Welcome to the first project of the Machine Learning Engineer Nanodegree! In this notebook, some template code has already been provided for you, and you will need to implement additional functionality to successfully complete this project. You will not need to modify the included code beyond what is requested. Sections that begin with **'Implementation'** in the header indicate that the following block of code will require additional functionality which you must provide. Instructions will be provided for each section and the specifics of the implementation are marked in the code block with a 'TODO' statement. Please be sure to read the instructions carefully!

In addition to implementing code, there will be questions that you must answer which relate to the project and your implementation. Each section where you will answer a question is preceded by a **'Question X'** header. Carefully read each question and provide thorough answers in the following text boxes that begin with **'Answer:'**. Your project submission will be evaluated based on your answers to each of the questions and the implementation you provide.

Note:Code and Markdown cells can be executed using theShift + Enterkeyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode.

In this project, you will evaluate the performance and predictive power of a model that has been trained and tested on data collected from homes in suburbs of Boston, Massachusetts. A model trained on this data that is seen as a *good fit* could then be used to make certain predictions about a home — in particular, its monetary value. This model would prove to be invaluable for someone like a real estate agent who could make use of such information on a daily basis.

The dataset for this project originates from the UCI Machine Learning Repository. The Boston housing data was collected in 1978 and each of the 506 entries represent aggregated data about 14 features for homes from various suburbs in Boston, Massachusetts. For the purposes of this project, the following preprocessing steps have been made to the dataset:

- 16 data points have an
`'MEDV'`

value of 50.0. These data points likely contain**missing or censored values**and have been removed. - 1 data point has an
`'RM'`

value of 8.78. This data point can be considered an**outlier**and has been removed. - The features
`'RM'`

,`'LSTAT'`

,`'PTRATIO'`

, and`'MEDV'`

are essential. The remaining**non-relevant features**have been excluded. - The feature
`'MEDV'`

has been**multiplicatively scaled**to account for 35 years of market inflation.

Run the code cell below to load the Boston housing dataset, along with a few of the necessary Python libraries required for this project. You will know the dataset loaded successfully if the size of the dataset is reported.

In [1]:

```
# Import libraries necessary for this project
import numpy as np
import pandas as pd
from sklearn.model_selection import ShuffleSplit
# Import supplementary visualizations code visuals.py
import visuals as vs
# Pretty display for notebooks
%matplotlib inline
# Load the Boston housing dataset
data = pd.read_csv('housing.csv')
prices = data['MEDV']
features = data.drop('MEDV', axis = 1)
# Success
print("Boston housing dataset has {} data points with {} variables each.".format(*data.shape))
```

In this first section of this project, you will make a cursory investigation about the Boston housing data and provide your observations. Familiarizing yourself with the data through an explorative process is a fundamental practice to help you better understand and justify your results.

Since the main goal of this project is to construct a working model which has the capability of predicting the value of houses, we will need to separate the dataset into **features** and the **target variable**. The **features**, `'RM'`

, `'LSTAT'`

, and `'PTRATIO'`

, give us quantitative information about each data point. The **target variable**, `'MEDV'`

, will be the variable we seek to predict. These are stored in `features`

and `prices`

, respectively.

For your very first coding implementation, you will calculate descriptive statistics about the Boston housing prices. Since `numpy`

has already been imported for you, use this library to perform the necessary calculations. These statistics will be extremely important later on to analyze various prediction results from the constructed model.

In the code cell below, you will need to implement the following:

- Calculate the minimum, maximum, mean, median, and standard deviation of
`'MEDV'`

, which is stored in`prices`

.- Store each calculation in their respective variable.

In [2]:

```
# TODO: Minimum price of the data
minimum_price = np.min(prices)
# TODO: Maximum price of the data
maximum_price = np.max(prices)
# TODO: Mean price of the data
mean_price = np.mean(prices)
# TODO: Median price of the data
median_price = np.median(prices)
# TODO: Standard deviation of prices of the data
std_price = np.std(prices)
# Show the calculated statistics
print("Statistics for Boston housing dataset:\n")
print("Minimum price: ${}".format(minimum_price))
print("Maximum price: ${}".format(maximum_price))
print("Mean price: ${}".format(mean_price))
print("Median price ${}".format(median_price))
print("Standard deviation of prices: ${}".format(std_price))
```

As a reminder, we are using three features from the Boston housing dataset: `'RM'`

, `'LSTAT'`

, and `'PTRATIO'`

. For each data point (neighborhood):

`'RM'`

is the average number of rooms among homes in the neighborhood.`'LSTAT'`

is the percentage of homeowners in the neighborhood considered "lower class" (working poor).`'PTRATIO'`

is the ratio of students to teachers in primary and secondary schools in the neighborhood.

