Spark ML algorithms, including LinearRegression, require that the input features be consolidated into a single column containing vectors. The provided DataFrame schema shows individual columns for each potential feature (e.g., reviewscoresrating, bedrooms, beds). Before training the model, these individual columns must be assembled into a single feature vector column, which is conventionally named "features". This is typically accomplished using the VectorAssembler transformer. The model's fit method is then called on this transformed DataFrame, which now includes the required vector column.

A. The transform method is used to apply a trained model to generate predictions on new data, not for training the model itself.

C. Changes are mandatory because the input DataFrame's format, with separate feature columns, is incompatible with the Spark ML LinearRegression estimator's requirements.

D. While using a Pipeline is a best practice for organizing ML workflows, it is not a strict necessity. The required transformations can be applied sequentially without a Pipeline.

F. This is the opposite of the required action. Spark ML requires combining individual feature columns into a single vector column, not splitting them apart.

---

1. Apache Spark Official Documentation

MLlib Programming Guide

"Feature Extractors

Transformers

and Selectors": This guide explicitly describes the VectorAssembler transformer. It states

"VectorAssembler is a transformer that combines a given list of columns into a single vector column. It is useful for combining raw features and features generated by different feature transformers into a single feature vector

in order to train ML models like logistic regression and decision trees." This directly supports the necessity of creating a feature vector.

Source: https://spark.apache.org/docs/latest/ml-features.html#vectorassembler

2. Databricks Official Documentation

"Tutorial: ML end-to-end on Databricks": In the "Feature engineering" section of this official tutorial

the VectorAssembler is used to combine multiple feature columns into a single features column before the model is trained. This demonstrates the standard

required workflow.

Source: https://docs.databricks.com/en/machine-learning/end-to-end-example.html

Section: "Feature engineering".

3. Apache Spark Official Documentation

MLlib Programming Guide

"Main Concepts": The "Estimator" section explains that an Estimator abstracts the concept of a learning algorithm. Its fit() method accepts a DataFrame to train a model. All provided code examples for estimators like LinearRegression or LogisticRegression show them being trained on a DataFrame that has already been preprocessed to include a "features" vector column.

Source: https://spark.apache.org/docs/latest/ml-guide-main.html#estimators

A pandas API on Spark DataFrame is an abstraction layer built directly on top of a native Spark DataFrame. It acts as a wrapper, utilizing the underlying distributed Spark DataFrame for data storage and computation. To provide the familiar, pandas-like API and features (such as a specific index), it maintains additional metadata alongside the Spark DataFrame. This design allows data scientists to leverage the distributed power of Spark using the well-known pandas syntax, effectively scaling their single-node workflows to big data environments without a steep learning curve.

A. pandas API on Spark DataFrames are distributed, not single-node. Their primary purpose is to enable distributed computation using a pandas-like interface.

B. They are a wrapper API and are not inherently more performant than the native, highly optimized Spark DataFrame API.

D. Both are built on Spark's immutable data structures. The pandas API on Spark does not change this fundamental characteristic.

E. They are fundamentally related; a pandas API on Spark DataFrame cannot exist without an underlying Spark DataFrame.

1. Apache Spark Documentation

Pandas API on Spark

Internals: "Internally

pandas API on Spark DataFrames are composed of a Spark DataFrame and an 'internal frame'. The internal frame holds the information about index and column labels to map the pandas-like API to the Spark DataFrame." This directly supports that it is made up of a Spark DataFrame and additional metadata.

Source: Apache Spark 3.5.1 Documentation

Pandas API on Spark

Internals section.

2. Databricks Documentation

Pandas API on Spark: "The pandas API on Spark provides pandas-equivalent APIs that work on Apache Spark... You can create a pandas API on Spark DataFrame by calling pyspark.pandas.frompandas or pyspark.pandas.readcsv. You can also convert to and from pandas API on Spark DataFrames and PySpark DataFrames..." This demonstrates the direct relationship and interoperability

refuting that they are unrelated (E) and confirming they are built upon Spark's foundation.

