Predictive, Prescriptive Analytics for Decision Making

Identify independent variables such as cement and water and the dependent variable concrete strength to predict with linear regression, regression analysis, and the regression line estimated by ordinary least squares.

Explore the intercept-only linear regression model with a real profit example, compute sum of squares and residuals, and compare against a model with an independent variable.

Develop linear regression with an independent variable to predict profit from sales, estimating intercept and regression coefficient with the oil estimator, and compare models by sum of squares.

Interpret the balance of variability by the total sum of squares, partitioned into regression and error, with R-squared showing the percentage of variance explained.

Evaluate regression model performance using mean absolute error, root mean squared error, and mean absolute percentage error; compute absolute and squared errors to compare model accuracy.

This lecture outlines the key assumptions of linear regression—linear relationships, multivariate normality, constant variance residuals with no autocorrelation, and normally distributed errors—plus diagnostic plots and tests.

Analyze residuals in simple linear regression to validate assumptions using residual plots and normal probability plots, checking linearity, independence, equal variances, normality, and outliers.

Apply visual and statistical checks to validate linear regression assumptions using tests like Durbin-Watson for autocorrelation, Shapiro-Wilk for normality, and VIF for multicollinearity, alongside goodness-of-fit assessments.

Explore correlation and causation in regression, interpret correlation coefficients and matrices, and distinguish between association and cause while noting confounding variables.

Explore how heat maps and scatter plots reveal variable relationships for exploratory data analysis, visualizing a correlation matrix with seaborn on matplotlib to show positive, negative, and no correlations.

Apply a use case of multiple linear regression for predictive modeling of concrete strength using eight independent variables. Build a Python statsmodels regression, add a constant, and interpret the summary.

Learn to interpret regression outputs by assessing model significance, R-squared, p-values, and coefficients to determine independent variable impact and use the model for predictions.

Explore simple and multiple linear regression by linking theory to real world use cases, from predicting crop yield from rainfall to forecasting air pollution and election outcomes.

Learn time series data and forecasting, including univariate analysis, historical patterns, and the time and frequency domain approaches, plus components like trend, seasonal, and irregular.

Learn to visualize and explore time series data with common plots, identify trends and seasonality, handle missing values, and use Python, Pandas, and Matplotlib to plot monthly and quarterly aggregates.

Analyze time series by decomposing into trend, seasonality, cyclicity, and irregular components, and apply deterministic or stochastic trend modeling and seasonal adjustment for forecasting.

Distinguish stationary from non stationary series by mean and variance, and no trend or seasonality; use checks, ADF and KPSS tests, resampling concepts like upsampling and downsampling, for predictive analytics.

Explore time series forecasting fundamentals, including data partition into training and validation sets, forecast horizon, forecast range, prediction interval, and measures of predictive accuracy such as MAE, RMSE, and MAPE.

Explore forecasting methods for time series, including simple methods, moving and weighted averages, and additive or multiplicative decomposition, with Python steps to build an additive model.

Learn the basics of exponential smoothing and how simple exponential smoothing forecasts time series data using an alpha-weighted decay, favoring recent observations for univariate data.

Explore Holt's method, a double exponential smoothing approach that models level and trend with alpha and beta, yielding trend-aware forecasts; illustrated in Python with airline passenger data.

Explore Holt-Winters exponential smoothing to forecast time series with trend and seasonality, using additive or multiplicative seasonal components, with Python implementation and model evaluation.

Explore time series forecasting using autocorrelation and partial autocorrelation through ACF and PACF, lag and lag difference, and autoregression, with Python plots to reveal trend, seasonality, and residuals.

Explain how ARIMA combines auto regressive, integrated, and moving average components to forecast time series, determine p, d, q with plots and AIC, and distinguish stationary from non-stationary data.

Learn to build an ARIMA model in Python with monthly sales data, test stationarity with ADF, difference to stationary, and select p, d, q from ACF/PACF for forecasting.

Time series forecasting serves as a predictive model across economics, sales, budgeting, e-commerce, energy, agriculture, travel, and operations, leveraging seasonality and trend to inform pricing, inventory, and resource planning.

Explore prescriptive analytics as the method for choosing the best action from data, and compare it with descriptive and predictive analytics to drive actionable decisions.

Explore how the cost function assesses the sum of squared error and guides gradient descent to update coefficients with learning rate alpha, minimizing the difference between predicted and actual values.

Gradient descent fundamentals are explored, including steps, learning rate, batched and stochastic variants, and best practices to optimize coefficients and cost functions.

Leverage stochastic gradient descent regression to predict FNB spend from adults, children, and roommates, fit a regression model, and evaluate it with R-squared and error metrics.

Explore linear programming as a deterministic technique to optimally allocate finite resources, maximizing or minimizing a linear objective under known constraints, with applications from scheduling to portfolio management.

Identify the four components of a linear programming problem: objective function, decision variables, constraints, and non-negativity, and apply them to a case maximizing product profits.

Formulate a linear programming model for a two-product laptop mix by defining x1 and x2 and maximizing profit, using production, quality check, and storage constraints.

Apply the graphical method to a two-variable linear programming model for laptops A and B, plotting constraints to maximize profit with Z = 60 X1 + 50 X2.

Learn the simplex method for building a linear programming model and solve a product-mix problem with Excel Solver to maximize profit from laptops Type A and B.

Explore the assumptions of linear programming—certainty, linearity, proportionality, adaptivity, and continuity—and how known constants, linear relationships, independent contributions, and fractional solutions shape model choice.

Explore the business applications of linear programming, from product mix and blending to media allocation, portfolio optimization, and workforce, production, and transportation scheduling.

Examine predictive modeling algorithms based on parametric and non parametric methods, comparing their assumptions, advantages, and disadvantages for learning the mapping function from training data for decision making.

Explore the trade-off between accuracy and explainability in predictive modeling, contrasting parametric and non-parametric approaches with real-world use cases like fraud detection, loan default, and price prediction.

Apply a comprehensive framework to choose the right model or test for business problems, covering data types, problem types, and the analytics lifecycle from descriptive to prescriptive.