Remainder(color) = 3/6 I(2/3,1/3) + 1/6 I(1/1,0/1) + 2/6 I(0/2,2/2)
                    |     |   |      |                |
                    |     |   |      1 of 6 is blue   2 of 6 are green
                    |     |   |
                    |     |   1 of the red is negative
                    |     |
                    |     2 of the red are positive
                    |
                    |
                    3 out of 6 are red

                 = 1/2 * (-2/3 log2 2/3  - 1/3 log2 1/3)
                     + 1/6 * (-1 log21 - 0 log20)
                     + 2/6 * (-0 log20 - 1 log21)

                 = 1/2 * (-2/3(log22 - log23) - 1/3(log21 - log23))
                     + 1/6 * 0
                     + 2/6 * 0

                 = 1/2 * (-2/3(1 - 1.58) - 1/3(0 - 1.58))

		 = 1/2 * 0.914

		 = 0.457

Gain(color) = I(3/6, 3/6) - Remainder(color)

            = 1.0 - 0.457

            = 0.543

Remainder(shape) = 4/6 I(2/4, 2/4) + 2/6 I(1/2, 1/2)
                    4 are square       2 are round

		 = 4/6 * (-.5 * log .5 -.5 * log .5) + 2/6 * (-.5 * log .5 - .5 * log .5)

                 = .667 * (.5 + .5) + .333 * (.5 + .5)

                 = .667 + .333

		 = 1.0

Gain(shape) = I(3/6, 3/6) - Remainder(shape)

	    = 1.0 - 1.0

	    = 0.0

Remainder(size)  = 4/6 I(3/4, 1/4) + 2/6 I(0/2, 2/2)
                     4 are big         2 are small

                 = .667 * (-.75 * log .75 - .25 * log .25) + .333 * (-0 * log 0 - 1 * log 1)

		 = 0.541

Gain(size)  = I(3/6, 3/6) - Remainder(size)

	    = 1.0 - 0.541

	    = 0.459

Max(.543, .086, .459) = .543, so color is best. Make the root node's attribute color and partition the examples for the resulting children nodes as shown:

Green has examples 4 and 6, which are both negative (-), so we make it a negative classification node and it has no child nodes (there is no further information to be extracted from it.) Similarly, blue has example 2, which is positive (+) so we make it a positive classification node and it has no children.