3. Predictive data analytics models are often used as tools for process quality control and fault detection. The task in this question is to create a naive Bayes model to monitor a waste water treatment plant.33 The table below lists a dataset containing details of activities at a waste water treatment plant for 14 days. Each day is described in terms of six descriptive features that are generated from different sensors at the plant. SS-IN measures the solids coming into the plant per day; SED-IN measures the sediment coming into the plant per day; COND-IN measures the electrical conductivity of the water coming into the plant.34 The features SS-OUT, SED-OUT, and COND-OUT are the corresponding measurements for the water flowing out of the plant. The target feature, STATUS, reports the current situation at the plant: ok, everything is working correctly; settler, there is a problem with the plant settler equipment; or solids, there is a problem with the amount of solids going through the plant.

a. Create a naive Bayes model that uses probability density functions to model the descriptive features in this dataset (assume that all the descriptive features are normally distributed).

b. What prediction will the naive Bayes model return for the following query?

SS-IN = 222, SED-IN = 4.5, COND-IN = 1,518, SS-OUT = 74 SED-OUT = 0.25, COND-OUT = 1,642

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SS SED COND SS SED COND ID -IN -IN IN .OUT -OUT OUT STATUS 12345 168 3 1,814 15 0.001 1,879 ok 156 3 1,358 14 0.01 1,425 ok 176 3.5 2.200 16 0.005 2.140 ok 256 3 2,070 27 0.2 2,700 ok 230 5 1,410 131 3.5 1,575 settler 6 116 3 1,238 104 0.06 1,221 settler 7 242 7 1,315 104 0.01 1,434 settler 8 242 4.5 1,183 78 0.02 1,374 settler 9 174 2.5 1,110 73 1.5 1,256 settler 10 1,004 35 1,218 81 1,172 33.3 solids 11 1,228 46 1,889 82.4 1,932 43.1 solids 12 964 17 2,120 20 1,030 1,966 solids 13 2,008 32 1,257 13 1,038 1.289 solids