1          OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 72         
 73         /* MathReg2.sas  */
 74         %include '/home/u1407221/441s24/SAS08/ReadLabelMath2.sas';
 NOTE: Format YNFMT is already on the library WORK.FORMATS.
 NOTE: Format YNFMT has been output.
 NOTE: Format CRSFMT is already on the library WORK.FORMATS.
 NOTE: Format CRSFMT has been output.
 NOTE: Format NFMT is already on the library WORK.FORMATS.
 NOTE: Format NFMT has been output.
 NOTE: Format NCFMT is already on the library WORK.FORMATS.
 NOTE: Format NCFMT has been output.
 
 NOTE: PROCEDURE FORMAT used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              250.09k
       OS Memory           30116.00k
       Timestamp           02/23/2024 08:05:49 PM
       Step Count                        124  Switch Count  0
       Page Faults                       0
       Page Reclaims                     26
       Page Swaps                        0
       Voluntary Context Switches        0
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           32
       
 
 
 NOTE: The infile '/home/u1407221/441s24/data/math.data.txt' is:
       Filename=/home/u1407221/441s24/data/math.data.txt,
       Owner Name=u1407221,Group Name=oda,
       Access Permission=-rw-r--r--,
       Last Modified=10Feb2024:16:04:10,
       File Size (bytes)=90324
 
 NOTE: 1158 records were read from the infile '/home/u1407221/441s24/data/math.data.txt'.
       The minimum record length was 76.
       The maximum record length was 76.
 NOTE: Missing values were generated as a result of performing an operation on missing values.
       Each place is given by: (Number of times) at (Line):(Column).
       180 at 120:24   
 NOTE: The data set WORK.MATH has 1158 observations and 37 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              1176.40k
       OS Memory           30888.00k
       Timestamp           02/23/2024 08:05:49 PM
       Step Count                        125  Switch Count  2
       Page Faults                       0
       Page Reclaims                     167
       Page Swaps                        0
       Voluntary Context Switches        19
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           776
       
 
 
 NOTE: There were 1158 observations read from the data set WORK.MATH.
 NOTE: The data set WORK.REPLIC has 579 observations and 37 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              1411.71k
       OS Memory           31276.00k
       Timestamp           02/23/2024 08:05:49 PM
       Step Count                        126  Switch Count  2
       Page Faults                       0
       Page Reclaims                     155
       Page Swaps                        0
       Voluntary Context Switches        15
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           520
       
 
 
 NOTE: There were 1158 observations read from the data set WORK.MATH.
 NOTE: The data set WORK.EXPLORE has 579 observations and 28 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              1407.28k
       OS Memory           31276.00k
       Timestamp           02/23/2024 08:05:49 PM
       Step Count                        127  Switch Count  2
       Page Faults                       0
       Page Reclaims                     130
       Page Swaps                        0
       Voluntary Context Switches        14
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           520
       
 
 235        title2 'Basic Regression Diagnostics';
 236        
 237        proc reg data = explore plots(only) = ResidualPlot;
 238             title3 'Model I: hsgpa hscalc hsengl totscore mtongue';
 239             model grade = hsgpa hscalc hsengl totscore mtongue;
 240             output out = Explor H         = hatval
 241                                 predicted = yhat
 242                                 residual  = resid
 243                                 rstudent  = delstud;
 244                                          /* Deleted Studentized Residual */
 245        /* Could have included LCL and UCL for upper and lower limits of a
 246           95% prediction interval for each case in the file */
 247        
 248        /*  proc contents; */
 249        
 250        /* Rules of thumb say investigate x values for outliers if
 251             * Hat value > 3p/n (Is residual close to the error term?)
 252             * Hat value > 0.2  (Is betahat approximtely multivariate normal?)   */
 253        
 
 NOTE: The data set WORK.EXPLOR has 579 observations and 32 variables.
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.43 seconds
       user cpu time       0.23 seconds
       system cpu time     0.03 seconds
       memory              26998.03k
       OS Memory           54212.00k
       Timestamp           02/23/2024 08:05:49 PM
       Step Count                        128  Switch Count  4
       Page Faults                       0
       Page Reclaims                     6457
       Page Swaps                        0
       Voluntary Context Switches        354
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           3288
       
 
 254        proc iml;
 NOTE: IML Ready
 255             n = 289;
 255      !               p = 6;
 255      !                      ceiling = 3*p/n;
 256             print "Investigate x if hat values are > 0.2 or greater than " ceiling;
 257        
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.03 seconds
       user cpu time       0.03 seconds
       system cpu time     0.00 seconds
       memory              1121.06k
       OS Memory           52656.00k
       Timestamp           02/23/2024 08:05:49 PM
       Step Count                        129  Switch Count  0
       Page Faults                       0
       Page Reclaims                     199
       Page Swaps                        0
       Voluntary Context Switches        0
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           144
       
