Podcast
Questions and Answers
Polynomial regression can help predict better by fitting the curvature of actual data.
Polynomial regression can help predict better by fitting the curvature of actual data.
True (A)
The order of the polynomial refers to the smallest exponent in any of the terms.
The order of the polynomial refers to the smallest exponent in any of the terms.
False (B)
Bayes Information Criterion (BIC) is a method used for assessing the performance of regression models.
Bayes Information Criterion (BIC) is a method used for assessing the performance of regression models.
True (A)
K-fold cross validation involves splitting data into two groups: training and testing samples.
K-fold cross validation involves splitting data into two groups: training and testing samples.
Enhancing the linear model can be achieved by incorporating polynomial features.
Enhancing the linear model can be achieved by incorporating polynomial features.
You must include every single x term when working with polynomials in regression.
You must include every single x term when working with polynomials in regression.
Polynomial regression is limited to only first-order terms.
Polynomial regression is limited to only first-order terms.
Stratified sampling is a technique used in k-fold cross validation.
Stratified sampling is a technique used in k-fold cross validation.
The movie 'Iron Man 3' had a higher budget than 'Frozen'.
The movie 'Iron Man 3' had a higher budget than 'Frozen'.
The revenue earned by 'Despicable Me 2' was less than $90,000,000.
The revenue earned by 'Despicable Me 2' was less than $90,000,000.
'Gravity' is 91 minutes long.
'Gravity' is 91 minutes long.
'The Hunger Games: Mocking Jay' generated a revenue of $42,000,000.
'The Hunger Games: Mocking Jay' generated a revenue of $42,000,000.
'Fast & Furious 6' had a longer runtime than 'Frozen'.
'Fast & Furious 6' had a longer runtime than 'Frozen'.
The 'Test set' refers to the training data used in machine learning.
The 'Test set' refers to the training data used in machine learning.
The model evaluates performance by measuring the distance from predicted values to actual values.
The model evaluates performance by measuring the distance from predicted values to actual values.
The highest revenue movie on the list is 'Frozen'.
The highest revenue movie on the list is 'Frozen'.
The algorithm used in polynomial regression is a linear regression model.
The algorithm used in polynomial regression is a linear regression model.
The relationship between features in polynomial regression cannot be non-linear.
The relationship between features in polynomial regression cannot be non-linear.
The Bayes Information Criterion (BIC) is used for model order selection.
The Bayes Information Criterion (BIC) is used for model order selection.
In the BIC formula, 'n' represents the number of features.
In the BIC formula, 'n' represents the number of features.
The sum of squared error (SSe) is calculated as part of the BIC evaluation.
The sum of squared error (SSe) is calculated as part of the BIC evaluation.
Polynomial regression only works with one feature at a time.
Polynomial regression only works with one feature at a time.
The natural logarithm (ln) is used in various statistical methods, including BIC.
The natural logarithm (ln) is used in various statistical methods, including BIC.
The output of polynomial regression cannot be linear regardless of the input features.
The output of polynomial regression cannot be linear regardless of the input features.
Linear regression can be executed by importing LinearRegressio from sklearn.
Linear regression can be executed by importing LinearRegressio from sklearn.
To make predictions using Linear Regression, you first fit the model on the training data using LR.fit(X_train, Y_train).
To make predictions using Linear Regression, you first fit the model on the training data using LR.fit(X_train, Y_train).
The slope of the regression line is indicated by the variable $b$ and is calculated to be 1.16.
The slope of the regression line is indicated by the variable $b$ and is calculated to be 1.16.
The box office data visualization demonstrates the relationship between movie budget and box office earnings.
The box office data visualization demonstrates the relationship between movie budget and box office earnings.
The predict function is used to fit the Linear Regression model to the training data.
The predict function is used to fit the Linear Regression model to the training data.
Adding polynomial features to a model can help balance complexity and generalisability.
Adding polynomial features to a model can help balance complexity and generalisability.
The learning objectives of the lecture include describing different regression models.
