## Boston housing prices - A report on model evaluation and validation

#### 1) Statistical Analysis and Data Exploration

##### Number of data points (houses)?
``````506

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##### Number of features?
``````13

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##### Minimum and maximum housing prices?
``````Minimum price: 5 Maximum price: 50

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##### Mean and median Boston housing prices?
``````Mean: 22.533 Median: 21.2

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##### Standard deviation?
``````9.188

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#### 2) Evaluating Model Performance

##### Which measure of model performance is best to use for predicting Boston housing data and analyzing the errors?
``````"explained_variance_score" is used as the measure of model
performance.

``````
##### Why do you think this measurement most appropriate? Why might the other measurements not be appropriate here?
``````Using other metrics, lead GridSearch to choose models that were less complex
and underfit the data. I got really bizarre results when I tried to correlate
the predicted prices with the actual prices. I evaluated mean_absolute_error,
mean_squared_error, r2_score and finally explained_variance_score. I still
intuitively couldn't understand explained_variance_score performs well though.

``````
##### Why is it important to split the Boston housing data into training and testing data? What happens if you do not do this?
``````If we don't split the data into test and training set, and train the
model on complete data set we may end up with the model that
overfits just the training data and fails to generalize. So it
is important to split the data into training and testing sets, and
use the testing set for validation of the model.

``````
##### What does grid search do and why might you want to use it?
``````"grid search" takes a parameter grid as one of the inputs (parameter grid
depends on the estimator used) and runs training for each of the
parameter from the grid. It also takes scorer function as input
and uses it to compare the runs and choose the best parameter
set. It is useful when we don't know what parameter will be ideal
for an estimator and want to try a set of parameters and choose
the best one.

``````
##### Why is cross validation useful and why might we use it with grid search?
``````Splitting data into training and test set makes less data
available for training. With cross validation in place, we get the
advantage of training and testing on the complete data set. This is
because, in each iteration of cross validation, portion of data is used
for testing and the remaining for training. This repeats till the model
is trained and tested on all the available data.

``````

#### 3) Analyzing Model Performance

##### Look at all learning curve graphs provided. What is the general trend of training and testing error as training size increases?
``````The training error increases as the training size increased. This
is because, when the data size is smal, any model can easily fit
it reasonably well. But as the training size increases, it is not
so easy to find a model that fits all the data points well. So the
training error increases with the size of the data.

On the other hand, the testing error is high when the data size is small. This
is because when the size of the data is less, any trivial model
can fit the data well but the model won't generalize for the new
data points. But as the training size increases, the model gets
complex in an attempt to fit the data reasonably well, and it is
likely that it fits the testing data also well. So, the training
error reduces with the increase in the size of the data.

``````
##### Look at the learning curves for the decision tree regressor with max depth 1 and 10 (first and last learning curve graphs). When the model is fully trained does it suffer from either high bias/underfitting or high variance/overfitting?
``````With max_depth 1, when the model is fully trained, it suffers from high
bias(underfitting) as the model is not complex enough for the
data. Throwing more data into the model doesn't seem to help
because the model couldn't get complex enough to represent the
data accurately.

With max_depth 10, when the model is fully
trained, it suffers from high variance i.e. it overfits the
data. This was shown in the learning curve while observing the
changes to training error. With high enough max_depth, the model
got complex, closely followed the data (we can say it pretty much
memorized the data) but failed to generalize for new set of data.

``````
##### Look at the model complexity graph. How do the training and test error relate to increasing model complexity? Based on this relationship, which model (max depth) best generalizes the dataset and why?
``````The training and testing error reduces as the model
complexity increases. But after certain stage, the model becomes
unnecessarily complex as there is no improvement in the model
performance but just the complexity increases.

``````

#### 4) Model Prediction

``````Desired model complexity: 5
Predicted price: 20.96776316

``````
##### Compare prediction to earlier statistics and make a case if you think it is a valid model.
``````I tried to plot the predictions with earlier prices to see if the
model is valid. I expected a linear trend in the scatter
plot. What I could see was the trend was linear for the most part
with more data points scattered when the model complexity was 4
than when it was 7. I got predictions in the range of 19.0 to
21.0.

Example scatter plot from a run:

``````