** Using your intuition, for each of the three features above, do you think that an increase in the value of that feature would lead to an **increase** in the value of 'MEDV' or a **decrease

`'MEDV'`

? Justify your answer for each.**Hint:** This problem can phrased using examples like below.

- Would you expect a home that has an
`'RM'`

value(number of rooms) of 6 be worth more or less than a home that has an`'RM'`

value of 7? - Would you expect a neighborhood that has an
`'LSTAT'`

value(percent of lower class workers) of 15 have home prices be worth more or less than a neighborhood that has an`'LSTAT'`

value of 20? - Would you expect a neighborhood that has an
`'PTRATIO'`

value(ratio of students to teachers) of 10 have home prices be worth more or less than a neighborhood that has an`'PTRATIO'`

value of 15?

**Answer: **

- In general, the average number of rooms (RM) can be used as the implication of house sizes. And bigger houses normally are more expensive than the small one. Thus, in this case, higher RM could lead to an increase of 'MEDV'.
- LSTAT (the % of lower class) indicates the financial status of neighborhood. Since the lower class workers cannot afford the luxurious house or live in very expensive areas, it is fair to assume that this house is also located in lower class area. In conclusion, higher LSTAT decreases the home price ('MEDV').
- PTRATIO is the ratio of students to teachers. I think the higher MEDV (expensive house) should be the place where it is closer to the expensive public school that has a small numbers of students to teachers per classrom. Thus, the lower value of 'PTRATIO' may increase the value of 'MEDV'

In this second section of the project, you will develop the tools and techniques necessary for a model to make a prediction. Being able to make accurate evaluations of each model's performance through the use of these tools and techniques helps to greatly reinforce the confidence in your predictions.

It is difficult to measure the quality of a given model without quantifying its performance over training and testing. This is typically done using some type of performance metric, whether it is through calculating some type of error, the goodness of fit, or some other useful measurement. For this project, you will be calculating the *coefficient of determination*, R^{2}, to quantify your model's performance. The coefficient of determination for a model is a useful statistic in regression analysis, as it often describes how "good" that model is at making predictions.

The values for R^{2} range from 0 to 1, which captures the percentage of squared correlation between the predicted and actual values of the **target variable**. A model with an R^{2} of 0 is no better than a model that always predicts the *mean* of the target variable, whereas a model with an R^{2} of 1 perfectly predicts the target variable. Any value between 0 and 1 indicates what percentage of the target variable, using this model, can be explained by the **features**. *A model can be given a negative R ^{2} as well, which indicates that the model is arbitrarily worse than one that always predicts the mean of the target variable.*

For the `performance_metric`

function in the code cell below, you will need to implement the following:

- Use
`r2_score`

from`sklearn.metrics`

to perform a performance calculation between`y_true`

and`y_predict`

. - Assign the performance score to the
`score`

variable.

In [3]:

```
# TODO: Import 'r2_score'
from sklearn.metrics import r2_score
def performance_metric(y_true, y_predict):
""" Calculates and returns the performance score between
true and predicted values based on the metric chosen. """
# TODO: Calculate the performance score between 'y_true' and 'y_predict'
score = r2_score(y_true, y_predict)
# Return the score
return score
```

Assume that a dataset contains five data points and a model made the following predictions for the target variable:

True Value | Prediction |
---|---|

3.0 | 2.5 |

-0.5 | 0.0 |

2.0 | 2.1 |

7.0 | 7.8 |

4.2 | 5.3 |

Run the code cell below to use the `performance_metric`

function and calculate this model's coefficient of determination.

In [4]:

```
# Calculate the performance of this model
score = performance_metric([3, -0.5, 2, 7, 4.2], [2.5, 0.0, 2.1, 7.8, 5.3])
print("Model has a coefficient of determination, R^2, of {:.3f}.".format(score))
```

- Would you consider this model to have successfully captured the variation of the target variable?
- Why or why not?

