Quantitative Economics and Market Modeling

Identify the independent variable, dependent variable, domain, and range of a function.

Evaluate a function from its formula, table, or graph.

Calculate and interpret the slope and intercept of a linear function.

Construct the equation of a line from two data points.

Distinguish linear, polynomial, and exponential patterns from formulas and graphs.

Apply shifts and rescalings to a function and predict their effects on its graph.

Construct and interpret a piecewise function representing a rule such as a tax or tariff schedule.

Plot tabular data and single-variable functions in Python using simple sequences of inputs.

Apply exponent rules to simplify expressions.

Use logarithms to solve an exponential equation.

Solve a quadratic equation by factoring or the quadratic formula.

Solve and graph a linear or quadratic inequality.

Solve a system of two linear equations by substitution and elimination.

Translate a word problem about market quantities into a system of equations.

Solve and verify a two-equation system with Python.

Write a reusable Python function that evaluates a mathematical model over a sequence of inputs.

Calculate an average rate of change from a formula or dataset.

Estimate an instantaneous rate of change using progressively smaller intervals.

Calculate a derivative from the difference quotient for a simple polynomial.

Differentiate sums and powers of functions.

Apply the product and quotient rules for differentiation.

Apply the chain rule to a composite function.

Differentiate exponential and logarithmic functions.

Calculate and interpret a marginal effect and point elasticity.

Find critical points of a differentiable one-variable function.

Identify absolute maxima and minima on a closed interval.

Optimize a one-variable revenue, cost, or profit model.

Find basic antiderivatives using the reverse power rule.

Interpret a definite integral as net accumulation over an interval.

Use the Fundamental Theorem of Calculus to evaluate a definite integral.

Evaluate a definite integral using a simple substitution.

Approximate a definite integral numerically in Python.

Perform scalar multiplication and addition with vectors.

Use a dot product to calculate a weighted total.

Determine whether two vectors are linearly independent.

Perform matrix addition and multiplication with compatible matrices.

Express a system of linear equations in the form Ax=b.

Solve a linear system by row reduction.

Use the ranks of coefficient and augmented matrices to classify a system as having no solution, one solution, or infinitely many solutions.

Perform vector and matrix calculations with NumPy.

Interpret a two-variable function using slices and contour plots.

Calculate first-order partial derivatives of a two-variable function.

Use a gradient to identify the direction of steepest increase.

Use a total differential to approximate the effect of simultaneous input changes.

Find and classify unconstrained critical points using the second-derivative test.

Form a Lagrangian for a two-variable equality-constrained optimization problem.

Solve a two-variable equality-constrained optimization problem.

Visualize and numerically check a multivariable optimization result in Python.

Represent a random experiment using a sample space and events.

Calculate probabilities using complements and the addition rule.

Use permutations and combinations to calculate classical probabilities.

Calculate and interpret a conditional probability.

Calculate joint probabilities using the multiplication rule and distinguish independent from dependent events.

Apply Bayes’ rule to update a probability after observing evidence.

Simulate repeated random events in Python.

Compare theoretical probabilities with simulated relative frequencies.

Distinguish discrete and continuous random variables.

Calculate an expected value from a discrete probability distribution.

Calculate variance and standard deviation from a probability distribution.

Calculate event probabilities using a binomial distribution.

Standardize a normally distributed variable and calculate a probability.

Calculate and interpret covariance and correlation between two random variables.

Generate random observations from a specified distribution in Python.

Demonstrate and explain the Central Limit Theorem using simulated sample means.

Load a tabular dataset into Python and inspect its variables and data types.

Resolve common problems involving missing values, duplicate records, and incorrect data types, and document the decisions made.

Calculate and interpret descriptive statistics for a dataset.

Create histograms, box plots, and scatter plots in Python to examine distributions and relationships.

Identify selection bias, measurement error, and confounding in a proposed study.

Calculate and interpret the standard error and a confidence interval for a population mean.

Conduct and interpret a hypothesis test for a population mean.

Construct and interpret a bootstrap confidence interval in Python.

Explain least squares as the minimization of squared prediction errors.

Fit and interpret a simple linear regression model in Python.

Use residuals and R-squared to assess a fitted regression model.

Interpret confidence intervals and p-values for regression coefficients while accounting for the assumptions that justify them.

Fit and interpret a multiple linear regression model.

Represent and interpret a categorical predictor using indicator variables.

Use logarithmic transformations to model percentage relationships.

Diagnose nonlinearity, unequal error variance, and influential observations using residual plots.

Formulate a focused, quantitatively testable question about a market or economic relationship.

Select a suitable dataset and define outcome, predictor, and control variables that match the research question.

Clean and document a market dataset in a reproducible Python workflow.

Use descriptive statistics and plots to examine a dataset before modelling.

Estimate a regression model that matches the structure of the research question.

Perform sensitivity checks by changing reasonable model specifications.

Distinguish predictive association from a justified causal claim when interpreting results.

Communicate methods, uncertainty, limitations, and findings in a reproducible Python notebook.