Datamining vit chennai

1. Regression Trees
Hno lot Income Class Class
1 18.4 60 0 Owner
2 16.8 85.5 0 Owner
3 21.6 64.8 0 Owner
4 20.8 61.5 0 Owner
5 23.6 87 0 Owner
6 19.2 110.1 0 Owner
7 17.6 108 0 Owner
8 22.4 82.8 0 Owner
9 20 69 0 Owner
10 20.8 93 0 Owner
11 22 51 0 Owner
12 20 81 0 Owner
13 19.6 75 1 Non Owner
14 20.8 52.8 1 Non Owner
15 17.2 64.8 1 Non Owner
16 20.4 43.2 1 Non Owner
17 17.6 84 1 Non Owner
18 17.6 49.2 1 Non Owner
19 16 59.4 1 Non Owner
20 18.4 66 1 Non Owner
21 16.4 47.4 1 Non Owner
22 18.8 33 1 Non Owner
23 14 51 1 Non Owner
24 14.8 63 1 Non Owner
Median 19 64.8
Scatterplot of Lot Size vs. Income for 24 owners and non-owners of riding mowers

2. Gini Index (Class) = ( ∑ )
Non Owner=12
Owner=12
Gini (class) = (1-(12/24)2
+(12/24)2
) = 0
Median of lot = 19
Splitting the 24 observations by Lot Size value of 19 approximately
Lot <=19 (Lower Rectangle)
lot Income Class Class
14 51 1 Non Owner
14.8 63 1 Non Owner
16 59.4 1 Non Owner
16.4 47.4 1 Non Owner
16.8 85.5 0 Owner
17.2 64.8 1 Non Owner
17.6 108 0 Owner
17.6 84 1 Non Owner
17.6 49.2 1 Non Owner
18.4 60 0 Owner
18.4 66 1 Non Owner
18.8 33 1 Non Owner
Gini(lot - LR) = (1 – (3/12)2
– (9/12)2
) = 0.375

3. Lot>19 (Upper Rectangle)
lot Income Class Class
19.2 110.1 0 Owner
19.6 75 1 Non Owner
20 69 0 Owner
20 81 0 Owner
20.4 43.2 1 Non Owner
20.8 61.5 0 Owner
20.8 93 0 Owner
20.8 52.8 1 Non Owner
21.6 64.8 0 Owner
22 51 0 Owner
22.4 82.8 0 Owner
23.6 87 0 Owner
Gini(lot - UR) = (1 – (9/12)2
– (3/12)2
) = 0.375
Avg of LR and UR = 12/24(0.375)+12/24(0.375) = 0.375
Median(Income) = 64.8
Income<=64.8 (Lower Rectangle)
lot Income Class Class
18.8 33 1 Non Owner
20.4 43.2 1 Non Owner
16.4 47.4 1 Non Owner
17.6 49.2 1 Non Owner
22 51 0 Owner
14 51 1 Non Owner
20.8 52.8 1 Non Owner
16 59.4 1 Non Owner
18.4 60 0 Owner
20.8 61.5 0 Owner
14.8 63 1 Non Owner
21.6 64.8 0 Owner
17.2 64.8 1 Non Owner
Gini(Income) = (1 – (4/13)2
– (9/13)2
) = 0.4261

4. Income>64.8 (Upper Rectangle)
lot Income Class Class
18.4 66 1 Non Owner
20 69 0 Owner
19.6 75 1 Non Owner
20 81 0 Owner
22.4 82.8 0 Owner
17.6 84 1 Non Owner
16.8 85.5 0 Owner
23.6 87 0 Owner
20.8 93 0 Owner
17.6 108 0 Owner
19.2 110.1 0 Owner
Gini(Income) = (1 – (8/11)2
– (3/11)2
) = 0.3967
Avg of LR and UR = 14/24(0.4261)+11/24(0.397) = 0.431
Lot Income
0.375 (Min) 0.431
Minimum Gini Avg is for Lot. So choose lot as root
Tree: Step 1 – Identifying the root
Sort Lower rectangle of Lot <=19 with respect to Income and try analysing the class and
finalize the income points after which the classes has never changed. Its 84 and 85.5.
Median(84, 85.5) = 84.75
LR of Lot<=19
lot Income Class Class
Lot
19
12 12

5. 18.8 33 1 Non Owner
16.4 47.4 1 Non Owner
17.6 49.2 1 Non Owner
14 51 1 Non Owner
16 59.4 1 Non Owner
18.4 60 0 Owner
14.8 63 1 Non Owner
17.2 64.8 1 Non Owner
18.4 66 1 Non Owner
17.6 84 1 Non Owner
16.8 85.5 0 Owner
17.6 108 0 Owner
If we continue splitting the mower data, the next split is on the Income variable at the value
84.75.
Splitting the 24 observations by Lot Size value of 19K, and then Income value of 84.75K
LR of Lot<=19 and Income <=84.75
lot Income Class Class
18.8 33 1 Non Owner
16.4 47.4 1 Non Owner
17.6 49.2 1 Non Owner
14 51 1 Non Owner
16 59.4 1 Non Owner
18.4 60 0 Owner
14.8 63 1 Non Owner
17.2 64.8 1 Non Owner
18.4 66 1 Non Owner
17.6 84 1 Non Owner
LR of Lot<=19 and Income >84.75

6. lot Income Class Class
16.8 85.5 0 Owner
17.6 108 0 Owner
Sort Lower rectangle of Lot <=19, Income <=84.75 with respect to the class and finalize the
lot points after which the classes has never changed. Its 17.6 and 18.4.
Median(17.6,18.4) = 18
LR of Lot<=19, Income <=84.75, Lot <=18
lot Income Class Class
14 51 1 Non Owner
14.8 63 1 Non Owner
16 59.4 1 Non Owner
16.4 47.4 1 Non Owner
17.2 64.8 1 Non Owner
17.6 49.2 1 Non Owner
17.6 84 1 Non Owner
2
Lot
19
12 12
Income
84.75
Owner
10
Lot
19
12 12

7. LR of Lot<=19, Income <=84.75, Lot >18
lot Income Class Class
18.4 66 1 Non Owner
18.4 60 0 Owner
18.8 33 1 Non Owner
Sort Lower rectangle of Lot <=19, Income <=84.75, Lot>18 with respect to the class and
finalize the lot points after which the classes has never changed. Its 18.8 and 18.4.
Median(18.8,18.4) = 18.6
LR of Lot<=19, Income <=84.75, Lot >18, Lot<=18.6
lot Income Class Class
18.4 66 1 Non Owner
18.4 60 0 Owner
LR of Lot<=19, Income <=84.75, Lot >18, Lot>18.6
lot Income Class Class
18.8 33 1 Non Owner
Lot
19
12 12

8. LR of Lot<=19, Income <=84.75, Lot >18, Lot<=18.6
lot Income Class Class
18.4 66 1 Non Owner
18.4 60 0 Owner
Sort Lower rectangle of Lot <=19, Income <=84.75, Lot>18, Lot<=18.6 with respect to the
class and finalize the income points after which the classes has never changed. Its 60 and 66
Median(66,60) = 63
LR of Lot<=19, Income <=84.75, Lot >18, Lot<=18.6, Income<=63
lot Income Class Class
18.4 60 0 Owner
LR of Lot<=19, Income <=84.75, Lot >18, Lot<=18.6, Income>63
lot Income Class Class
18.4 66 1 Non Owner
Final Left Regression Tree
Lot
19
12 12