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E-TRADE TOGETHER GLOBAL ACADEMY

Applied Statistics & Data Modeling

Level 3 · Probability, Statistics & Data · Prerequisite: Course 3.2

ACADEMICALLY APPROVED · DESKTOP RUNTIME VERIFIED · MOBILE QA ENVIRONMENT BLOCKED

8 canonical classes · 3 laboratories · 4 module assessments · project · final

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MODULE 1

Regression & Model Building

Build and select conditional models using honest validation evidence.

Learning outcomes: Interpret coefficients; compare candidates; prevent test leakage.

Dependencies: Course 3.2 regression, sampling and inference.

3.3.1 · v1 · 70–90 min

Multiple regression

Learning objectives

  • Identify response and predictors
  • write and interpret a multiple linear model
  • compute fitted values and residuals
  • interpret a coefficient holding other included predictors fixed
  • separate prediction, association and causation.

Worked examples

Worked example 1

Question: Predict synthetic energy use from machine hours and temperature. Data/model: ŷ=12+1.8(hours)+0.5(temp−20).

Assumptions and limitations

comparable machines, linear mean relation, stable measurement. Calculation: at 6 hours and 24°C, ŷ=12+10.8+2=24.8 kWh. Observed 27.0 gives e=2.2 kWh. Validation: substitute units and verify ŷ+e=y. Interpretation: holding temperature fixed, one additional modeled hour is associated with 1.8 kWh higher mean use. Limitation: maintenance condition is omitted; no causal claim.

Worked examples

Worked example 1

Question: Compare a wage model before and after adding experience. Data: simple-model education slope 2.4; multiple-model slope 1.5 after experience enters. Goal: explain the change. Method: omitted-variable reasoning. Result: the education coefficient changes because education and experience share information in this synthetic sample. Validation: coefficients answer different conditional questions. Limitation: neither coefficient proves an educational treatment effect.

Guided practice

  • For ŷ=5+3x₁−2x₂, calculate at (2,1) and interpret β₂.
  • With observed y=10, calculate the residual.

Common mistake and counterexample

Incorrect: “Because β₁>0 after adjustment, increasing x₁ will increase y.” Failure: adjustment covers only included, measured structure. Correction: report a conditional association and state the design needed for causal interpretation. Verify by listing omitted causes, measurement limits and assignment mechanism.

Knowledge check and mastery evidence

M1 identify roles; M2 compute fitted value; M3 compute residual; M4 write a noncausal conditional interpretation. Evidence: correct notation, units and caveat. Criterion: 4/4 with M4 mandatory. Related lab: Model Selection Study.

Next lesson

Model selection.