1          OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 72         
 73         /* MathReg3.sas  */
 74         %include '/home/u1407221/441s24/SAS08/ReadLabelMath2.sas';
 NOTE: Format YNFMT has been output.
 NOTE: Format CRSFMT has been output.
 NOTE: Format NFMT has been output.
 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              327.93k
       OS Memory           25252.00k
       Timestamp           02/24/2024 05:11:05 PM
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 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           0.02 seconds
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       memory              1176.34k
       OS Memory           26536.00k
       Timestamp           02/24/2024 05:11:05 PM
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       Involuntary Context Switches      0
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       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              1412.75k
       OS Memory           26924.00k
       Timestamp           02/24/2024 05:11:05 PM
       Step Count                        26  Switch Count  2
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       Voluntary Context Switches        13
       Involuntary Context Switches      0
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       Block Output Operations           528
       
 
 
 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       0.00 seconds
       system cpu time     0.00 seconds
       memory              1409.87k
       OS Memory           26924.00k
       Timestamp           02/24/2024 05:11:05 PM
       Step Count                        27  Switch Count  2
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 235        title2 'Replication and Prediction';
 236        
 237        /* Plan:
 238        
 239        1. Non-obvious findings from the exploratory analysis (based on Model I,
 240            which predicts grade from hsgpa hscalc hsengl totscore mtongue) were
 241              a. HS Engl negative
 242              b. mtongue negative
 243              c. totscore positive (diagnostic test matters controlling for HS)
 244           Test these on the replication with a Bonferroni correction for 3 tests.
 245           The other two results (HS GPA and HS Calculus) were obvious.
 246        
 247        2. See if prediction intervals work as advertised on replication data.
 248        
 249        3. Try prediction of letter grade.
 250        
 251        4. Try predictions of grade for some imaginary students.
 252        
 253        /* Test the three findings: Point 1 above */
 254        
 255        proc reg data = replic  plots = none;
 256             title3 'Try to replicate HS Engl neg, mtongue neg, totscore pos';
 257             title4 'with a Bonferroni correction (check p < 0.05/3 = 0.01666667)';
 258             model grade = hsgpa hscalc hsengl totscore mtongue;
 259        
 260        /* Point 2: Look at prediction intervals  */
 261        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.06 seconds
       user cpu time       0.06 seconds
       system cpu time     0.02 seconds
       memory              5302.25k
       OS Memory           30400.00k
       Timestamp           02/24/2024 05:11:05 PM
       Step Count                        28  Switch Count  3
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 262        data predict;
 263             set math; /* Combined data set */
 264             keeper =  grade+hsgpa+hscalc+hsengl+totscore+mtongue;
 265             /* keeper will be missing if any of the vars are missing */
 266             if keeper ne .; /* Discards all other cases */
 267             grade2 = grade; /* Save value of grade for future use */
 268             if sample=2 then grade=. ;
 269             /* Response variable is now missing for replication sample.
 270                But it is preserved in grade2 */
 271        
 
 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).
       486 at 264:21   21 at 264:27    4 at 264:34     65 at 264:41    7 at 264:50     
 NOTE: There were 1158 observations read from the data set WORK.MATH.
 NOTE: The data set WORK.PREDICT has 575 observations and 39 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              1424.53k
       OS Memory           30252.00k
       Timestamp           02/24/2024 05:11:05 PM
       Step Count                        29  Switch Count  2
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 272        proc reg plots=none data=predict;
 273                            /* Data table predict is the default anyway */
 274             title3 'Re-running Model I to generate y-hat and prediction intervals';
 275             model grade = hsgpa hscalc hsengl totscore mtongue;
 276             output out = predataI   predicted = Yhat
 277                                     L95       = lowpred
 278                                     U95       = hipred;
 279             /* Data set predataI has everything in predict plus
 280                Yhat and the lower and upper 95% prediction limits. */
 281        
 282        /* Does 95 Percent Prediction Interval really contain 95 percent of grades?
 283           Recall that the data fail all tests for normality, and the prediction
 284           intervals are based on normal theory.  */
 285        
 