 
 258        proc univariate plot data=Explor;
 259             var hatval;
 260             where grade ne .;
 261        
 
 NOTE: PROCEDURE UNIVARIATE used (Total process time):
       real time           0.25 seconds
       user cpu time       0.12 seconds
       system cpu time     0.01 seconds
       memory              4784.62k
       OS Memory           54448.00k
       Timestamp           02/23/2024 08:05:50 PM
       Step Count                        130  Switch Count  3
       Page Faults                       0
       Page Reclaims                     933
       Page Swaps                        0
       Voluntary Context Switches        342
       Involuntary Context Switches      1
       Block Input Operations            0
       Block Output Operations           928
       
 
 262        proc sgplot;
 263             histogram hatval;
 264             where grade ne .;
 265        
 
 266        proc sort data=Explor;
 NOTE: PROCEDURE SGPLOT used (Total process time):
       real time           0.16 seconds
       user cpu time       0.06 seconds
       system cpu time     0.00 seconds
       memory              3407.06k
       OS Memory           55216.00k
       Timestamp           02/23/2024 08:05:50 PM
       Step Count                        131  Switch Count  7
       Page Faults                       0
       Page Reclaims                     689
       Page Swaps                        0
       Voluntary Context Switches        265
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           592
       
 NOTE: There were 393 observations read from the data set WORK.EXPLOR.
       WHERE grade not = .;
 
 267             by hatval;
 
 NOTE: There were 579 observations read from the data set WORK.EXPLOR.
 NOTE: The data set WORK.EXPLOR has 579 observations and 32 variables.
 NOTE: PROCEDURE SORT used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              1711.56k
       OS Memory           55220.00k
       Timestamp           02/23/2024 08:05:50 PM
       Step Count                        132  Switch Count  2
       Page Faults                       0
       Page Reclaims                     131
       Page Swaps                        0
       Voluntary Context Switches        11
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           520
       
 
 268        proc print data = Explor;
 269             where hatval > 0.06228 and grade ne .;
 270             var id hatval  hsgpa hscalc hsengl totscore mtongue grade delstud;
 271        
 272        /* Try re-running the analysis without the two suspect observations */
 273        
 
 NOTE: There were 2 observations read from the data set WORK.EXPLOR.
       WHERE (hatval>0.06228) and (grade not = .);
 NOTE: PROCEDURE PRINT used (Total process time):
       real time           0.01 seconds
       user cpu time       0.01 seconds
       system cpu time     0.00 seconds
       memory              1129.53k
       OS Memory           54700.00k
       Timestamp           02/23/2024 08:05:50 PM
       Step Count                        133  Switch Count  0
       Page Faults                       0
       Page Reclaims                     99
       Page Swaps                        0
       Voluntary Context Switches        0
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           8
       
 
 274        proc reg plots=none data=explore;
 275             title3 'Re-running without participants 50 and 340';
 276             model grade = hsgpa hscalc hsengl totscore mtongue;
 277             where id ne 340 and id ne 50;
 278        
 279        /* What is a big (Studentized deleted) residual? If the model is correct,
 280           each one has a t distribution with n-p-1 = 283 df (practically standard
 281           normal), so the Studentized deleted residual can be treated directly as
 282           a t-test statistic. Values that are too big in absolute value will cause
 283           rejection of the null hypothesis that x_i*beta is the same for this case
 284           and the other n-1 cases. Tests are NOT independent, but use a Bonferroni
 285           correction for n = 289 tests. Get the critical value from proc iml. */
 286        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.04 seconds
       user cpu time       0.04 seconds
       system cpu time     0.00 seconds
       memory              3358.37k
       OS Memory           56516.00k
       Timestamp           02/23/2024 08:05:50 PM
       Step Count                        134  Switch Count  4
       Page Faults                       0
       Page Reclaims                     309
       Page Swaps                        0
       Voluntary Context Switches        17
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           80
       
 
 287        proc iml;
 NOTE: IML Ready
 288             title3 'Critical value for Joint t-test on Studentized Deleted Residuals';
 289             Alpha = 0.05/289;
 289      !                        print Alpha;
 290             Critval = tinv(1-Alpha/2,283);
 290      !                                     print Critval;
 291        
 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              577.21k
       OS Memory           54436.00k
       Timestamp           02/23/2024 08:05:50 PM
       Step Count                        135  Switch Count  1
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       Page Reclaims                     56
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       Voluntary Context Switches        7
       Involuntary Context Switches      0
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       Block Output Operations           72
       