** Hint: ** The R2 score is the proportion of the variance in the dependent variable that is predictable from the independent variable. In other words:

- R2 score of 0 means that the dependent variable cannot be predicted from the independent variable.
- R2 score of 1 means the dependent variable can be predicted from the independent variable.
- R2 score between 0 and 1 indicates the extent to which the dependent variable is predictable.
- R2 score of 0.40 means that 40 percent of the variance in Y is predictable from X.

**Answer:**
R2 score is used for evaluating the variance of dependent and independent varaibles. R2 score of 1 means that model can completely predict the right value of Y ( All actual value == All predicted value). In this case, the obtained value is 0.923 which is pretty close to 1. Thus, it is legitimately to say this model has successfully captured the variation of the target variable.

Your next implementation requires that you take the Boston housing dataset and split the data into training and testing subsets. Typically, the data is also shuffled into a random order when creating the training and testing subsets to remove any bias in the ordering of the dataset.

For the code cell below, you will need to implement the following:

- Use
`train_test_split`

from`sklearn.cross_validation`

to shuffle and split the`features`

and`prices`

data into training and testing sets.- Split the data into 80% training and 20% testing.
- Set the
`random_state`

for`train_test_split`

to a value of your choice. This ensures results are consistent.

- Assign the train and testing splits to
`X_train`

,`X_test`

,`y_train`

, and`y_test`

.

In [5]:

```
# TODO: Import 'train_test_split'
from sklearn.model_selection import train_test_split
# TODO: Shuffle and split the data into training and testing subsets
X_train, X_test, y_train, y_test = train_test_split(features, prices, test_size=0.2, random_state=123)
# Success
print("Training and testing split was successful.")
```

- What is the benefit to splitting a dataset into some ratio of training and testing subsets for a learning algorithm?

**Hint:** Think about how overfitting or underfitting is contingent upon how splits on data is done.

**Answer: **
We split the data to simulate the real world scenario. In the real situation, you cannot see the data in the future. So, when we develop our models, we have to split the data and assume the test set data as the unseen data in the future so that we will be able to evaluate our models on them. If you don't split the data, you don't know how good or bad your models are and end up with the overfit model which does very well on our local machine and training data but suck at the production and unseen data.

In this third section of the project, you'll take a look at several models' learning and testing performances on various subsets of training data. Additionally, you'll investigate one particular algorithm with an increasing `'max_depth'`

parameter on the full training set to observe how model complexity affects performance. Graphing your model's performance based on varying criteria can be beneficial in the analysis process, such as visualizing behavior that may not have been apparent from the results alone.

The following code cell produces four graphs for a decision tree model with different maximum depths. Each graph visualizes the learning curves of the model for both training and testing as the size of the training set is increased. Note that the shaded region of a learning curve denotes the uncertainty of that curve (measured as the standard deviation). The model is scored on both the training and testing sets using R^{2}, the coefficient of determination.

Run the code cell below and use these graphs to answer the following question.

In [6]:

```
# Produce learning curves for varying training set sizes and maximum depths
vs.ModelLearning(features, prices)
```

- Choose one of the graphs above and state the maximum depth for the model.
- What happens to the score of the training curve as more training points are added? What about the testing curve?
- Would having more training points benefit the model?

**Hint:** Are the learning curves converging to particular scores? Generally speaking, the more data you have, the better. But if your training and testing curves are converging with a score above your benchmark threshold, would this be necessary?
Think about the pros and cons of adding more training points based on if the training and testing curves are converging.

**Answer: **

Max_depth=3

On the training curve, score of the training curve drops just a few points after adding more data points. In contrast, the testing curve rises hugely when adding more data points. Both curves are converging and staling around 0.8 score. Generally, the more data you add to the model, the better. However, unlike Deep learning, the traditional machine learning algorithms such as decision tree or linear regression have the point of diminishing returns making the models doesn't improve. Thus, adding more training points after it converged costs your time to train and may not be worth.

The following code cell produces a graph for a decision tree model that has been trained and validated on the training data using different maximum depths. The graph produces two complexity curves — one for training and one for validation. Similar to the **learning curves**, the shaded regions of both the complexity curves denote the uncertainty in those curves, and the model is scored on both the training and validation sets using the `performance_metric`

function.

** Run the code cell below and use this graph to answer the following two questions Q5 and Q6. **

In [7]:

```
vs.ModelComplexity(X_train, y_train)
```

- When the model is trained with a maximum depth of 1, does the model suffer from high bias or from high variance?
- How about when the model is trained with a maximum depth of 10? What visual cues in the graph justify your conclusions?

