Decision Tree Regression

Mean Square Error

$$MSE = \frac{\sum_{i=1}^n{(x_i - \bar{x})^2}}{n}$$

1. Student Performance Prediction

S.No.	Assessment	Assignment	Project	Result (%)
	X			y
1	Good	Yes	Yes	9.5
2	Average	Yes	No	7.0
3	Good	No	Yes	7.5
4	Poor	No	No	4.5
5	Good	Yes	Yes	9.8
6	Average	No	Yes	8.0
7	Good	No	No	7.5
8	Poor	Yes	Yes	6.5
9	Average	No	No	5.8
10	Good	Yes	Yes	8.9

Step 1: Calculate MSE_y

$$\bar{y}=7.5$$

$$MSE_y = \frac{(9.5-7.5)^2 + (7.0-7.5)^2 + (7.5-7.5)^2 +(4.5-7.5)^2 +(9.8-7.5)^2 +(8.0-7.5)^2 +(7.5-7.5)^2 +(6.5-7.5)^2 +(5.8-7.5)^2 +(8.9-7.5)^2}{10}$$

Step 2: Calculate MSE _Project

	0 (No)	1 (Yes)
	7 4.5 7.5 5.8	9.5 7.5 9.8 8 5.5 8.9
Mean	6.2	8.2
MSE	1.345	2.0933
MSE _Project	$$\frac{4}{10} * 1.345 + \frac{6}{10}*2.0933=1.794$$

Step 3: Select min MSE Predict

S.No.	Assessment	Assignment	Project	Result (%)
1	Average	Yes	Yes	?
2	Poor	No	Yes	?
3	Poor	Yes	No	?

2. Predict Play Golf

Outlook	Temp	Humidity	Windy	Play
Sunny	Hot	High	False	2
Sunny	Hot	High	True	3
Overcast	Hot	High	False	9
Rainy	Mild	High	False	7
Rainy	Cool	Normal	False	6
Rainy	Cool	Normal	True	1
Overcast	Cool	Normal	True	8
Sunny	Mild	High	False	4
Sunny	Cool	Normal	False	6
Rainy	Mild	Normal	False	8
Sunny	Mild	Normal	True	7
Overcast	Mild	High	True	10
Overcast	Hot	Normal	False	9
Rainy	Mild	High	True	1

Predict

Outlook	Temp	Humidity	Windy	Play
Sunny	Cool	High	False	?
Rainy	Hot	Normal	True	?
Overcast	Mild	High	False	?