🏁 Wrap-up quiz¢

This quiz requires some programming to be answered.

Open the dataset house_prices.csv with the following command:

ames_housing = pd.read_csv("../datasets/house_prices.csv", na_values="?")
target_name = "SalePrice"
data = ames_housing.drop(columns=target_name)
target = ames_housing[target_name]

ames_housing is a pandas dataframe. The column β€œSalePrice” contains the target variable. Note that we instructed pandas to treat the character β€œ?” as a marker for cells with missing values also known as β€œnull” values.

To simplify this exercise, we will only used the numerical features defined below:

numerical_features = [
    "LotFrontage", "LotArea", "MasVnrArea", "BsmtFinSF1", "BsmtFinSF2",
    "BsmtUnfSF", "TotalBsmtSF", "1stFlrSF", "2ndFlrSF", "LowQualFinSF",
    "GrLivArea", "BedroomAbvGr", "KitchenAbvGr", "TotRmsAbvGrd", "Fireplaces",
    "GarageCars", "GarageArea", "WoodDeckSF", "OpenPorchSF", "EnclosedPorch",
    "3SsnPorch", "ScreenPorch", "PoolArea", "MiscVal",
]

data_numerical = data[numerical_features]

We will compare the generalization performance of a decision tree and a linear regression. For this purpose, we will create two separate predictive models and evaluate them by 10-fold cross-validation.

Thus, use sklearn.linear_model.LinearRegression and sklearn.tree.DecisionTreeRegressor to create the model. Use the default parameters for both models.

Note: missing values should be handle with a scikit-learn sklearn.impute.SimpleImputer and the default strategy ("mean"). Be also aware that a linear model requires to scale the data. You can use a sklearn.preprocessing.StandardScaler.

Question

Is the decision tree model better in terms of \(R^2\) score than the linear regression?

  • a) Yes

  • b) No

Select a single answer

Instead of using the default parameter for decision tree regressor, we will optimize the depth of the tree. Using a grid-search (sklearn.model_selection.GridSearchCV) with a 10-fold cross-validation, answer to the questions below. Vary the max_depth from 1 level up to 15 levels.

Question

What is the optimal tree depth for the current problem?

  • a) The optimal depth is ranging from 3 to 5

  • b) The optimal depth is ranging from 5 to 8

  • c) The optimal depth is ranging from 8 to 11

  • d) The optimal depth is ranging from 11 to 15

Select a single answer

Question

A tree with an optimal depth has a score of:

a) ~0.74 and is better than the linear model b) ~0.72 and is equal to the linear model c) ~0.7 and is worse than the linear model

Select a single answer

Instead of using only the numerical dataset you will now use the entire dataset available in the variable data.

Create a preprocessor by dealing separately with the numerical and categorical columns. For the sake of simplicity, we will assume the following:

  • categorical columns can be selected if they have an object data type;

  • numerical columns can be selected if they do not have an object data type. It will be the complement of the numerical columns.

Do not optimize the max_depth parameter for this exercise.

Fix the random state of the tree by passing the parameter random_state=0

Question

Are the performance in terms of \(R^2\) better by incorporating the categorical features in comparison with the previous tree with the optimal depth?

  • a) No, the generalization performance is the same: ~0.7

  • b) The generalization performance is slightly better: ~0.72

  • c) The generalization performance is better: ~0.74

Select a single answer