 NOTE: The data set WORK.PREDATAI has 575 observations and 42 variables.
 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              3192.81k
       OS Memory           31940.00k
       Timestamp           02/24/2024 05:11:05 PM
       Step Count                        30  Switch Count  4
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       Voluntary Context Switches        34
       Involuntary Context Switches      0
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       Block Output Operations           584
       
 
 286        data predictB;
 287             set predataI;
 288             if (lowpred < grade2 < hipred) then ininterval='Yes';
 289                else ininterval='No';
 290        
 
 NOTE: There were 575 observations read from the data set WORK.PREDATAI.
 NOTE: The data set WORK.PREDICTB has 575 observations and 43 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.01 seconds
       memory              1304.93k
       OS Memory           30636.00k
       Timestamp           02/24/2024 05:11:05 PM
       Step Count                        31  Switch Count  2
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 291        proc freq data=predictB;
 292             title3 'Does 95 Percent Prediction Interval Work?';
 293             tables sample * ininterval / nocol nopercent;
 294        
 
 NOTE: There were 575 observations read from the data set WORK.PREDICTB.
 NOTE: PROCEDURE FREQ used (Total process time):
       real time           0.02 seconds
       user cpu time       0.02 seconds
       system cpu time     0.00 seconds
       memory              1489.90k
       OS Memory           30896.00k
       Timestamp           02/24/2024 05:11:05 PM
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 295        proc print data=predataI;
 296             title3 'Look at predictions for the replication sample';
 297             var id sample grade2 Yhat lowpred hipred;
 298             where sample = 2;
 299        /* Should predicted marks be used to advise students? */
 300        
 301        /* Keep trying. Try to predict letter grade. */
 302        
 
 NOTE: There were 288 observations read from the data set WORK.PREDATAI.
       WHERE sample=2;
 NOTE: PROCEDURE PRINT used (Total process time):
       real time           0.31 seconds
       user cpu time       0.31 seconds
       system cpu time     0.00 seconds
       memory              4210.28k
       OS Memory           34220.00k
       Timestamp           02/24/2024 05:11:05 PM
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 303        data predictC;
 304             set predictB;
 305             if         80 <= grade2 <= 100 then lgrade = 'A';
 306                else if 70 <= grade2 <=  79 then lgrade = 'B';
 307                else if 60 <= grade2 <=  69 then lgrade = 'C';
 308                else if 50 <= grade2 <=  59 then lgrade = 'D';
 309                else if  0 <= grade2 <=  49 then lgrade = 'F';
 310             label lgrade = 'Letter Grade';
 311             pregrade = round(Yhat);
 312             if         80 <= pregrade <= 100 then prelgrade = 'A';
 313                else if 70 <= pregrade <=  79 then prelgrade = 'B';
 314                else if 60 <= pregrade <=  69 then prelgrade = 'C';
 315                else if 50 <= pregrade <=  59 then prelgrade = 'D';
 316                else if  0 <= pregrade <=  49 then prelgrade = 'F';
 317             label prelgrade = 'Predicted Letter Grade';
 318        
 
 NOTE: There were 575 observations read from the data set WORK.PREDICTB.
 NOTE: The data set WORK.PREDICTC has 575 observations and 46 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              1326.59k
       OS Memory           34220.00k
       Timestamp           02/24/2024 05:11:05 PM
       Step Count                        34  Switch Count  2
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 319        proc freq;
 320             title3 'Accuracy of predicting Letter Grades From Model I';
 321             tables sample*prelgrade*lgrade / nocol nopercent;
 322             /* Will yield separate table for each sample. */
 323        
 324        /* Predict grade for a new student with hsgpa=80 hscalc=90 hsengl=70
 325           totscore=15. For just a prediction (no interval), proc glm is easier. */
 326        
 
