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Unit 3 of 4 · MBA Sem 2

Unit 3: Predictive modeling

Business Analytics for Decision Making notes · PTU syllabus (MBA 201-26)

3 min read7 topics10 exam questions
On this page
  1. Unit summary
  2. Business forecasting methods
  3. Correlation analysis
  4. Linear regression
  5. Testing the assumptions of regression
  6. Logistic regression
  7. K-nearest neighbours and decision trees
  8. Model evaluation techniques
  9. Key terms
  10. Quick revision
  11. Important questions

Unit summary

Predictive models estimate what is likely to happen so that managers can act early. This unit covers business forecasting methods, correlation and regression, testing regression assumptions — multicollinearity, heteroscedasticity and autocorrelation — linear and logistic regression, K-nearest neighbours, decision trees and model evaluation using SPSS.

After this unit you can

  • Explain business forecasting methods
  • Apply correlation and linear regression and test their assumptions
  • Apply logistic regression, KNN and decision trees
  • Evaluate predictive models

PTU syllabus topics

  • Business forecasting methods
  • correlation and regression analysis
  • testing assumptions (multicollinearity, heteroscedasticity, autocorrelation)
  • linear regression
  • logistic regression
  • K-nearest neighbors
  • decision trees
  • model evaluation techniques using SPSS
ComparisonPredictive models
Predicts
Example

Linear regression

A number

Next quarter's sales

Logistic regression

Probability of a class

Will this customer churn?

k-NN

Class from similar cases

Credit risk band

Decision tree

Class or number by rules

Loan approval

1

Topic 1

Business forecasting methods

ClassificationForecasting methods
Forecasting

  • Qualitative

    Expert opinion, Delphi method, sales force composite, market surveys

  • Time series

    Moving averages, exponential smoothing, trend projection, ARIMA

  • Causal (econometric)

    Regression on drivers such as price, income, advertising

  • Machine learning

    Decision trees, ensembles, neural networks

  • Steps: define the purpose and horizon, collect data, choose the method, build and validate, forecast, monitor errors.
  • Forecast accuracy: MAD (mean absolute deviation), MSE, MAPE (mean absolute percentage error).
2

Topic 2

Correlation analysis

r = Σ(x − x̄)(y − ȳ) / √[Σ(x − x̄)² × Σ(y − ȳ)²] r lies between −1 and +1: +1 perfect positive, −1 perfect negative, 0 no linear correlation.

Example

x: 1, 2, 3, 4, 5 and y: 2, 4, 5, 4, 5. With x̄ = 3 and ȳ = 4: Σdxdy = 6, Σdx² = 10, Σdy² = 6, so r = 6/√60 ≈ 0.77 — fairly high positive correlation.

The probable error PE = 0.6745 (1 − r²)/√n; if r > 6 PE, correlation is significant.

3

Topic 3

Linear regression

Regression estimates the value of one variable from another. Two regression lines exist:

  • y on x: y − ȳ = byx (x − x̄), with byx = r × σy/σx
  • x on y: x − x̄ = bxy (y − ȳ), with bxy = r × σx/σy

The principle of least squares fits the line that minimises the sum of squared vertical deviations.

Key termsProperties of regression coefficients
Geometric mean
r = ±√(byx × bxy)
Same sign
byx, bxy and r all have the same sign
Both cannot exceed 1
If one is above 1, the other is below 1
Independent of origin
But not of scale
Lines meet
At (x̄, ȳ)
ComparisonCorrelation vs regression
Correlation
Regression

Purpose

Measures strength of relationship

Predicts one variable from another

Symmetry

rxy = ryx

byx ≠ bxy

Cause and effect

Not implied

Treats one as dependent

  • Multiple regression: Y = b0 + b1X1 + b2X2 + … + e; each b shows the effect of one variable holding the others constant.
  • Goodness of fit: R² (share of variation explained), adjusted R² (penalises extra variables), F-test for the overall model, t-tests for individual coefficients.

Exam tip

In SPSS: Analyze → Regression → Linear; read Model Summary (R²), ANOVA (F, Sig.) and Coefficients (B, Beta, t, Sig.).