**Hint:** High bias is a sign of underfitting(model is not complex enough to pick up the nuances in the data) and high variance is a sign of overfitting(model is by-hearting the data and cannot generalize well). Think about which model(depth 1 or 10) aligns with which part of the tradeoff.

**Answer: **

- When the model is trained with a maximum depth of 1, it suffers from high bias (underfitting) because both training and valid score are very low.
- When the model is trained with a maximum depth of 10, the high variance (overfitting) is playing a huge role here because the training score is 1.0 (full score) but the validation score is very low. This happens when your model is trying to memorize everything in the training set (capture even noises) but doesn't generalize well with other data sets (too much noises in the model).

- Which maximum depth do you think results in a model that best generalizes to unseen data?
- What intuition lead you to this answer?

** Hint: ** Look at the graph above Question 5 and see where the validation scores lie for the various depths that have been assigned to the model. Does it get better with increased depth? At what point do we get our best validation score without overcomplicating our model? And remember, Occams Razor states "Among competing hypotheses, the one with the fewest assumptions should be selected."

**Answer: **

- Maximun depth 4
- At maximum depth 4, the validation score has the highest score on the graph. Besides, The training score doesn't look bad; avoid picking too high score on training set since it might overfit the data (like max_depth 10). When both training and validation set have good performance like this, we could fairly guess that it could do pretty well on unseen data too.

In this final section of the project, you will construct a model and make a prediction on the client's feature set using an optimized model from `fit_model`

.

- What is the grid search technique?
- How it can be applied to optimize a learning algorithm?

** Hint: ** When explaining the Grid Search technique, be sure to touch upon why it is used, what the 'grid' entails and what the end goal of this method is. To solidify your answer, you can also give an example of a parameter in a model that can be optimized using this approach.

**Answer: **

- Grid search technique is to use all hyperparameters given by users to create all the possible combinations that the model can be tested to find the best hyperparameters.
- We use the grid search technique to find the optimal value that perform well at training set and validation set. For example, in the Boston housing project, if the decision tree uses max depth equal to ten, it is the overfitting model and does not generalize with other data set such as test data. Therefore, we have to find the max depth value that performs best on both training and validation set by giving the range of value we want grid search to find and let it find that perfect value for you.

What is the k-fold cross-validation training technique?

What benefit does this technique provide for grid search when optimizing a model?

**Hint:** When explaining the k-fold cross validation technique, be sure to touch upon what 'k' is, how the dataset is split into different parts for training and testing and the number of times it is run based on the 'k' value.

When thinking about how k-fold cross validation helps grid search, think about the main drawbacks of grid search which are hinged upon **using a particular subset of data for training or testing** and how k-fold cv could help alleviate that. You can refer to the docs for your answer.

**Answer: **

- K-fold is the technique to evaluate the model performance by spliting training data into k folds( 5-fold = 5 folds). Then assign k-1 folds as the training set and the rest, a single fold, as the validation set. Importantly, we gonna repeat this process k times by ensuring that every fold is used as the validation set once. After repeating this process k times, we calculate the average of k-validation score and that average score becomes the final score.
- This technique is used widely because we want to make sure that every data points in the training set has been used at least once as the validation set. unlike the normal cross validation that ends up with fixed subset of data for training or testing. In the worst case of normal cross validation, one of the sets may contain a lot of outliers/noises leading to bad performance and high bias/variance.
- Using k-fold strategy with grid search cv, as I disscussed above, it is the great method to make your model robusted and generalized with unseen data.

Your final implementation requires that you bring everything together and train a model using the **decision tree algorithm**. To ensure that you are producing an optimized model, you will train the model using the grid search technique to optimize the `'max_depth'`

parameter for the decision tree. The `'max_depth'`

parameter can be thought of as how many questions the decision tree algorithm is allowed to ask about the data before making a prediction. Decision trees are part of a class of algorithms called *supervised learning algorithms*.

In addition, you will find your implementation is using `ShuffleSplit()`

for an alternative form of cross-validation (see the `'cv_sets'`

variable). While it is not the K-Fold cross-validation technique you describe in **Question 8**, this type of cross-validation technique is just as useful!. The `ShuffleSplit()`

implementation below will create 10 (`'n_splits'`

) shuffled sets, and for each shuffle, 20% (`'test_size'`

) of the data will be used as the *validation set*. While you're working on your implementation, think about the contrasts and similarities it has to the K-fold cross-validation technique.

