hw5report
- 1. Abstract: I have createdthisreportto examine qualitypropertiesfromawine dataset.Thiswine datasetis focusedona wine vineyardfrom portugual calledvinhoverde. Thisvineyardcreatesaclassof wines that are consideredextrodinary exceptinthe eyesof the French.Thisdatasetcontainsalarge sample (over1000 observations) inwhichexpertwine tastersprovidefeedbackonthe qualityof the redwines producedbyvinhoverde.These qualityratingsare attachedtothe individual red winequantitative charactersiticsthatare trackedthroughoutthe productionof eachindividual bottle of theirredwine. Thisdatasetcontains12 quantitative variablesthathave beendeterminedtodefine quality characteristicsof a bottle of wine. Iam usingthe dependentvariablequalityandthe independent variablesare: fixed_acidity volatile_acidity citric_acid residual_sugar chlorides free_sulfur_dioxide total_sulfur_dioxide density pH sulphates and alcohol content. These independent variables have been predertermined to define the final taste of a wine. From this context I want to create a model that can show what quantitative characteristics are associated with the dependent variable quality wines. To me wine is an interesting subject I am currently taking the wine class offered at KSU and this is where I fell in love with Vinho Verde wines and I hope to one day be able to make my own wines so if I can create a model that can quantify and key in on the characteristics that I like about this wine then I feel that this modeling information will give me great insight into quality wine characteristics. This dataset comes from a website called https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/ that is a database dedicated to free datasets that are useful from around the world. Simple Statistics Table 1 Variable N Mean Std Dev Sum Minimum Maximum fixed_acidity 1599 8.31964 1.74110 13303 4.60000 15.90000 volatile_acidity 1599 0.52782 0.17906 843.98500 0.12000 1.58000 citric_acid 1599 0.27098 0.19480 433.29000 0 1.00000 residual_sugar 1599 2.53881 1.40993 4060 0.90000 15.50000 chlorides 1599 0.08747 0.04707 139.85900 0.01200 0.61100 free_sulfur_dioxide 1599 15.87492 10.46016 25384 1.00000 72.00000 total_sulfur_dioxide 1599 46.46779 32.89532 74302 6.00000 289.00000 density 1599 0.99675 0.00189 1594 0.99007 1.00369 pH 1599 3.31111 0.15439 5294 2.74000 4.01000 sulphates 1599 0.65815 0.16951 1052 0.33000 2.00000 alcohol 1599 10.42298 1.06567 16666 8.40000 14.90000 quality 1599 5.63602 0.80757 9012 3.00000 8.00000 As we can see fromtable1there are almost1600 observationsand thatthere isa large range of means.
- 2. Analysis of Variance Table2 Source DF Sum of Squares Mean Square F Value Pr > F Model 11 375.75440 34.15949 81.35 <.0001 Error 1587 666.41070 0.41992 Corrected Total 1598 1042.16510 Root MSE 0.64801 R-Square 0.3606 Dependent Mean 5.63602 Adj R-Sq 0.3561 CoeffVar 11.49767 Parameter Estimates Table3 Variable DF Parameter Estimate Standard Error t Value Pr > |t| Variance Inflation Intercept 1 21.96521 21.19457 1.04 0.3002 0 fixed_acidity 1 0.02499 0.02595 0.96 0.3357 7.76751 volatile_acidity 1 -1.08359 0.12110 -8.95 <.0001 1.78939 citric_acid 1 -0.18256 0.14718 -1.24 0.2150 3.12802 residual_sugar 1 0.01633 0.01500 1.09 0.2765 1.70259 chlorides 1 -1.87423 0.41928 -4.47 <.0001 1.48193 free_sulfur_dioxide 1 0.00436 0.00217 2.01 0.0447 1.96302 total_sulfur_dioxide 1 -0.00326 0.00072873 -4.48 <.0001 2.18681 density 1 -17.88116 21.63310 -0.83 0.4086 6.34376 pH 1 -0.41365 0.19160 -2.16 0.0310 3.32973 sulphates 1 0.91633 0.11434 8.01 <.0001 1.42943 alcohol 1 0.27620 0.02648 10.43 <.0001 3.03116 For the First Model that I want to introduce I created a simple first order model wheras quality is my dependent variable and my independent variables are fixed_acidity volatile_acidity citric_acid residual_sugar chlorides free_sulfur_dioxide total_sulfur_dioxide density pH sulphates and alcohol content. My hypothesis test is that I can build a model that shows the chemical characteristics of these independent variable is correlated to the variable quality. If we take a look at table 2 we can see that there is a the overall global f test shows that this model overall could be useful but I am concerned because the adjusted r value is relatively low at 36%. This means that while the overall model maybe usefull there could be some independent variables that attribute to the quality variable not accounted for in this model. I have set my alpha level at 90% and when we take a look at table 3 there are7 independent variables that I will include into my model volatile_acidity chlorides free_sulfur_dioxide total_sulfur_dioxide ph sulphates and alcohol.Before model we must take a look at table3 and see if there is any potential multicollinearity. Based on the VIF from table3 none of the variables have a VIF greater than 10 so there is not potential multicollinarity concerns in this model so my proposed model is :
