In the Patsy example, after fitting a model with `np.linalg.lstsq(X, y)`, how are the model column names reattached to the resulting coefficient array?
Explanation
This question tests the user's knowledge of how to leverage the metadata stored by Patsy to create more interpretable model results.
Other questions
What is the primary method described for turning a pandas DataFrame into a NumPy array, which serves as the point of contact between pandas and other analysis libraries?
What is the result when the to_numpy method is used on a DataFrame containing heterogeneous data, such as a mix of numeric types and strings?
What is the recommended approach for converting only a subset of a DataFrame's columns into a NumPy array?
Which pandas function is used to convert a categorical variable into 'dummy' or 'indicator' variables?
What is the primary purpose of the Patsy library as described in the chapter?
In the Patsy formula syntax 'y ~ x0 + x1', what does the plus symbol (+) signify?
When using `patsy.dmatrices('y ~ x0 + x1', data)`, what additional term is typically included in the resulting design matrix X by default?
How can you prevent Patsy from automatically adding an intercept term to a model's design matrix?
What are 'stateful transformations' in the context of Patsy, and why do they require special handling for new data?
Which Patsy function is used to apply stateful transformations to new, out-of-sample data using the saved information from an original in-sample dataset?
How can you instruct Patsy to treat a numeric column as a categorical variable when creating dummy variables?
What are the two main interfaces provided by the statsmodels library for fitting linear models?
When using the array-based interface in statsmodels (e.g., `sm.OLS`), what function is typically used to add an intercept column to an existing matrix of predictors?
In statsmodels, after fitting a model using the `.fit()` method, what does the `.summary()` method on the results object provide?
What is a key advantage of using the statsmodels formula API (`smf`) with a pandas DataFrame, as demonstrated in the chapter?
In the scikit-learn example using the Titanic dataset, how were the missing values in the 'Age' column handled before fitting the model?
Which scikit-learn method is used to train a model on a training dataset?
What is the primary purpose of cross-validation in model training, as described in the chapter?
Which scikit-learn helper function is shown to perform cross-validation by handling the data splitting process and returning scores for each split?
When creating a model for the Titanic dataset, the 'Sex' column was converted into an 'IsFemale' column. How was this encoding performed?
In the Patsy formula 'v2 ~ key1 + key2 + key1:key2', what does the term 'key1:key2' represent?
Which class from `statsmodels.tsa.ar_model` is used to fit an autoregressive time series model?
In the `cross_val_score(model, X_train, y_train, cv=4)` example, how many scores are returned in the resulting array?
What is the primary distinction between the kinds of models found in statsmodels versus other libraries mentioned, like scikit-learn?
When using `patsy.dmatrices` with a nonnumeric term like `'key1'` which has categories 'a' and 'b', and an intercept is included, how is the term represented in the design matrix?
How can you convert a two-dimensional ndarray back to a pandas DataFrame with specified column names?
What does the Patsy function `I()` allow you to do within a formula string?
After fitting a statsmodels OLS model with the formula API on a DataFrame, what is the data type of the `results.params` attribute?
How do you obtain predicted values for new, out-of-sample data using a fitted statsmodels model?
According to the chapter, what is a key difference in the API for logistic regression between scikit-learn's `LogisticRegression` and `LogisticRegressionCV`?
In the autoregressive model example `model = AutoReg(values, MAXLAGS)`, what does the `MAXLAGS` argument represent?
What is the first value in the `results.params` array for the fitted `AutoReg` model in the statsmodels example?
In scikit-learn, what is the standard method to obtain predictions on a test dataset (`X_test`) from a fitted model instance (`model`)?
Based on the code snippet `data['category'] = pd.Categorical(['a', 'b', 'a', 'a', 'b'], categories=['a', 'b'])`, what is the purpose of the `categories` argument?
In the example where a DataFrame `df3` with numeric and string columns is converted using `df3.to_numpy()`, what is the resulting array's `dtype`?
In the Patsy formula `y ~ standardize(x0) + center(x1)`, what is the effect of the `center(x1)` transformation?
What is the key difference between the formula `y ~ x0 + x1` and `y ~ x0 * x1` in Patsy?
When fitting the initial Ordinary Least Squares model in the statsmodels section (`model = sm.OLS(y, X)`), why was the model fit without an explicit intercept term in the call?
In the scikit-learn example `model.fit(X_train, y_train)`, what does `X_train` represent?
What workflow is described as common for model development in the first paragraph of Chapter 12.1?
Based on the code `dummies = pd.get_dummies(data.category, prefix='category')`, what is the purpose of the `prefix` argument?
What type of library is Patsy described as being inspired by?
What is the result of running the code `(y_true == y_predict).mean()` in the scikit-learn section?
Why might it be simpler and less error-prone to use Patsy when you have more than simple numeric columns?
What are the three predictors used to create the `X_train` NumPy array for the Titanic survival model?
When the formula API of statsmodels (`smf.ols`) is used with the formula 'y ~ col0 + col1 + col2', what does the resulting `results.tvalues` attribute contain?
In the scikit-learn section, what is the default scoring metric for `cross_val_score` described as being dependent on?
What type of data is the `to_numpy` method primarily intended for, according to the text?
When creating a logistic regression model in scikit-learn with `model = LogisticRegression(C=10)`, what does the `C` parameter typically control?