Question

Learning for Numeric Prediction

(a) Let the weights of a two-input perceptron be: w₀ = 0:2, w1 = 0:5 and w₂ = 0:5. Assuming that x₀ = 1, what is the output of the perceptron when:

[i] x₁ = 1 and x₂ = 1 ?

[ii] x₁ = 1 and x₂ = 1 ?

Letting w₀ = 0:2 and keeping x₀ = 1, w₁ = 0:5 and w₂ = 0:5, what is the perceptron output when:

[iii] x₁ = 1 and x₂ = 1 ?

[iv] x₁ = 1 and x₂ = 1 ?

(b) Here is a regression tree with leaf nodes denoted A, B and C:

X <= 5 : A
X > 5 :
| X <= 9: B
| X > 9: C

This is the training set from which the regression tree was learned:

Write down the output (class) values and number of instances that appear in each of the leaf nodes A, B and C of the tree.