operations            0
       Block Output Operations           24
       
 
 96         data auto;
 97              set cars;
 98              mpg = 100/lper100k * 0.6214/0.2642;
 99              Country = Cntry; /* I just like the spelling more */
 100             label Country  = 'Location of Head Office'
 101                   lper100k = 'Litres per 100 kilometers'
 102                   mpg      = 'Miles per Gallon'
 103                   weight   = 'Weight in kg'
 104                   length   = 'Length in meters';
 105        /* Indicator dummy vars: Ref category is Japanese */
 106             if country = 'US' then c1=1;  else c1=0;
 107             if country = 'Europ' then c2=1;  else c2=0;
 108             if country = 'Japan' then c3=1;  else c3=0;
 109             label c1 = 'US = 1'
 110                   c2 = 'Europe = 1'
 111                   c3 = 'Japan';
 112             /* Interaction Terms */
 113             cw1 = c1*weight; cw2 = c2*weight; cw3 = c3*weight;
 114         cL1 = c1*length; cL2 = c2*length; cL3 = c3*length;
 115        
 116        /* This way of creating dummy variables is safe only because
 117           Country is never missing. If it could be missing, better is
 118             if country = ' ' then c1 = .;
 119                else if country = 'US' then c1=1;
 120                else c1=0;
 121             if country =  ' ' then c2 = .;
 122                else if country = 'Europ' then c2=1;
 123                else c2=0;
 124             if country =  ' ' then c3 = .;
 125                else if country = 'Japan' then c3=1;
 126                else c3=0;
 127        Note that a blank space is the missing value code for character variables,
 128        while a period is missing for numeric variables.  */
 129        
 
 NOTE: There were 100 observations read from the data set WORK.CARS.
 NOTE: The data set WORK.AUTO has 100 observations and 15 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              963.90k
       OS Memory           34476.00k
       Timestamp           02/21/2024 06:18:32 PM
       Step Count                        90  Switch Count  2
       Page Faults                       0
       Page Reclaims                     166
       Page Swaps                        0
       Voluntary Context Switches        16
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           272
       
 
 130        proc freq;
 131             title2 'Check dummy variables';
 132             tables (c1 c2 c3)*country / norow nocol nopercent;
 133        
 
 NOTE: There were 100 observations read from the data set WORK.AUTO.
 NOTE: PROCEDURE FREQ used (Total process time):
       real time           0.05 seconds
       user cpu time       0.05 seconds
       system cpu time     0.01 seconds
       memory              1552.93k
       OS Memory           34736.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        91  Switch Count  5
       Page Faults                       0
       Page Reclaims                     237
       Page Swaps                        0
       Voluntary Context Switches        31
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           552
       
 
 134        proc means;
 135             title2 'Means of quantitative variables';
 136             var weight length lper100k mpg;
 137        
 138        
 139        /* First an analysis with country only. */
 140        
 141        /* Questions for every significance test:
 142             * What is E(y|x) for the model SAS is using?
 143             * Give the null hypothesis in symbols.
 144             * Do you reject H0 at alpha = 0.05? Answer Yes or No.
 145             * In plain, non-statistical language, what do you conclude? */
 146        
 147        
 
 NOTE: There were 100 observations read from the data set WORK.AUTO.
 NOTE: PROCEDURE MEANS used (Total process time):
       real time           0.02 seconds
       user cpu time       0.02 seconds
       system cpu time     0.00 seconds
       memory              6584.53k
       OS Memory           40124.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        92  Switch Count  2
       Page Faults                       0
       Page Reclaims                     1468
       Page Swaps                        0
       Voluntary Context Switches        27
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           8
       
 
 148        proc means;
 149             title2 'Litres per 100 k Broken Down by Country';
 150             class Country;
 151             var lper100k;
 152        
 
 NOTE: There were 100 observations read from the data set WORK.AUTO.
 NOTE: PROCEDURE MEANS used (Total process time):
       real time           0.02 seconds
       user cpu time       0.01 seconds
       system cpu time     0.01 seconds
       memory              9060.34k
       OS Memory           43196.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        93  Switch Count  2
       Page Faults                       0
       Page Reclaims                     2009
       Page Swaps                        0
       Voluntary Context Switches        19
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           0
       