Please note that ShuffleSplit has different parameters in scikit-learn versions 0.17 and 0.18.
For the `fit_model`

function in the code cell below, you will need to implement the following:

- Use
`DecisionTreeRegressor`

from`sklearn.tree`

to create a decision tree regressor object.- Assign this object to the
`'regressor'`

variable.

- Assign this object to the
- Create a dictionary for
`'max_depth'`

with the values from 1 to 10, and assign this to the`'params'`

variable. - Use
`make_scorer`

from`sklearn.metrics`

to create a scoring function object.- Pass the
`performance_metric`

function as a parameter to the object. - Assign this scoring function to the
`'scoring_fnc'`

variable.

- Pass the
- Use
`GridSearchCV`

from`sklearn.grid_search`

to create a grid search object.- Pass the variables
`'regressor'`

,`'params'`

,`'scoring_fnc'`

, and`'cv_sets'`

as parameters to the object. - Assign the
`GridSearchCV`

object to the`'grid'`

variable.

- Pass the variables

In [8]:

```
import sklearn
print('The scikit-learn version is {}.'.format(sklearn.__version__))
```

In [9]:

```
# TODO: Import 'make_scorer', 'DecisionTreeRegressor', and 'GridSearchCV'
from sklearn.metrics import make_scorer
from sklearn.tree import DecisionTreeRegressor
from sklearn.model_selection import GridSearchCV
def fit_model(X, y):
""" Performs grid search over the 'max_depth' parameter for a
decision tree regressor trained on the input data [X, y]. """
# Create cross-validation sets from the training data
# sklearn version 0.18: ShuffleSplit(n_splits=10, test_size=0.1, train_size=None, random_state=None)
# sklearn versiin 0.17: ShuffleSplit(n, n_iter=10, test_size=0.1, train_size=None, random_state=None)
#cv_sets = ShuffleSplit(X.shape[0], n_iter = 10, test_size = 0.20, random_state =1)
cv_sets = ShuffleSplit(n_splits=10, test_size=0.2, train_size=None, random_state=123)
# TODO: Create a decision tree regressor object
regressor = DecisionTreeRegressor()
# TODO: Create a dictionary for the parameter 'max_depth' with a range from 1 to 10
params = {'max_depth': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]}
# TODO: Transform 'performance_metric' into a scoring function using 'make_scorer'
scoring_fnc = make_scorer(performance_metric)
# TODO: Create the grid search cv object --> GridSearchCV()
# Make sure to include the right parameters in the object:
# (estimator, param_grid, scoring, cv) which have values 'regressor', 'params', 'scoring_fnc', and 'cv_sets' respectively.
grid = GridSearchCV(regressor, params, scoring_fnc, cv=cv_sets)
# Fit the grid search object to the data to compute the optimal model
grid = grid.fit(X, y)
# Return the optimal model after fitting the data
return grid.best_estimator_
```

Once a model has been trained on a given set of data, it can now be used to make predictions on new sets of input data. In the case of a *decision tree regressor*, the model has learned *what the best questions to ask about the input data are*, and can respond with a prediction for the **target variable**. You can use these predictions to gain information about data where the value of the target variable is unknown — such as data the model was not trained on.

- What maximum depth does the optimal model have? How does this result compare to your guess in
**Question 6**?

Run the code block below to fit the decision tree regressor to the training data and produce an optimal model.

In [10]:

```
# Fit the training data to the model using grid search
reg = fit_model(X_train, y_train)
# Produce the value for 'max_depth'
print("Parameter 'max_depth' is {} for the optimal model.".format(reg.get_params()['max_depth']))
```

** Hint: ** The answer comes from the output of the code snipped above.

**Answer: **
Parameter 'max_depth' is 4 for the optimal model. The result is the same to what I guessed in question 6.

Imagine that you were a real estate agent in the Boston area looking to use this model to help price homes owned by your clients that they wish to sell. You have collected the following information from three of your clients:

Feature | Client 1 | Client 2 | Client 3 |
---|---|---|---|

Total number of rooms in home | 5 rooms | 4 rooms | 8 rooms |

Neighborhood poverty level (as %) | 17% | 32% | 3% |

Student-teacher ratio of nearby schools | 15-to-1 | 22-to-1 | 12-to-1 |

- What price would you recommend each client sell his/her home at?
- Do these prices seem reasonable given the values for the respective features?