 NOTE: There were 575 observations read from the data set WORK.PREDICTC.
 NOTE: PROCEDURE FREQ used (Total process time):
       real time           0.07 seconds
       user cpu time       0.06 seconds
       system cpu time     0.01 seconds
       memory              1375.50k
       OS Memory           34480.00k
       Timestamp           02/24/2024 05:11:06 PM
       Step Count                        35  Switch Count  5
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 327        proc glm data = explore;
 328             model grade = hsgpa hscalc hsengl mtongue totscore;
 329             estimate 'New Student 1' intercept 1  hsgpa 80  hscalc 90  hsengl 70
 330                                      mtongue 1 totscore 15;
 331             estimate 'New Student 2' intercept 1  hsgpa 80  hscalc 90  hsengl  0
 332                                      mtongue 1 totscore 15;
 333        
 334        /* Prediction for Y_{n+1} is the same as estimate of E[Y|X]. CI from proc glm
 335           is for E[Y|X]. PREDICTION interval for Y_{n+1} is wider. */
 336        
 
 NOTE: PROCEDURE GLM used (Total process time):
       real time           0.06 seconds
       user cpu time       0.06 seconds
       system cpu time     0.00 seconds
       memory              2030.46k
       OS Memory           35000.00k
       Timestamp           02/24/2024 05:11:06 PM
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 337        data student;
 338             hsgpa=80; hscalc=90; hsengl=70; mtongue=1; totscore=15; id = -1; output;
 339             hsgpa=80; hscalc=90;  hsengl=0; mtongue=1; totscore=15; id = -2; output;
 
 NOTE: The data set WORK.STUDENT has 2 observations and 6 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.00 seconds
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       memory              670.03k
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       Timestamp           02/24/2024 05:11:06 PM
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 340        proc print;
 341        
 
 NOTE: There were 2 observations read from the data set WORK.STUDENT.
 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              667.25k
       OS Memory           33960.00k
       Timestamp           02/24/2024 05:11:06 PM
       Step Count                        38  Switch Count  0
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 342        data together;
 343             set explore student;
 344             /* All variables not assigned will be missing for new observations */
 345        
 
 NOTE: There were 579 observations read from the data set WORK.EXPLORE.
 NOTE: There were 2 observations read from the data set WORK.STUDENT.
 NOTE: The data set WORK.TOGETHER has 581 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              1602.56k
       OS Memory           34480.00k
       Timestamp           02/24/2024 05:11:06 PM
       Step Count                        39  Switch Count  2
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 346        proc reg noprint data=together;
 347             title3 'Fit Model I to predict new student data';
 348             model grade = hsgpa hscalc hsengl mtongue totscore;
 349             output out = guess      predicted = PredictedY
 350                                     L95       = LowerLimit
 351                                     U95       = UpperLimit;
 352        
 
 NOTE: The data set WORK.GUESS has 581 observations and 31 variables.
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              2671.65k
       OS Memory           35780.00k
       Timestamp           02/24/2024 05:11:06 PM
       Step Count                        40  Switch Count  4
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       Block Output Operations           568
       
 
 353        data newguess;
 354             set guess;
 355             if id < 0; /* Discard all other cases */
 356        
 
 NOTE: There were 581 observations read from the data set WORK.GUESS.
 NOTE: The data set WORK.NEWGUESS has 2 observations and 31 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              1163.09k
       OS Memory           34220.00k
       Timestamp           02/24/2024 05:11:06 PM
       Step Count                        41  Switch Count  2
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       Involuntary Context Switches      0
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 357        proc print;
 358             title3 'Prediction intervals for new students';
 359             var id hsgpa hscalc hsengl totscore predictedY LowerLimit UpperLimit;
 360        
 361        quit;
 
 NOTE: There were 2 observations read from the data set WORK.NEWGUESS.
 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              687.75k
       OS Memory           33960.00k
       Timestamp           02/24/2024 05:11:06 PM
       Step Count                        42  Switch Count  1
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 362        
 363        
 364        
 365        
 366        
 367        OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 379