 
 153        proc reg plots=none; /* Suppress diagnostic plots for now*/
 154             title2 'Regression with Just Country';
 155             model lper100k = c1 c2;
 156             USvsEURO: test c1=c2;
 157        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.05 seconds
       user cpu time       0.05 seconds
       system cpu time     0.00 seconds
       memory              2434.21k
       OS Memory           37568.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        94  Switch Count  2
       Page Faults                       0
       Page Reclaims                     262
       Page Swaps                        0
       Voluntary Context Switches        21
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           80
       
 
 158        proc glm;
 159             title2 'Compare Oneway with proc glm';
 160             class country;
 161             model lper100k = country;
 162        
 
 NOTE: PROCEDURE GLM used (Total process time):
       real time           0.35 seconds
       user cpu time       0.13 seconds
       system cpu time     0.02 seconds
       memory              21981.09k
       OS Memory           52664.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        95  Switch Count  3
       Page Faults                       0
       Page Reclaims                     5073
       Page Swaps                        0
       Voluntary Context Switches        488
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           1352
       
 
 163        proc reg simple plots=none data=auto; /* simple gives descriptive stats */
 164             title2 'Country, Weight and Length';
 165             model lper100k = c1 c2 weight length;
 166             country: test c1 = c2 = 0;     /* Country controlling for wgt, length */
 167             USvsEURO: test c1=c2;          /* US vs. Europe controlling for wgt, length */
 168             wgt_len: test weight=length=0; /* wgt, length controlling for Country */
 169        
 170        /* Proportions of remaining variation, using a = sF/(n-p+sF) */
 171        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.09 seconds
       user cpu time       0.09 seconds
       system cpu time     0.00 seconds
       memory              3159.28k
       OS Memory           53696.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        96  Switch Count  2
       Page Faults                       0
       Page Reclaims                     313
       Page Swaps                        0
       Voluntary Context Switches        21
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           152
       
 
 172        proc iml;
 NOTE: IML Ready
 173             title2 'Proportion of remaining variation';
 174             print "Country controlling for Weight and Length";
 175             n = 100;
 175      !               p = 5;
 175      !                      s = 2;
 176             F = 6.90;
 176      !                 a = s*F/(n-p + s*F);
 177             print a;
 178        
 179             print "Weight and Length controlling for Country";
 180             F = 115.16;
 180      !                   a = s*F/(n-p + s*F);
 181             print a;
 182        
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.01 seconds
       user cpu time       0.02 seconds
       system cpu time     0.00 seconds
       memory              606.65k
       OS Memory           51876.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        97  Switch Count  1
       Page Faults                       0
       Page Reclaims                     56
       Page Swaps                        0
       Voluntary Context Switches        10
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           0
       
 
 183        proc glm data=auto plots=none;
 184             title2 'Country, weight and length with proc glm';
 185             class country;
 186             model lper100k = weight length country;
 187             lsmeans country / pdiff tdiff adjust = bon;
 188        
 189        /* Reproduce Bonferroni p-values from proc reg output */
 
 NOTE: PROCEDURE GLM used (Total process time):
       real time           0.07 seconds
       user cpu time       0.07 seconds
       system cpu time     0.00 seconds
       memory              1921.53k
       OS Memory           53176.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        98  Switch Count  3
       Page Faults                       0
       Page Reclaims                     288
       Page Swaps                        0
       Voluntary Context Switches        25
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           328
       
 
 190        proc iml;
 NOTE: IML Ready
 191             title2 "Reproduce Bonferroni p-values from proc reg output";
 192             USvsJap = 0.0010;
 192      !                        EURvsJap = 0.4448;
 192      !                                           USvsEUR = 0.0113;
 193             print "Uncorrected" USvsJap EURvsJap USvsEUR;
 194             BonUSvsJap = 3*USvsJap;
 194      !                              BonEURvsJap = 3*EURvsJap;
 194      !                                                        BonUSvsEUR = 3*USvsEUR;
 195             print "Bonferroni " BonUSvsJap BonEURvsJap BonUSvsEUR;
 196        
 197        /* Reproduce LS means from proc reg output
 198           Hold weight and length fixed at sample mean values. */
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.01 seconds
       user cpu time       0.02 seconds
       system cpu time     0.00 seconds
       memory              547.84k
       OS Memory           51876.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        99  Switch Count  1
       Page Faults                       0
       Page Reclaims                     57
       Page Swaps                        0
       Voluntary Context Switches        10
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           8
       