**Hint:** Use the statistics you calculated in the **Data Exploration** section to help justify your response. Of the three clients, client 3 has has the biggest house, in the best public school neighborhood with the lowest poverty level; while client 2 has the smallest house, in a neighborhood with a relatively high poverty rate and not the best public schools.

Run the code block below to have your optimized model make predictions for each client's home.

In [11]:

```
# Produce a matrix for client data
client_data = [[5, 17, 15], # Client 1
[4, 32, 22], # Client 2
[8, 3, 12]] # Client 3
# Show predictions
for i, price in enumerate(reg.predict(client_data)):
print("Predicted selling price for Client {}'s home: ${:,.2f}".format(i+1, price))
```

**Answer: **
Client 1's home: 408,870.00, Client 2's home: 232,662.50, Client 3's home: 892,850.00

From the data exploration part: Minimum price: 105000.0
Maximum price: 1024800.0
Mean price: 454342.9447852761
Median price 438900.0
Standard deviation of prices: 165340.27765266786

These prices seem reasonable because

- Client 1's price is closer to the mean (with only 1 standard deviation) of the data because it is an average house with 5 rooms, average of lower class population and average public school. When every features is average, our model must think like us that the price should be the average price too!.
- Client 2's price is 232,662.50 and turns out to be the cheapest house in the prediction which makes sense because it has a lot of lower class people living there (32%), only 4 rooms (small house) and with the mediocre schools telling us that this might be located in the lower class area.
- Client 3's price is also reasonable because it is the biggest house (8 rooms), very low students/techers ratio comparing to others and with only 3% of lower class in the area. Moreover, the maximum price in this dataset is 1024800 which client 3's price is very close to that price.
- There are no houses in the predicted selling price that exceed the maximum or less than the minimum price in the data set.

An optimal model is not necessarily a robust model. Sometimes, a model is either too complex or too simple to sufficiently generalize to new data. Sometimes, a model could use a learning algorithm that is not appropriate for the structure of the data given. Other times, the data itself could be too noisy or contain too few samples to allow a model to adequately capture the target variable — i.e., the model is underfitted.

**Run the code cell below to run the fit_model function ten times with different training and testing sets to see how the prediction for a specific client changes with respect to the data it's trained on.**

In [12]:

```
vs.PredictTrials(features, prices, fit_model, client_data)
```

- In a few sentences, discuss whether the constructed model should or should not be used in a real-world setting.

**Hint:** Take a look at the range in prices as calculated in the code snippet above. Some questions to answering:

- How relevant today is data that was collected from 1978? How important is inflation?
- Are the features present in the data sufficient to describe a home? Do you think factors like quality of apppliances in the home, square feet of the plot area, presence of pool or not etc should factor in?
- Is the model robust enough to make consistent predictions?
- Would data collected in an urban city like Boston be applicable in a rural city?
- Is it fair to judge the price of an individual home based on the characteristics of the entire neighborhood?

**Answer: **

- The machine learning alogorithm learns from the past and tries to predict the future. However, if the past is too old, it may not correctly predict the future. Using the old data to generate model in this case is like software developer wants to earn a living in 2018 with windows-95 and knowledge/information in 1995.
- This model drops a lot of features such as square feet, the facilities in home. In the real world, this is so important as you can see it on Airbnb website listing a lot of features. I suspect this model is going to work pretty well in the production.
- Data collected in different areas, regions, and countries are different because we are humans who have different cultures, currencies and ideologies. Thus, we cannot use the same model for every areas but has to learn from that particular area.
- Thus, you cannot use data collected in an urban city to predict the rural city; it has totally different characteristics/ behaviors/features. For the best performance, we have to collect the new data instead.
- I think it is fair to judge the price of an individual home based on the characteristics of the entire neighborhood because this is called 'statistics'. It has a high chance that this individual home is not an outlier and be the same as the majority of that area.
- In conclusion, 1978 environment is not the same as 2018. A lot of variables varies such as economy, inflation, population, lifestyle. So it's not a good idea to use this 1978 model in a real-world setting.

Note: Once you have completed all of the code implementations and successfully answered each question above, you may finalize your work by exporting the iPython Notebook as an HTML document. You can do this by using the menu above and navigating to

File -> Download as -> HTML (.html). Include the finished document along with this notebook as your submission.

In [ ]:

```
```