Source: Databricks Documentation > Develop on Databricks > Libraries and scripts > Pandas API on Spark.

3. Learning Spark

2nd Edition (O'Reilly)

Chapter 11: Pandas API on Spark: "The pandas API on Spark was created to provide a pandas-like API on top of Spark

so that data scientists can make an easy transition from a single-node machine to a distributed environment... Under the hood

every pandas API on Spark DataFrame is backed by a PySpark DataFrame."

Source: Chambers

B.

& Zaharia

M. (2020). Learning Spark

2nd Edition. O'Reilly Media

Inc. Chapter 11

"What Is the pandas API on Spark?" section.

The question asks for the invalid explanation for the observed difference in Root Mean Squared Error (RMSE) between the two models. RMSE is a standard, widely used, and fundamentally valid metric for evaluating the performance of regression models. It measures the square root of the average of squared differences between predicted and actual values, providing an estimate of the error magnitude in the units of the label. Therefore, the statement that RMSE is an invalid evaluation metric for regression problems is factually incorrect and constitutes an invalid explanation. The other options describe plausible scenarios, including a common error (B) where predictions on a transformed scale are not converted back to the original scale before evaluation.

A. This is a plausible scenario. The second model could be more accurate, but the RMSE was miscalculated (e.g., as described in B), leading to a misleadingly high value.

B. This is a very likely and valid explanation. Failing to apply the exponential function to the second model's log-scale predictions before comparing them to the original price would result in a massive, meaningless RMSE.

C. This describes an irrelevant action. There is no reason to take the log of the first model's predictions, so this does not explain the observed difference. However, it is not a fundamentally false statement about ML principles like option E.

D. This is a simple and valid possibility. The first model, which directly models price, might genuinely be a better fit for the data than the log-transformed model.

1. Databricks Official Documentation

pyspark.ml.evaluation.RegressionEvaluator: The official API documentation for PySpark's RegressionEvaluator class lists rmse (Root Mean Squared Error) as the default metric for evaluation. This confirms its validity and standard use within the Databricks ecosystem.

Source: Apache Spark 3.5.0 Documentation > PySpark > pyspark.ml > pyspark.ml.evaluation. Section: metricName.

2. Databricks Official Documentation

"Regression: predict house prices" Tutorial: This official Databricks tutorial builds a regression model and explicitly uses RMSE to evaluate its performance. The "Evaluate the model" section states

"First

we'll look at the root mean squared error (RMSE). This metric is the square root of the mean squared error. It is a common metric to evaluate regression models."

Source: Databricks Machine Learning Guide > Tutorials > Regression: predict house prices.

3. University Courseware

"An Introduction to Statistical Learning": This is a standard textbook in many university statistics and machine learning programs. In Chapter 2

"Statistical Learning

" Section 2.1.5

"Measuring the Quality of Fit

" the Mean Squared Error (MSE) is introduced as the primary method for assessing the accuracy of a regression model. RMSE is the square root of MSE and is used for the same purpose

often preferred because its units are the same as the response variable.

Source: James

G.

Witten

D.

Hastie

T.

& Tibshirani

R. (2021). An Introduction to Statistical Learning: with Applications in R (2nd ed.). Springer. (Page 30).

4. University Courseware

"An Introduction to Statistical Learning" on Transformations: In Chapter 3

"Linear Regression

" Section 3.3.3

"Other Considerations in the Regression Model

" the text discusses addressing non-linearity by transforming variables. A common approach is replacing the response Y with log(Y). When making predictions with such a model

one must remember to transform the prediction back to the original scale for interpretation and evaluation

which supports why option (B) is a valid potential explanation for error.

Source: James

G.

Witten

D.

Hastie

T.