4

Topic 4

Testing the assumptions of regression

ClassificationRegression assumptions and tests
Assumptions

  • Linearity

    Scatter and residual plots

  • Normality of residuals

    Histogram, P–P plot of residuals

  • No multicollinearity

    VIF below 10 (stricter: below 5), tolerance above 0.1

  • Homoscedasticity

    Residual vs predicted plot shows no funnel; Breusch–Pagan test

  • No autocorrelation

    Durbin–Watson statistic near 2 (1.5 to 2.5 acceptable)

  • Remedies: drop or combine correlated predictors (multicollinearity), transform variables or use robust errors (heteroscedasticity), add lagged variables or use time-series models (autocorrelation).

Exam tip

In SPSS: under Linear Regression → Statistics tick Collinearity diagnostics and Durbin–Watson; under Plots put ZRESID against ZPRED.

5

Topic 5

Logistic regression

Logistic regression predicts a binary outcome (buy or not, default or not) by modelling the log-odds as a linear function of predictors.

Key formulasLogistic model

  • Probability

    P = 1 ÷ (1 + e^−(b0 + b1X1 + …))

  • Odds ratio

    Exp(B) — change in odds for a one-unit rise in X

  • Output: omnibus test, Nagelkerke R², Hosmer–Lemeshow test, classification table, Exp(B).

Exam tip

In SPSS: Analyze → Regression → Binary Logistic.

Example

A bank's model gives Exp(B) = 1.8 for "missed EMI in last year" — a borrower with a missed EMI has 1.8 times the odds of default.

6

Topic 6

K-nearest neighbours and decision trees

  • KNN: classifies a new case by the majority class of its k closest cases (distance on standardised variables); simple but slow on large data and sensitive to the choice of k. SPSS: Analyze → Classify → Nearest Neighbor.
  • Decision tree: splits data repeatedly on the variable that best separates outcomes, producing if–then rules. Algorithms: CHAID, CART (CRT), QUEST, C4.5. SPSS: Analyze → Classify → Tree.
ClassificationExample decision tree for loan default
Applicant

  • Income below ₹30,000

    Check credit score — below 650 high risk; otherwise medium risk

  • Income ₹30,000 or more

    Check existing EMIs — above 50% of income medium risk; otherwise low risk

  • Strengths of trees: easy to explain, handle mixed data; weakness: may overfit — controlled by pruning and minimum node size.
7

Topic 7

Model evaluation techniques

  • Validation: split data into training and test sets (e.g., 70:30), or use k-fold cross-validation, to check performance on unseen data.
Key formulasEvaluation measures

  • R² and adjusted R²

    Variation explained (regression)

  • RMSE

    √(mean of squared errors)

  • Accuracy

    (TP + TN) ÷ total

  • Precision

    TP ÷ (TP + FP)

  • Recall (sensitivity)

    TP ÷ (TP + FN)

  • F1 score

    2 × precision × recall ÷ (precision + recall)

  • ROC curve and AUC: plot sensitivity against 1 − specificity; AUC near 1 is excellent, 0.5 is no better than chance.
  • Overfitting vs underfitting: a model too complex fits noise; one too simple misses patterns.

Key terms

Multicollinearity
High correlation among predictors
Heteroscedasticity
Unequal variance of residuals
Durbin–Watson
Statistic testing autocorrelation of residuals
Logistic regression
Model for a binary outcome
Confusion matrix
Table of predicted vs actual classes

Quick revision

  • Forecasting: qualitative, time series, causal, machine learning; MAD, MAPE.
  • Correlation; linear and multiple regression; R², adjusted R².
  • Assumptions: linearity, normality, VIF, homoscedasticity, Durbin–Watson.
  • Logistic regression (Exp(B)); KNN; decision trees (CHAID, CART).
  • Evaluation: train–test, cross-validation, confusion matrix, ROC–AUC.

Important exam questions

Practice questions written to the PTU exam pattern for this unit's syllabus: short answers (Section A style) and long answers (Sections B and C style).

Short-answer questions

  1. Q1.Name two qualitative forecasting methods.
  2. Q2.What is multicollinearity and how is it detected?
  3. Q3.What does a Durbin–Watson value of 2 indicate?
  4. Q4.When is logistic regression used?
  5. Q5.What is the k in KNN?
  6. Q6.Define precision and recall.

Long-answer questions

  1. Q1.Discuss the methods of business forecasting.
  2. Q2.Explain linear regression and the tests of its assumptions.
  3. Q3.Explain logistic regression, KNN and decision trees as predictive tools.
  4. Q4.Explain the techniques used to evaluate predictive models.

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