UCLA Coefficients Independent Variables and Classification Methods Worksheet

Description

3 questions(Do it by hand… you may use R for double-checking, if you want)
A sample of size n = 6 contains two independent variables X1, X2 and one categorical
response variable Y . However, response for the 3rd sampling unit is missing.
X1 -2 -1 0 1 2 3
X2 2 -2 0 0 3 2
Y B B ??? A A B
Your task is to reconstruct the missing Y3 by different classification methods.
(a) Predict Y3 by KNN method with k = 1.

(b) Predict Y3 by KNN method with k = 3.
(c) Logistic regression, without the 3rd sampling unit, produced the following results.
> z = 1*(y==“B”)

> lreg = glm( z ∼ x1 + x2, family=binomial)

> summary(lreg)
Coefficients:
(Intercept)
x1

x2
Estimate the probability that Y3 = “B”.
Estimate
0.8373
-0.4494
-0.0778
(d) Suppose that X1 and X2 are independent Normal random variables with the same
variance σ2 = 1. Assuming equal prior probabilities P(A) = P(B) = 0.5, predict Y3 by
the linear discriminant analysis.

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Tags:
logistic regression

independent variables

categorical response

classification methods

independent normal

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