![to classify some of those points in the bottom right and top right,but still not accurate as it left the houses
in the center.Now I further run Regression Tree to better the Model and predictions
6.1.3 Making a Regression Tree Model
• Training and Splitting median house value
• Finding and adding important variables to regression- latitude,longitude + median income +
population
• Making Regression Tree
-
Figure 6.8: Appendix Ref 8
Results: The median income is the most important variable and split ,and decision starts from there,then
algorithm further distinguish between more income values,and then algorithm makes decision based on the
locations,longitude and latitude
tree.sse= [1] 3.269545e+13](https://image.slidesharecdn.com/supervisedlearning2-pages-deleted-200901132128/85/Supervised-learning-1-6-320.jpg)
Supervised learning 1
- 1. Chapter 5 Call Housing Data I worked on the Call-housing dataset provided by Prof Cesa Bianchi.This data shows various variable that may or maynot be effect the prices of houses in a certain area.I explored the relationship between prices of houses with the aid of Decision trees and Regression tress and tried to built a model initially of how prices vary by location across a region. longitude and latitude = Location of the areas of the particular houses housing median age= Median age of houses in that Area total rooms = Total Rooms of the houses in that area total bedrooms= Total bedrooms out of those total tooms population = Population living in that Area households = Number of households in that area median income = Median Income of the household living in the area median house value:= Median House Values in that area ocean proximity = Houses Proximity from Ocean Classified into < 1H OCEAN NEAR BAY INLAND ISLAND NEAR OCEAN
- 2. Chapter 6 Decision Tree with Data on R 6.1 Analyzing the Data Figure 6.1: Appendix Ref 1 There are 20640 observations corresponding to 20640 census tracts. I am interested in building a model of how prices vary by location across a region. So, let’s first see how the points are laid out. Figure 6.2: Appendix Ref 2
- 3. Now lets plot Different Region types on the Map.As from Data study and real estate knowledge we know that Houses near oceans tend to be more expensive and on islands being more exclusive tend to be high Luxury. < 1H OCEAN =Purple NEAR BAY =Blue INLAND =Black ISLAND =Green NEAR OCEAN=Pink Figure 6.3: Appendix Ref 3 6.1.1 2. Applying Linear Regression to the problem Since, this is a regression problem as the target value to be predicted is continuous(house price), it is but natural to look up to Linear Regression algorithm to solve the problem. As seen in the last figure that the house prices were distributed over the area in an interesting way according to ocean proximity, certainly not the kind of linear way and I feel Linear Regression is not going to work very well here. Figure 6.4: Appendix Ref 4
- 4. • R-squared is around 0.24, which is not great. • The latitude is not significant, which means the north-south location differences aren’t going to be really used at all. This also seems unlikely. • Longitude is significant, but negative which means that as we go towards the east house prices decrease linearly, which is also unlikely. To see how this linear regression model looks on a plot.So I can plot the census tracts again and then plot the above-median house prices with bright red dots. The red dots will tell the actual positions in data where houses are costly. We shall then test the same fact with Linear Regression predictions using blue sign, Figure 6.5: Appendix Ref 5 The linear regression model has plotted a blue euro sign for every time it thinks the census tract is above value 3,00,000. It’s almost a sharp line that the linear regression defines. Also notice the shape is almost vertical since the latitude variable was not very significant in the regression. The blue and the red dots do not overlap especially in the east and north west. It turns out, the linear regression model isn’t really doing a good job. And it has completely ignored everything to the right and left side of the picture. So that’s interesting and pretty wrong.
- 5. 6.1.2 Applying Regression Trees to the problem I built a regression tree by using the rpart command.I am predicting median house value as a function of latitude and longitude, using the dataset. Figure 6.6: Appendix Ref 6 The leaves of the tree are important. • In a classification tree, the leaves would be the classification that I assign . • In regression trees, instead predicting the number.That number here is the average of the median house prices in that bucket. Figure 6.7: Appendix Ref 7 The fitted values are greater than 3,00,000, the colour is blue, The Regression tree has done a much better job and has kind of overlapped the red dots. It has left the low value area out, and has correctly managed
- 6. to classify some of those points in the bottom right and top right,but still not accurate as it left the houses in the center.Now I further run Regression Tree to better the Model and predictions 6.1.3 Making a Regression Tree Model • Training and Splitting median house value • Finding and adding important variables to regression- latitude,longitude + median income + population • Making Regression Tree - Figure 6.8: Appendix Ref 8 Results: The median income is the most important variable and split ,and decision starts from there,then algorithm further distinguish between more income values,and then algorithm makes decision based on the locations,longitude and latitude tree.sse= [1] 3.269545e+13
- 7. Figure 6.9: Appendix Ref 9 6.1.4 Conclusions Even though the Decision Trees appears to be working very well in certain conditions, it comes with its own drawbacks.The model has very high chances of “over-fitting”. If no limit is set, in the worst case, it will end up putting each observation into a leaf node. Maybe If i further try to use PCA and Cross validation with Regression maybe I can remove the problem of overfitting that I can see with decision tree right now.For that I am going to do futher implementation of PCA and Cross validation on the project of UNSUPERVISED LEARNING with this same data .