The learning objectives of the lecture include describing different regression models.
Logistic regression is only applicable in Weeks 6 and 7 of the course.
Logistic regression is only applicable in Weeks 6 and 7 of the course.
Three regression lines plotted under different conditions would yield identical results regardless of the data variances.
Three regression lines plotted under different conditions would yield identical results regardless of the data variances.
Support Vector Machines are outlined as a basic model for classification in Week 8.
Support Vector Machines are outlined as a basic model for classification in Week 8.
An instance of Linear Regression can be created using LR = LinearRegression().
An instance of Linear Regression can be created using LR = LinearRegression().
Using interaction terms in a model can help illuminate relationships between variables.
Using interaction terms in a model can help illuminate relationships between variables.
Overfitting refers to a model performing poorly on both training and unseen data.
Overfitting refers to a model performing poorly on both training and unseen data.
It is essential to have a holdout set to assess how a model will perform on unseen data.
It is essential to have a holdout set to assess how a model will perform on unseen data.
Deep learning approaches such as CNN and LSTM are classified as traditional linear models.
Deep learning approaches such as CNN and LSTM are classified as traditional linear models.
Feature selection techniques can assist in determining which variables to include in a model.
Feature selection techniques can assist in determining which variables to include in a model.
The budget for 'Despicable Me 2' was $76,020,023.
The budget for 'Despicable Me 2' was $76,020,023.
'Frozen' had a higher revenue than 'Iron Man 3'.
'Frozen' had a higher revenue than 'Iron Man 3'.
The movie 'Gravity' had a run time of 91 minutes.
The movie 'Gravity' had a run time of 91 minutes.
Data leakage occurs when knowledge of the training set leaks into the test set.
Data leakage occurs when knowledge of the training set leaks into the test set.
'Fast & Furious 6' had a lower budget than 'Gravity'.
'Fast & Furious 6' had a lower budget than 'Gravity'.
The revenue for 'The Hunger Games: Mocking Jay' was $42,000,000.
The revenue for 'The Hunger Games: Mocking Jay' was $42,000,000.
The training set is used to apply the learned model for performance testing.
The training set is used to apply the learned model for performance testing.
The movie with the shortest run time in the list is 'Frozen'.
The movie with the shortest run time in the list is 'Frozen'.
Flashcards
Linear Regression
Linear Regression
A method for predicting continuous data. In linear regression, the relationship between variables is assumed to be linear. The model is represented by a straight line equation that aims to minimize the difference between predicted and actual values.
LinearRegression
LinearRegression
A class within the Scikit-learn (sklearn) library that is used to implement the Linear Regression model.
Fitting a model
Fitting a model
The process of training a model by providing it with data. The model uses this data (X_train) to learn the relationship between input variables and the target variable (Y_train).
X_test
X_test
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Y_test
Y_test
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y_predict
y_predict
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Evaluation metrics
Evaluation metrics
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Data splits
Data splits
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Polynomial Regression
Polynomial Regression
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Model Order
Model Order
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Bayes Information Criterion (BIC)
Bayes Information Criterion (BIC)
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Number of Parameters (p)
Number of Parameters (p)
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Number of Observations (n)
Number of Observations (n)
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Sum of Squared Error (SSe)
Sum of Squared Error (SSe)
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Natural Logarithm (ln)
Natural Logarithm (ln)
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Model Order Selection
Model Order Selection
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Order of a Polynomial
Order of a Polynomial
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k-Fold Cross Validation
k-Fold Cross Validation
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Stratified Sampling
Stratified Sampling
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Enhancing Linear Model with Polynomials
Enhancing Linear Model with Polynomials
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Model Fitting
Model Fitting
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Training a model
Training a model
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Test set
Test set
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Data leakage
Data leakage
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Training Set
Training Set
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Model Evaluation
Model Evaluation
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Model Selection
Model Selection
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Residual Plot
Residual Plot
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Performance Evaluation
Performance Evaluation
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Holdout Data
Holdout Data
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Bias-Variance trade-off
Bias-Variance trade-off
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Interaction terms
Interaction terms
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Feature selection
Feature selection
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Holdout set
Holdout set
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Overfitting
Overfitting
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Underfitting
Underfitting
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Predictive modeling
Predictive modeling
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Study Notes
Learning from Data Lecture 4
- Lecture covered regression models, comparing models, and data splits
- Included linear regression syntax, import, creating an instance of the class, fitting the data and predict the expected value
- Recap from Lecture 3, determining the slope and Y-intercept of the regression line
- Learning objectives included describing regression models, understanding polynomial regression, and understanding data splits and cross-validation.