 
 199        proc iml;
 NOTE: IML Ready
 200             title2 "Reproduce LS means from proc reg output";
 201        /*         yhat = b0 + b1*c1 + b2*c2 + b3*xbar1      + b4*xbar2 */
 202             EuropLSM = -5.28270 - 0.50652 + 0.00546*1413.21 + 2.34597*4.8492;
 203             JapanLSM = -5.28270           + 0.00546*1413.21 + 2.34597*4.8492;
 204             US_LSM   = -5.28270  -1.99424 + 0.00546*1413.21 + 2.34597*4.8492;
 205             print EuropLSM JapanLSM US_LSM;
 206        run;
 NOTE: Module MAIN is undefined in IML; cannot be RUN.
 207        quit;
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.01 seconds
       user cpu time       0.01 seconds
       system cpu time     0.01 seconds
       memory              532.09k
       OS Memory           51876.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        100  Switch Count  1
       Page Faults                       0
       Page Reclaims                     55
       Page Swaps                        0
       Voluntary Context Switches        11
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           0
       
 
 207      !       /* Try quitting iml. Needed for ods below. */
 208        
 209        /* Reproduce LS means a more sophisticated way. */
 210        
 211        /*
 212        ods trace on;
 213        proc reg simple data=auto plots=none;
 214             model lper100k = c1 c2 weight length;
 215        run;
 216        ods trace off;
 217        */
 218        
 219        
 220        options replace=yes;
 221        ods output SimpleStatistics=simplestats;
 222        ods output ParameterEstimates=parest;
 223        proc reg simple data=auto plots=none;
 224             model lper100k = c1 c2 weight length;
 225        run;
 
 NOTE: The data set WORK.PAREST has 5 observations and 9 variables.
 NOTE: The data set WORK.SIMPLESTATS has 6 observations and 7 variables.
 226        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.06 seconds
       user cpu time       0.06 seconds
       system cpu time     0.00 seconds
       memory              3131.25k
       OS Memory           54472.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        101  Switch Count  5
       Page Faults                       0
       Page Reclaims                     518
       Page Swaps                        0
       Voluntary Context Switches        36
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           600
       
 
 227        proc print data=simplestats;
 228             title2 "Simple Statistics";
 
 NOTE: There were 6 observations read from the data set WORK.SIMPLESTATS.
 NOTE: PROCEDURE PRINT used (Total process time):
       real time           0.02 seconds
       user cpu time       0.02 seconds
       system cpu time     0.00 seconds
       memory              661.25k
       OS Memory           52392.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        102  Switch Count  1
       Page Faults                       0
       Page Reclaims                     64
       Page Swaps                        0
       Voluntary Context Switches        10
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           8
       
 
 229        proc print data=parest;
 230             title2 "Parameter Estimates";
 231        
 
 NOTE: There were 5 observations read from the data set WORK.PAREST.
 NOTE: PROCEDURE PRINT used (Total process time):
       real time           0.01 seconds
       user cpu time       0.02 seconds
       system cpu time     0.00 seconds
       memory              726.53k
       OS Memory           52392.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        103  Switch Count  1
       Page Faults                       0
       Page Reclaims                     72
       Page Swaps                        0
       Voluntary Context Switches        9
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           16
       
