Regression Modelling in Machine Learning
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Questions and Answers

What type of regularization does Ridge Regression employ?

  • Dropout regularization
  • Elastic Net regularization
  • L1 regularization
  • L2 regularization (correct)

    • Which statement is true about Lasso Regression?

  • It is not effective for feature selection.
  • It uses the square of weights as a penalty.
  • It can shrink some coefficients to exactly zero. (correct)
  • It always includes all features in the model.

    • What happens to the cost function of Ridge Regression as the value of λ approaches zero?

  • It becomes completely undefined.
  • It turns into the cost function of Lasso Regression.
  • It has no effect on the cost function.
  • It becomes similar to the cost function of linear regression. (correct)

    • What is a primary use of Ridge Regression?

    <p>To address high collinearity between independent variables.</p> Signup and view all the answers

    What distinguishes Lasso Regression from Ridge Regression concerning feature selection?

    <p>Lasso Regression neglects certain features entirely.</p> Signup and view all the answers

    Which of the following statements is false regarding Ridge Regression?

    <p>It can shrink coefficients to exactly zero.</p> Signup and view all the answers

    What is a characteristic of Lasso Regression in comparison to Ridge Regression?

    <p>It provides a pathway to feature selection.</p> Signup and view all the answers

    Which regularization technique is more appropriate when the goal is to retain all features in the model?

    <p>Ridge Regression is preferred.</p> Signup and view all the answers

    What is the primary benefit of Lasso regression?

    <p>It helps in reducing overfitting and performs feature selection.</p> Signup and view all the answers

    Which method is computationally efficient for selecting a subset of predictors?

    <p>Forward stepwise selection</p> Signup and view all the answers

    Which selection method begins with a model containing no predictors?

    <p>Forward stepwise selection</p> Signup and view all the answers

    What is the main concept behind best subset selection?

    <p>To fit a separate model for every possible subset of predictors.</p> Signup and view all the answers

    Principal component analysis is primarily used for which of the following?

    <p>Transforming predictors to reduce dimensionality.</p> Signup and view all the answers

    Which method iteratively removes the least useful predictor from the model?

    <p>Backward stepwise selection</p> Signup and view all the answers

    What type of variable selection approach does shrinkage represent?

    <p>It controls variance by shrinking coefficients.</p> Signup and view all the answers

    What defines the major limitation of best subset selection?

    <p>It is computationally infeasible for large predictor sets.</p> Signup and view all the answers

    What does the intercept of the regression line represent in this context?

    <p>The predicted external marks when internal marks are zero</p> Signup and view all the answers

    Which step in the OLS algorithm involves squaring the differences of X?

    <p>Step 5</p> Signup and view all the answers

    In the context of the regression equation M = 19.04 + 1.89 × M, what does 'M' represent?

    <p>External marks of students</p> Signup and view all the answers

    What defines the maximum point on a curve according to the provided content?

    <p>It has the highest y-coordinate and slope of zero</p> Signup and view all the answers

    What is the primary goal of the Ordinary Least Squares (OLS) method?

    <p>To minimize the sum of the squares of the errors</p> Signup and view all the answers

    What effect does multicollinearity have on the standard errors of coefficients?

    <p>Increases standard errors, making variables statistically insignificant</p> Signup and view all the answers

    Which of the following is NOT a step in calculating 'b' using the OLS algorithm?

    <p>Get the sum of squared differences of Y</p> Signup and view all the answers

    What does a residual indicate in the context of regression analysis?

    <p>The difference between predicted and actual points</p> Signup and view all the answers

    What does the Variance Inflation Factor (VIF) assess?

    <p>The extent of linear relationships among the independent variables</p> Signup and view all the answers

    In multiple linear regressions, what distinguishes it from simple linear regression?

    <p>It uses multiple predictor variables</p> Signup and view all the answers

    What does the regression equation $y = a_0 + a_1x + ε$ represent in regression analysis?

    <p>The relationship between a dependent variable and one or more independent variables</p> Signup and view all the answers

    Which assumption is violated when perfect multicollinearity is present?