& Tibshirani

R. (2021). An Introduction to Statistical Learning: with Applications in R (2nd ed.). Springer. (Page 93).

The primary concern is data leakage, which occurs when information from the test set is used to train the model. Standardizing the entire dataset before splitting allows the scaler to learn the mean and standard deviation from the test data, which then influences the transformation of the training data. The correct procedure is to split the data first, then fit the scaler only on the training data. This fitted scaler, which now contains the summary statistics of the training data, is then used to transform both the training and the test sets. The Spark ML Pipeline API is designed to correctly sequence these operations, ensuring that estimators (like StandardScaler) are fitted only on the training data during the pipeline.fit() call, and the resulting transformer is then applied to any dataset, including the test set.

A. Using global minimum and maximum values from the entire dataset is the definition of data leakage, which is the problem that needs to be solved.

B. This is also incorrect as it uses global statistics, leading to data leakage from the test set into the transformation process.

C. Cross-validation is a model validation technique, not a substitute for feature scaling. Scaling must still be performed correctly within each fold of the cross-validation process.

D. Standardizing the training data using statistics from the test data is a severe and fundamentally incorrect form of data leakage.

1. Databricks Official Documentation

"ML end-to-end example": This tutorial demonstrates the correct workflow. A Pipeline containing feature engineering stages is created. The documentation shows the pipeline being fitted only on the training data (pipelinemodel = pipeline.fit(traindf))

and then this fitted model is used to transform the test data (preddf = pipelinemodel.transform(testdf)). This directly supports the methodology described in the correct answer. (See: Databricks Documentation -> Machine Learning -> Tutorials -> ML end-to-end example -> Section: "Create a machine learning model").

2. Apache Spark Official Documentation

"ML Pipelines": The documentation explains that when a Pipeline.fit() method is called

it calls fit() on each Estimator stage (like StandardScaler) in sequence. The resulting Transformer becomes part of the PipelineModel. This PipelineModel can then be used to transform() new data. This confirms that the statistics for scaling are learned only from the data passed to fit()

which should be the training set. (See: Apache Spark 3.5.0 Documentation -> MLlib: Machine Learning Library -> ML Pipelines -> Section: "How it works").

3. Hastie

T.

Tibshirani

R.

& Friedman

J. (2009). The Elements of Statistical Learning. Springer. In Chapter 7

Section 10.2

"The Wrong and Right Way to Do Cross-validation

" the authors explicitly warn against this error. They state

"The test data should be strictly held out from all aspects of the model fitting

including feature scaling. Any preprocessing steps that use data

such as computing means and variances for standardization

must be learned from the training data only and then applied to the test data." This foundational principle of machine learning directly applies to a train-test split.

The Databricks Feature Store Client (fs) provides the gettable() method to retrieve a handle to a specific Feature Table. This method returns a Table object, which contains various metadata attributes associated with the table. The description attribute of this Table object holds the string that was provided as the description during the table's creation. Therefore, chaining .description to the fs.gettable("newtable") call directly accesses and returns this metadata string programmatically.

A. This is incorrect. The Feature Store Python API is designed to manage all aspects of a feature table programmatically, including retrieving its metadata.

B. The createtrainingset() method is used to join features from feature tables with a label DataFrame to create a dataset for model training, not to retrieve metadata.

D. The loaddf() method is called on a Table object to load the feature data itself into a Spark DataFrame, not to access its metadata description.

E. This line of code returns the entire Table object, not the specific description string. The question asks for the code that returns the description itself.

1. Databricks Official Documentation

"Manage feature tables": This document provides examples of interacting with feature tables. Under the section "Get a feature table"

it explicitly shows the code featuretable = fs.gettable(tablename) followed by print(featuretable.description) to access the description.

Source: Databricks Machine Learning Guide > Feature Store > Manage feature tables.

2. Databricks Official Documentation

"Feature Store Python API": The API reference details the FeatureStoreClient.gettable method

which returns a Table object. The documentation for the Table class lists description as a public attribute.

Source: Databricks API reference > Machine Learning APIs > Feature Store Python API > databricks.featurestore.client.FeatureStoreClient.gettable and the Table object definition.