Question

Thalassemia is detected based on two factors: x1 and x2. The following table contains x1 and x2 factors of 10 patients, and whether they were diagnosed with thalassemia or not.

x1	x2	Thalassemia
5	10	Negative
6	30	Negative
10	45	Negative
11	57	Positive
15	61	Negative
31	75	Positive
25	71	Negative
20	78	Positive
16	87	Positive
17	99	Positive

You decided to use logistic regression-based classification to determine if a new patient is thalassemia-positive or thalassemia-negative. Consider positive to be label 1 and negative to be label 0.

You have computed all the coefficients for the required linear regression model (as discussed in the class). The coefficients you came up with are:

beta0= -12.7948 (notice that it is a negative value)

beta1= -0.2167 (notice that it is a negative value)

beta2= 0.2612 (it is a positive value)

Note that beta1 is associated with x1 and beta2 is associated with x2. Therefore, beta0 is the intercept from the axis for the dependent variable.

You are ready with your logistic regression model. That is, you now throw away the training data and keep the model only. With the model, you can compute the probability of a new patient being thalassemia-positive.

Answer the following questions. All answers must be correct up to four digits after the decimal point.

What is the probability that a new patient with the following factors is thalassemia-positive (using the logistic regression-based model)?

x1=11, x2=57

Answer 1

Given:

beta0= -12.7948

beta1= -0.2167

beta2= 0.2612

and we want to find the probability that a new patient with the following factors is thalassemia-positive

we can write the logistic regression eqaution using given coeeficients

so

so here we have

x1=11, x2=57 put these values in above eqaution

p=

p=  

p=0.4280

the probability that a new patient with the following factors is thalassemia-positive is 0.4280