    <p>There is an exact linear relationship among independent variables</p> Signup and view all the answers

    What is the result of heteroskedasticity in regression analysis?

    <p>Erroneous predictions due to changing variance of the error term</p> Signup and view all the answers

    Which type of regression uses only one independent variable?

    <p>Simple Linear Regression</p> Signup and view all the answers

    What is the purpose of the linear regression coefficient $a_1$ in the equation?

    <p>It determines the slope of the regression line</p> Signup and view all the answers

    In the context of linear regression, what does high bias indicate?

    <p>Low accuracy of the model</p> Signup and view all the answers

    What is necessary for the OLS estimates to be effective?

    <p>Independent variables must have sufficient variation</p> Signup and view all the answers

    Which regression technique combines multiple types of regression to help improve prediction accuracy?

    <p>Elastic Net Regression</p> Signup and view all the answers

    What does the term ‘random error’ ($ε$) in the regression equation signify?

    <p>Unforeseen variations affecting the dependent variable</p> Signup and view all the answers

    Which of the following accurately describes low variance in a model's predictions?

    <p>Predicted values are consistent and close to each other</p> Signup and view all the answers

    What does the assumption about the number of observations and parameters in linear regression imply?

    <p>number of parameters must be less than observations</p> Signup and view all the answers

    What is a characteristic feature of Logistic Regression compared to Linear Regression?

    <p>It is used for categorical outcome prediction</p> Signup and view all the answers

    In regression analysis, what does the ‘intercept’ ($a_0$) represent?

    <p>It is the predicted value when all independent variables are zero</p> Signup and view all the answers

    How does Stepwise Regression function in the context of model building?

    <p>It adds or removes predictors based on their statistical significance</p> Signup and view all the answers

    What happens when the number of observations (n) is not much larger than the number of parameters (k)?

    <p>This may lead to overfitting and poor predictions.</p> Signup and view all the answers

    Under which condition is linear regression not usable?

    <p>When k &gt; n</p> Signup and view all the answers

    What does regularization aim to achieve in a machine learning model?

    <p>Prevent overfitting by adding extra information</p> Signup and view all the answers

    In linear regression, what is the purpose of the residual sum of squares (RSS)?

    <p>To optimize the parameters for accurate value prediction</p> Signup and view all the answers

    What happens to the magnitude of the feature in a regularization technique?

    <p>It is reduced toward zero.</p> Signup and view all the answers

    What is a critical factor in ensuring the least squares estimates perform well?

    <p>The number of observations (n) must be significantly larger than parameters (k).</p> Signup and view all the answers

    What does adding a complexity term in regularization help to address?

    <p>It helps prevent overfitting.</p> Signup and view all the answers

    Which of the following methods can improve the accuracy of linear regression?

    <p>Shrinkage Approach</p> Signup and view all the answers

    Study Notes

    Regression Modelling

    • Regression in machine learning uses mathematical methods to predict a continuous outcome (y) based on predictor variables (x).
    • Linear regression is a popular method due to its ease of use in predicting and forecasting.
    • Linear regression models show a linear relationship between the dependent (y) and one or more independent (x) variables.
    • The mathematical representation of linear regression is: y = a0 + a1x + ε
      • a0: intercept of the line
      • a1: linear regression coefficient (scaling factor for each input)
      • ε: random error
    • The values for x and y are training datasets used in the model.

    Types of Linear Regression

    • Simple linear regression utilizes a single predictor variable to predict a numerical dependent variable.
    • Multiple linear regression employs multiple predictor variables to predict a numerical dependent variable.