 
 292        proc univariate data=Explor normal plot;
 293             title3 'Studentized Deleted Residuals';
 294             var delstud;
 295        
 296        /* Tests for normality indicate residuals are not normal. One st resid
 297        greater than critical value. */
 298        
 
 NOTE: PROCEDURE UNIVARIATE used (Total process time):
       real time           0.24 seconds
       user cpu time       0.13 seconds
       system cpu time     0.01 seconds
       memory              4142.53k
       OS Memory           56236.00k
       Timestamp           02/23/2024 08:05:50 PM
       Step Count                        136  Switch Count  1
       Page Faults                       0
       Page Reclaims                     787
       Page Swaps                        0
       Voluntary Context Switches        365
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           944
       
 
 299        proc print data=Explor;
 300             title3 'Large Negative Studentized Deleted Residual';
 301             where delstud < -3.81 and delstud ne .;
 302        
 303         /* Next, a few more plots. */
 304        
 
 NOTE: There were 1 observations read from the data set WORK.EXPLOR.
       WHERE (delstud<-3.81) and (delstud not = .);
 NOTE: PROCEDURE PRINT used (Total process time):
       real time           0.02 seconds
       user cpu time       0.03 seconds
       system cpu time     0.00 seconds
       memory              1428.78k
       OS Memory           55468.00k
       Timestamp           02/23/2024 08:05:50 PM
       Step Count                        137  Switch Count  1
       Page Faults                       0
       Page Reclaims                     99
       Page Swaps                        0
       Voluntary Context Switches        10
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           40
       
 
 305        proc sgplot data=Explor;
 306             title3 'Plot of Y-hat by Y';
 307             scatter y=grade x=yhat;
 308        
 
 309        proc sgplot data=Explor;
 NOTE: PROCEDURE SGPLOT used (Total process time):
       real time           0.16 seconds
       user cpu time       0.08 seconds
       system cpu time     0.01 seconds
       memory              2849.96k
       OS Memory           56236.00k
       Timestamp           02/23/2024 08:05:50 PM
       Step Count                        138  Switch Count  2
       Page Faults                       0
       Page Reclaims                     571
       Page Swaps                        0
       Voluntary Context Switches        249
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           832
       
 NOTE: There were 579 observations read from the data set WORK.EXPLOR.
 
 310             title3 'Calculus sub-test by deleted studentized residual';
 311             scatter x=calc y=delstud;
 312        
 
 313        proc sgplot data=Explor;
 NOTE: PROCEDURE SGPLOT used (Total process time):
       real time           0.16 seconds
       user cpu time       0.07 seconds
       system cpu time     0.01 seconds
       memory              3403.25k
       OS Memory           56236.00k
       Timestamp           02/23/2024 08:05:50 PM
       Step Count                        139  Switch Count  2
       Page Faults                       0
       Page Reclaims                     562
       Page Swaps                        0
       Voluntary Context Switches        252
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           864
       
 NOTE: There were 579 observations read from the data set WORK.EXPLOR.
 
 314             title3 'Pre-calculus sub-test by deleted studentized residual';
 315             scatter x=precalc y=delstud;
 316        
 
 317        proc sgplot data=Explor;
 NOTE: PROCEDURE SGPLOT used (Total process time):
       real time           0.14 seconds
       user cpu time       0.07 seconds
       system cpu time     0.00 seconds
       memory              3387.75k
       OS Memory           56236.00k
       Timestamp           02/23/2024 08:05:51 PM
       Step Count                        140  Switch Count  2
       Page Faults                       0
       Page Reclaims                     552
       Page Swaps                        0
       Voluntary Context Switches        250
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           856
       
 NOTE: There were 579 observations read from the data set WORK.EXPLOR.
 
 318             title3 'Mother tongue by deleted studentized residual';
 319             scatter x=mtongue y=delstud;
 320        
 321        quit;
 
 NOTE: PROCEDURE SGPLOT used (Total process time):
       real time           0.15 seconds
       user cpu time       0.07 seconds
       system cpu time     0.01 seconds
       memory              3501.25k
       OS Memory           56236.00k
       Timestamp           02/23/2024 08:05:51 PM
       Step Count                        141  Switch Count  2
       Page Faults                       0
       Page Reclaims                     554
       Page Swaps                        0
       Voluntary Context Switches        253
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           856
       
 NOTE: There were 579 observations read from the data set WORK.EXPLOR.
 
 322        
 323        
 324        OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 336