 
 232        proc iml;
 NOTE: IML Ready
 233             title2 "Least squares means";
 234             use simplestats;
 235             read point 4 var {Mean} into xbar1;
 236             read point 5 var {Mean} into xbar2;
 237             close simplestats;
 238             use parest;
 239             read all var {Estimate} into b;
 240             close parest;
 241             /* Calculate y-hat values: U.S. first */
 242             /* Order is   Intercept c1 c2 weight length */
 243             x =                  {1  0  0   0       0};
 243      !                                                  /* Row vector */
 244             x[2] = 1;
 244      !                x[4] = xbar1;
 244      !                              x[5] = xbar2;
 245             US = x * b;
 246             /* Set dummy variables for Europe */
 247             x[2] = 0;
 247      !                x[3] = 1;
 248             Europe = x * b;
 249             /* Now Japan */
 250             x[3]=0;
 251             Japan = x * b;
 252             print US Europe Japan;
 253        
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.01 seconds
       user cpu time       0.01 seconds
       system cpu time     0.00 seconds
       memory              798.46k
       OS Memory           52392.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        104  Switch Count  1
       Page Faults                       0
       Page Reclaims                     129
       Page Swaps                        0
       Voluntary Context Switches        9
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           16
       
 
 254        proc iml;
 NOTE: IML Ready
 255             title2 "Repeat LS means from earlier";
 256        /*         yhat = b0 + b1*c1 + b2*c2 + b3*xbar1      + b4*xbar2 */
 257             EuropLSM = -5.28270 - 0.50652 + 0.00546*1413.21 + 2.34597*4.8492;
 258             JapanLSM = -5.28270           + 0.00546*1413.21 + 2.34597*4.8492;
 259             US_LSM   = -5.28270  -1.99424 + 0.00546*1413.21 + 2.34597*4.8492;
 260             print US_LSM EuropLSM JapanLSM ;
 261        run;
 NOTE: Module MAIN is undefined in IML; cannot be RUN.
 261      !      quit;
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.01 seconds
       user cpu time       0.01 seconds
       system cpu time     0.01 seconds
       memory              531.87k
       OS Memory           52132.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        105  Switch Count  1
       Page Faults                       0
       Page Reclaims                     56
       Page Swaps                        0
       Voluntary Context Switches        10
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           0
       
 
 262        
 263        proc reg data=auto plots = none;
 264             title2 'Country, Weight and Length with Interactions';
 265             model lper100k = c1 c2 weight length cw1 cw2 cL1 cL2;
 266             country: test c1 = c2 = 0;     /* Is it really still country?  */
 267             Interactions: test cw1 = cw2 = cL1 = cL2 = 0;
 268        
 269        /* Centering an explanatory variable by subtracting off the mean affects the
 270        intercept, but not the relationships among variables. I want to create a new
 271        data set with weight and length centered. It's not an issue for these data,
 272        but it's important to sbtract off the mean of the cases used in the regression.
 273        Also, to avoid confusion I will make sure the centered variables are nicely
 274        labelled. */
 275        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.06 seconds
       user cpu time       0.07 seconds
       system cpu time     0.00 seconds
       memory              2449.12k
       OS Memory           53952.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        106  Switch Count  2
       Page Faults                       0
       Page Reclaims                     274
       Page Swaps                        0
       Voluntary Context Switches        19
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           72
       
 
 276        data auto2;
 277             set auto;
 278             utility = lper100k + c1 + c2 + weight + length;
 279             if utility = . then delete;
 280             drop utility;
 281        
 
 NOTE: There were 100 observations read from the data set WORK.AUTO.
 NOTE: The data set WORK.AUTO2 has 100 observations and 15 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              981.53k
       OS Memory           52652.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        107  Switch Count  2
       Page Faults                       0
       Page Reclaims                     140
       Page Swaps                        0
       Voluntary Context Switches        11
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           264
       
 
 282        proc standard mean=0 data=auto2 out=cntrd;
 283             var weight length;
 284        
 285        /* In the new data set "cntrd," weight and length are adjusted to have mean
 286        zero (the sample means have been subtracted from each observation). If I had
 287        said mean=0 std=1, they would have been converted to z-scores.  All the other
 288        variables (including the product terms) are as they were before, and the
 289        labels are the same as before too. */
 290        
 
 NOTE: The data set WORK.CNTRD has 100 observations and 15 variables.
 NOTE: PROCEDURE STANDARD used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              861.46k
       OS Memory           52652.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        108  Switch Count  2
       Page Faults                       0
       Page Reclaims                     113
       Page Swaps                        0
       Voluntary Context Switches        14
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           264
       