    Common Regression Algorithms

    • Simple linear regression
    • Multiple linear regression
    • Polynomial regression
    • Multivariate adaptive regression splines
    • Logistic regression
    • Maximum likelihood estimation (least squares)

    Simple Linear Regression

    • This is the simplest regression model, involving only one predictor.
    • It assumes a linear relationship between the dependent variable and the predictor variable.
    • The equation for simple linear regression is: Y = a + bX, where
      • a: y-intercept
      • b: slope of the line
    • The slope (b) represents how much the line changes vertically for a one-unit change horizontally.
    • The y-intercept (a) represents the value of Y when X = 0

    Slope of a Simple Linear Regression Model

    • The slope represents the change in the vertical direction (y-axis) over a change in the horizontal direction (x-axis).
    • Slope = Change in Y / Change in X
    • Slope can be positive or negative depending on the relationship between the variables.

    Types of Slopes

    • Positive slope: The line moves upward from left to right -Negative slope: The line moves downwards from left to right
    • Curve linear positive: The line curves upward.
    • Curve linear Negative: The line curves downward.
    • No relationship: The points do not exhibit any linear or curved relationship.

    Error in Simple Regression

    • The regression equation may not always accurately represent the expected values.
    • An error value (ϵ) represents any deviation between predicted and actual values.
    • Marginal or residual error represent this error.

    Maximum and Minimum Points of Curves

    • Maximum points on a curve exhibit the highest y-coordinate and a slope of 0.
    • Minimum points on a curve exhibit the lowest y-coordinate and a slope of 0.

    Multiple Linear Regressions

    • Simple linear regression uses a single predictor variable.
    • In multiple linear regression, more than one predictor variable impacts the response variable.
    • The equation for multiple linear regression: Y = β0 + β1X1 + β2X2 + ... + βnXn +e, where:
      • Y: Output/Response variable
      • β0, β1, β2, ..., βn: Coefficients of the model
      • X1, X2, X3, ..., Xn: Various independent variables
      • e: Error term

    Assumptions for Multiple Linear Regression

    • Linear relationship between target and predictors.
    • Normally distributed residuals.
    • Little to no multicollinearity (correlation between independent variables).

    Improving Accuracy of the Linear Regression Model

    • Accuracy refers to how close an estimation is to the actual value.
    • Prediction refers to estimating values continuously.
    • High bias = low accuracy (values are not close to real values).
    • High variance = low prediction (values are widely scattered).
    • Low bias = high accuracy (values are close to real values).
    • Low variance = high prediction (values are close together).

    Shrinkage (Regularization) Approach

    • Prevents overfitting by adding extra information to the model.
    • Sometimes the model performs well on training data but poorly on unseen data.
      • This is caused by introducing noisy outputs(overfitting).
    • Regularization reduces the magnitude of variable coefficients that helps in generalizing the model well.

    How does Regularization Work?

    • Adding a penalty term(complexity term) to the model.
    • Models aim to minimize the cost function.
    • Two major types of regularization techniques are Ridge Regression and Lasso Regression.

    Ridge Regression

    • A type of linear regression where a small amount of bias is introduced to improve long-term predictions.
    • It reduces model complexity by regularizing coefficients.
    • It's also known as L2 regularization.

    Lasso Regression

    • Another regularization technique that aims to reduce model complexity by reducing coefficient magnitudes.
    • It's a technique similar to ridge regression, differing in the penalty term, which only includes absolute magnitudes of the variables.
    • It's also known as L1 regularization.

    Subset Selection

    • Identifying subset of predictors related to the response, and fitting the model using the subset of predictors.
    • Two types of subset selection:
      • Best subset selection considers all possible subsets.
      • Stepwise subset selection: iteratively adds/removes predictors to find the best subsets using forward/backward selection .

    Dimensionality Reduction

    • A technique where predictor variables are transformed to reduce the number of variables.
    • Principal component analysis (PCA) is a primary dimensionality reduction method.

    Elastic Net Regression

    • Combines lasso and ridge techniques to enhance model regularization by learning from their shortcomings to solve overfitting.
    • The elastic net improves lasso limitations by including more variables (until saturation).

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    Regression Modelling PDF

    Description

    This quiz covers the fundamentals of regression modelling, focusing on linear regression techniques in machine learning. It discusses both simple and multiple linear regression, providing a mathematical foundation and common algorithms used in these approaches. Test your knowledge on these essential concepts of predictive analytics.

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