Data Analytics Predictive Analytics and Modeling Syllabus

Predictive Analytics and Modeling syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Predictive Analytics and Modeling in Data Analytics, not a summary of it.

1. 1

   Regression Analysis

   4 topics

   • Multiple Linear Regression
   • Assumptions and Diagnostics
   • Logistic Regression
   • Regularization
2. 2

   Introduction to Machine Learning

   4 topics

   • Supervised vs Unsupervised Learning
   • Training, Validation and Test Splits
   • Overfitting and Underfitting
   • Bias-Variance Tradeoff
3. 3

   Classification and Clustering

   4 topics

   • Decision Trees and Random Forests
   • K-Nearest Neighbors
   • K-Means Clustering
   • Dimensionality Reduction with PCA
4. 4

   Model Evaluation

   4 topics

   • Regression Metrics
   • Classification Metrics
   • Confusion Matrix
   • Cross-Validation
5. 5

   Time Series Analysis

   4 topics

   • Trend, Seasonality and Cyclicity
   • Moving Averages and Smoothing
   • Forecasting Methods
   • Evaluating Forecasts

Predictive Analytics and Modeling flashcards for Data Analytics

19 of 51 cards from the Predictive Analytics and Modeling deck — real questions with worked answers.

1. What is the general form of a multiple linear regression model with $p$ predictors?

   $$y = \beta_{0} + \beta_{1}x_{1} + \beta_{2}x_{2} + \cdots + \beta_{p}x_{p} + \varepsilon$$ where $\beta_{0}$ is the intercept, each $\beta_{j}$ is a partial slope coefficient, and $\varepsilon$ is the random error term.

2. In multiple linear regression, how do you interpret a coefficient $\beta_{j}$?

   $\beta_{j}$ is the expected change in the response $y$ for a one-unit increase in predictor $x_{j}$, holding all other predictors constant (ceteris paribus).

3. What method estimates the coefficients in linear regression, and what quantity does it minimize?

   Ordinary Least Squares (OLS). It minimizes the residual sum of squares $$\text{RSS} = \sum_{i=1}^{n}\left(y_{i} - \hat{y}_{i}\right)^{2}.$$

4. What is the closed-form (normal equation) solution for the OLS coefficient vector $\hat{\beta}$?

   $$\hat{\beta} = \left(X^{\top}X\right)^{-1}X^{\top}y$$ where $X$ is the design matrix and $y$ is the response vector.

5. List the key assumptions of the classical linear regression model.

   Linearity of the relationship, independence of errors, homoscedasticity (constant error variance), normality of errors, and no perfect multicollinearity among predictors.

6. What is multicollinearity and which diagnostic detects it?

   Multicollinearity is high correlation among predictors, which inflates coefficient variance and destabilizes estimates. It is detected with the Variance Inflation Factor: $$\text{VIF}_{j} = \frac{1}{1 - R_{j}^{2}},$$ where $R_{j}^{2}$ is from regressing $x_{j}$ on all other predictors. $\text{VIF} > 5$–$10$ signals a problem.

7. What is heteroscedasticity and how can a residual plot reveal it?

   Heteroscedasticity is non-constant variance of the errors across fitted values. In a plot of residuals versus fitted values it appears as a funnel/fan shape rather than a constant-width band.

8. What plot checks the normality-of-residuals assumption, and what indicates a violation?

   A Q-Q (quantile-quantile) plot of the residuals. Points falling on the $45^{\circ}$ line indicate normality; systematic curvature or heavy tails indicate a violation.

9. What does the logistic (sigmoid) function output and what is its formula?

   It maps any real number to a probability in $(0,1)$: $$\sigma(z) = \frac{1}{1 + e^{-z}}.$$

10. Write the logistic regression model in terms of the log-odds (logit).

    $$\ln\!\left(\frac{p}{1-p}\right) = \beta_{0} + \beta_{1}x_{1} + \cdots + \beta_{p}x_{p}$$ where $p$ is the probability of the positive class.

11. How is a logistic regression coefficient interpreted after exponentiation?

    $e^{\beta_{j}}$ is the odds ratio: the multiplicative change in the odds of the positive outcome for a one-unit increase in $x_{j}$, holding other predictors constant.

12. What loss/cost function is minimized to fit logistic regression?

    The log loss (binary cross-entropy): $$J = -\frac{1}{n}\sum_{i=1}^{n}\left[y_{i}\ln \hat{p}_{i} + (1-y_{i})\ln(1-\hat{p}_{i})\right].$$

13. What problem do regularization techniques address, and how in general?

    They combat overfitting by adding a penalty on coefficient magnitudes to the loss, shrinking coefficients toward zero and reducing model variance.

14. State the Ridge (L2) regression objective.

    $$\min_{\beta}\ \sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2} + \lambda\sum_{j=1}^{p}\beta_{j}^{2}$$ where $\lambda \geq 0$ controls the strength of the L2 penalty.

15. State the Lasso (L1) regression objective and its distinctive property.

    $$\min_{\beta}\ \sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2} + \lambda\sum_{j=1}^{p}\lvert\beta_{j}\rvert.$$ The L1 penalty can shrink coefficients exactly to zero, performing automatic feature selection.

16. How do Ridge and Lasso differ in their effect on coefficients?

    Ridge (L2) shrinks all coefficients smoothly toward zero but rarely to exactly zero; Lasso (L1) can set some coefficients exactly to zero, yielding sparse models and feature selection. Elastic Net combines both penalties.

17. What is the core distinction between supervised and unsupervised learning?

    Supervised learning uses labeled data (input–output pairs) to learn a mapping for prediction (classification/regression); unsupervised learning uses unlabeled data to discover structure such as clusters or lower-dimensional representations.

18. Give two example tasks each for supervised and unsupervised learning.

    Supervised: regression (predicting a numeric value) and classification (predicting a category). Unsupervised: clustering (e.g., K-Means) and dimensionality reduction (e.g., PCA).

19. What are the purposes of the training, validation, and test splits?

    Training set: fit model parameters. Validation set: tune hyperparameters and select models. Test set: give an unbiased final estimate of generalization performance on unseen data.

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