- 3. Quality= 21.96521-1.08359vc-1.87423chl+0.00436freesulfur-0.00326totalsulfur- 0.41365ph+0.91633sulphates+0.27620alcohol Model 2. This next model I want to use the model format from the previous selection where quality is my dependent and fixed_acidity volatile_acidity citric_acid residual_sugar chlorides free_sulfur_dioxide total_sulfur_dioxide density pH sulphates and alcohol content are still my independent but I want to perform stepwise regression modeling techniques to see if I missed a potential independent variable that could be useful in my model. Based on table5 the stepwise selection procedure reported the same findings which were reported in model 1. Analysis of Variance table 4 Source DF Sum of Squares Mean Square F Value Pr > F Model 7 374.62804 53.51829 127.55 <.0001 Error 1591 667.53706 0.41957 Corrected Total 1598 1042.16510 Variable Table 5 Parameter Estimate Standard Error Type II SS F Value Pr > F Intercept 4.43010 0.40292 50.72257 120.89 <.0001 volatile_acidity -1.01275 0.10084 42.31760 100.86 <.0001 chlorides -2.01781 0.39754 10.80941 25.76 <.0001 free_sulfur_dioxide 0.00508 0.00213 2.39413 5.71 0.0170 total_sulfur_dioxide -0.00348 0.00068678 10.78662 25.71 <.0001 pH -0.48266 0.11756 7.07271 16.86 <.0001 sulphates 0.88267 0.10991 27.06045 64.50 <.0001 alcohol 0.28930 0.01680 124.48286 296.69 <.0001 Model 3: In this model I want to hypothesis that when I transform quality by only modeling high quality wines which I define as a rating of 7 or higher on a scale of 1-10 that I can create a model that indicates what chemical characteristics from the list of independent variables of these high quality wines can be looked at as significant in modeling quality. If we take at look at table 6 we see that the global test barely fails at the .10 alpha level I have set. With this inmind and the very low adjusted r squared at 11% I feel that this
- 4. model will not be helpful in predicting high quality wine. If we move down to table7 we see that the only independent variable that is usefull is alcohol at the .10 alpha level. This is an interesting result I was expecting a quite different result. With all of this information in mind I will reject this model and say that it will not be useful without further data mining. Analysis of Variance table 6 Source DF Sum of Squares Mean Square F Value Pr > F Model 5 0.68367 0.13673 1.82 0.1095 Error 211 15.82324 0.07499 Corrected Total 216 16.50691 Root MSE 0.27385 R-Square 0.0414 Dependent Mean 7.08295 Adj R-Sq 0.0187 CoeffVar 3.86627 Parameter Estimates table7 Variable DF Parameter Estimate Standard Error t Value Pr > |t| Variance Inflation Intercept 1 6.45590 0.26363 24.49 <.0001 0 volatile_acidity 1 0.09276 0.13284 0.70 0.4858 1.06803 chlorides 1 -0.67390 0.69427 -0.97 0.3328 1.12612 total_sulfur_dioxide 1 -0.00042984 0.00059115 -0.73 0.4680 1.06790 sulphates 1 0.16542 0.14371 1.15 0.2510 1.06872 alcohol 1 0.04624 0.01925 2.40 0.0172 1.06345 libname hw5 "ClientC$UsersJeanDesktophw5"; data hw5.redwine; Infile "ClientC$UsersJeanDesktophw5redwine.csv" dsd dlm= ";"; input fixed_acidity volatile_acidity citric_acid residual_sugar chlorides free_sulfur_dioxide total_sulfur_dioxide density pH sulphates alcohol quality; RUN; ods rtf; proc contents data=hw5.redwine; run; Proc means data=hw5.redwine; run;
- 5. proc corr data=hw5.redwine plots=matrix; var fixed_acidity volatile_acidity citric_acid residual_sugar chlorides free_sulfur_dioxide total_sulfur_dioxide density pH sulphates alcohol quality; run; proc reg data= hw5.redwine; model quality=fixed_acidity volatile_acidity citric_acid residual_sugar chlorides free_sulfur_dioxide total_sulfur_dioxide density pH sulphates alcohol /vif; run; quit; *stepwise selection; proc reg data= hw5.redwine; model quality=fixed_acidity volatile_acidity citric_acid residual_sugar chlorides free_sulfur_dioxide total_sulfur_dioxide density pH sulphates alcohol /selection=stepwise sle=0.1 sls=0.1; run; quit; proc reg data=hw5.redwine1; model quality= volatile_acidity chlorides total_sulfur_dioxide sulphates alcohol /selection=stepwise sle=0.1 sls=0.1; run; proc reg data=hw5.redwine1; model quality= volatile_acidity chlorides total_sulfur_dioxide sulphates alcohol /vif; run; ods rtf close; data hw5.redwine2; set hw5.redwine1; va2= volatile_acidity*volatile_acidity; chl2=chlorides*chlorides; tsd2=total_sulfur_dioxide*total_sulfur_dioxide; sul2=sulphates*sulphates; alc2=alcohol*alcohol; run; proc reg data=hw5.redwine2; model quality= volatile_acidity chlorides total_sulfur_dioxide sulphates alcohol va2 chl2 tsd2 sul2 alc2 /vif; run; proc reg data= hw5.redwine; model alcohol=fixed_acidity volatile_acidity citric_acid residual_sugar chlorides free_sulfur_dioxide total_sulfur_dioxide density pH sulphates /vif; run; quit; graph to show interaction effect; data hw5.redwine1; set hw5.redwine; if quality >= 7 then qualityindex='1'; if quality<7 then delete; *if numbids=10 then delete; run;
- 6. proc gplot data=sherry.gfclocks2; plot price*age=bid_group; proc reg data=sherry.exesal2; model y = x1-x10 /selection=stepwise sle=0.1 sls=0.1; run; quit;