Question

please use the bayes rule below to derive the probabilistic classifier. Do not create a python code, use figures i.e show how to derive the classifier by Input the values into the equation and calculate

The following is an extended version of the example given in the class. Two groups of persons, Healthy and No-Healthy (encoded as 0 and 1, respectively) are under study. Each person is represented by cholesterol level and heart beat rate. The following is the training set: D (, 0), (, 0), (, 0), (, 1), (, 1), (, 1)], where (, 0) means the person has cholesterol level and heart beat rate 3.4 and 70, respectively, and is in class 0. The other examples are interpreted similarly. Answer the following questions a. Give the probabilistic classifier b. Predict the health status for a person with cholesterol level 4.8 and heart beat rate 87. Construct the possibility classifier using Bayes Rule. p(xnewlc)p(c) p(c Xnew Use MLE to estimate μc and Lc. new Hc newl CFC)- (27t)2/2|S 11/2 7lc 7l Note: both μc and are 2D vectors, and is a 2x2 co-variance matrix. eaise Ve

Answer 1

SOLUTION::

A)probability classifier(solution provided in R)

call: g1(formula - y chol.level heart level) Deviance Residuals 0.13684 0.27193 -0. 36890-0.06707 0.31930 0.11492 0.13684 coefficients: Estimate std. Error t value pr(>ItI) (Intercept)-4.17976 1.20899-3.457 0.0259 * chol_level -0. 53705 0.28600 -1.878 0.1336 heart level 0.08384 0.02515 3. 334 0.0290 signif. codes: 0.001 0.01.05."0.11 Coispersion par aneter for gaussian family taken to be 0.09178588) Null deviance: 1.71429 on 6 degrees of freedom Residual deviance: 0. 36714 on 4 degrees of freedom AIC: 7.2298 Number of Fisher scoring iterations:2

so probability E_a => Y=-4.179-0.53 X₁+0.084 X₂

where, X₁ is cholesterol level

X₂ is heartbeat rate

b) predict the health status for a person

cholesterol level=48

heartbeat rate= 87

based on the above model:

Y=-4.179 -0.53704 * cholesterol level + 0.084*heartbeat rate

Y= -4.179 -0.53704 * 48+ 0.084*87

Y=0.53648

based on this status for a person=1   

Solution in R:

• Variables

chol_level = c(3.4, 4.2,4.8,3.5,5.0,5.4,3.4)
heart_level = c(70,80,85,85,90,95,70)
y = c(0,0,0,1,1,1,0)

• Dataframe

data = data.frame(chol_level,heart_level,y)

• Logistic regression model

model = glm(y~chol_level+heart_level)
summary(model)