 
 291        data centered;
 292             set cntrd;  /* Now centered has everything in cntrd */
 293            /* Re-create Interaction Terms and re-label explanatory vars*/
 294             cw1 = c1*weight; cw2 = c2*weight;
 295             cL1 = c1*length; cL2 = c2*length;
 296             label weight = 'Weight in kg (Centered)'
 297                   length = 'Length in cm (Centered)';
 298        
 299        /* By default, SAS procedures use the most recently created data set,
 300           but specify it anyway. */
 301        
 
 NOTE: There were 100 observations read from the data set WORK.CNTRD.
 NOTE: The data set WORK.CENTERED has 100 observations and 15 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.00 seconds
       user cpu time       0.01 seconds
       system cpu time     0.00 seconds
       memory              993.84k
       OS Memory           52652.00k
       Timestamp           02/21/2024 06:18:33 PM
       Step Count                        109  Switch Count  2
       Page Faults                       0
       Page Reclaims                     125
       Page Swaps                        0
       Voluntary Context Switches        14
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           264
       
 
 302        proc reg plots=none simple data=centered;
 303             title2 'Weight and length are now centered: Mean=0';
 304             model lper100k = c1 c2 weight length cw1 cw2 cL1 cL2;
 305             country: test c1 = c2 = 0;     /* Does this make better sense? */
 306             Interactions: test cw1 = cw2 = cL1 = cL2 = 0;
 307        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.08 seconds
       user cpu time       0.09 seconds
       system cpu time     0.00 seconds
       memory              2418.06k
       OS Memory           53952.00k
       Timestamp           02/21/2024 06:18:34 PM
       Step Count                        110  Switch Count  2
       Page Faults                       0
       Page Reclaims                     278
       Page Swaps                        0
       Voluntary Context Switches        19
       Involuntary Context Switches      1
       Block Input Operations            0
       Block Output Operations           104
       
 
 308        proc sgplot data=centered;
 309             title2 'Look at the regression lines';
 310             reg x=weight y=lper100k / group = country;
 311        
 
 312        proc reg plots=none data=centered;
 NOTE: PROCEDURE SGPLOT used (Total process time):
       real time           0.31 seconds
       user cpu time       0.07 seconds
       system cpu time     0.01 seconds
       memory              4009.43k
       OS Memory           54956.00k
       Timestamp           02/21/2024 06:18:34 PM
       Step Count                        111  Switch Count  2
       Page Faults                       0
       Page Reclaims                     926
       Page Swaps                        0
       Voluntary Context Switches        627
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           912
       
 NOTE: There were 100 observations read from the data set WORK.CENTERED.
 
 313             title2 'Drop Length: Weight is centered';
 314             model lper100k = c1 c2 weight cw1 cw2;
 315             Interactions: test cw1 = cw2 = 0;
 316             USvsEurSlope: test cw1 = cw2;
 317        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.06 seconds
       user cpu time       0.06 seconds
       system cpu time     0.00 seconds
       memory              2618.21k
       OS Memory           55744.00k
       Timestamp           02/21/2024 06:18:34 PM
       Step Count                        112  Switch Count  2
       Page Faults                       0
       Page Reclaims                     260
       Page Swaps                        0
       Voluntary Context Switches        18
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           88
       
 
 318        proc reg plots=none data=auto;
 319             title2 'Cell means coding with interactions. Weight is uncentered.';
 320             title3 'Compare F = 4.36 for interaction';
 321             model lper100k = c1 c2 c3 cw1 cw2 cw3 / noint ;
 322             Interactions:  test cw1 = cw2 = cw3;
 323             USvsEurSlope:  test cw1 = cw2;
 324             USvsJapSlope:  test cw1 = cw3;
 325             EurvsJapSlope: test cw2 = cw3;
 326        
 327        quit;
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.08 seconds
       user cpu time       0.08 seconds
       system cpu time     0.01 seconds
       memory              2500.03k
       OS Memory           55744.00k
       Timestamp           02/21/2024 06:18:34 PM
       Step Count                        113  Switch Count  3
       Page Faults                       0
       Page Reclaims                     263
       Page Swaps                        0
       Voluntary Context Switches        29
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           144
       
 
 328        
 329        
 330        
 331        
 332        OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 344