- Overview of different regression models, extending the linear model, and polynomial features
- Introduction to polynomial regression model, form, and Bayes Information Criterion (BIC)
- Introduction to data splits and cross-validation, training and testing samples, and k-fold cross-validation and stratified sampling
- Enhancing the linear model using polynomials to fit the curvature of the data. Polynomial regression aims to explain better and predict better
- Polynomials are a way to capture higher-order features
- Polynomial regression form and the order refers to the largest exponent.
- 1st and 2nd order polynomial regression definitions and examples of visualization
- Capture higher-order features and adding polynomial features.
- The resulting polynomial regression algorithm is still linear due to linear combination of features
- Discussing model order selection using Bayes Information Criterion (BIC) and its components (p, n, ln, SSE)
- How to measure complexity using BIC (n ln(SSE) - n ln(n) + lnp)
Extending the Linear Model
- Logistic regression was used for both regression and classification
- Support Vector Machines(SVM) for regression
- Used deep learning approaches such as MLP, CNN, and LSTM, bias-variance trade off is explained
Extending with Interaction Terms
- Interaction terms can enhance linear models as a way to extend
- Functional form selection involves checking relationships between variables and outcome, evaluating previous studies of interactions, establishing hypotheses, or using feature selection techniques.
- This is applied to other aspects of linear models in machine learning
Data Splits & Testing
- Data splits are crucial for evaluating the model's performance on unseen data.
- Data splitting creates training and testing sets to prevent fitting the model too closely to training data
- Data leakage is a concern. Knowledge of the test set could leak into the training set. Ensuring no overlap is essential for accurate results.
Beyond a Single Test Set
- Uses multiple training and testing pairs
- Calculates average error from testing sets, leading to statistically more significant results.
- How to obtain these sets from historical datasets
K-Fold Cross Validation
- K-fold cross-validation involves splitting data into multiple groups.
- Each group acts as a test set in some iterations
- Rest of data used as training set
- Model trained and evaluated on each iteration
- Model performance scores are averaged for better result
K-fold Cross Validation Python Syntax
- This section provided code examples for different data splits
Stratified Sampling
- Random sampling method that doesn't preserve the proportion within the sample.
- Stratified sampling technique ensures the same proportions of the dataset or feature of interest are preserved in the training and test data splits.
- This ensures the model generalizes and avoids issues with bias or overfitting.
Hold Out Cross-validation w/o Stratified Sampling
- Python code demonstration of how to evaluate the accuracy of target variables on the training and testing data using the train-test split method.
- In this method target variable properties were not consistent between the original, train and test sets.
Hold-out Cross-validation with Stratified Sampling
- Python code example that demonstrates usage of the
stratifyargument in train-test split to maintain the same proportion of the target variable in both the training and testing sets. StratifiedKFoldclass used to ensure consistent target variable proportions in each K-Fold iteration.
Lessons Learned
- The lecture summarized the key learning points, including multiple regression models, data splitting processes, and k-fold cross-validation with stratified sampling methods to select the best polynomial regression model.
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Description
This quiz covers key concepts from Lecture 4 on regression models, including linear and polynomial regression syntax, model comparison, and data splitting techniques. You'll learn about the importance of k-fold cross-validation and the Bayes Information Criterion (BIC) in improving predictive accuracy. Test your understanding of how to enhance linear models with polynomial features and their practical applications.
