Model Building (I)

ADS370 · R for Data Science · Week 12

Dr. Ruiwu Niu

Department of Applied Data Science · Hong Kong Shue Yan University

2026-04-14

> HKSYU_ADS370.exe --module MODEL_BUILDING_I --week 12

MODEL BUILDING [I]

Defining Models · Model Families · Practical Examples

ADS370 — R for Data Science  |  Week 12  |  Spring 2026
Instructor : Dr. Ruiwu Niu
Institution: Hong Kong Shue Yan University
References : Wickham & Grolemund (2017) Ch. 18–19  |  Mailund (2017) Ch. 6–7

Last Week’s Recap (1/2)

> LOAD MODULE: WEEK_11_REVIEW ▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░░ 82%

Week 11 — Exploratory Data Analysis

Variation — Every variable has a distribution. Visualise with geom_histogram() / geom_freqpoly() to detect outliers & unusual values.

Covariation — How do two variables move together? - Categorical × continuous → geom_boxplot() - Two continuous → geom_point(), geom_bin2d(), geom_hex()

Missing values — Never ignore. Use is.na(), na.rm = TRUE, or replace with ifelse(). Understand why they are missing.

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 5–6. | Mailund, T. (2017). Beginning data science in R. Apress. Ch. 2, 5.

Last Week’s Recap (2/2)

> LOAD MODULE: WEEK_11_REVIEW ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ 100% OK

Patterns, Models & EDA Cycle

┌─────────────────────────────────────────────────────┐
│  1 Generate Questions                               │
│       ↓                                             │
│  2 Visualise / Transform  (ggplot2, dplyr)          │
│       ↓                                             │
│  3 Refine Questions  ← residuals reveal new signal  │
│       ↑_______________________________________↑     │
│                  ITERATIVE LOOP                     │
└─────────────────────────────────────────────────────┘

“All models are wrong, but some are useful.” — George E. P. Box

Key insight from last week: models can remove a pattern from data, leaving residuals that expose the next hidden structure.

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 5–6. | Box, G. E. P. (1976). Science and statistics. Journal of the American Statistical Association, 71(356), 791–799. https://doi.org/10.1080/01621459.1976.10480949

Today’s Outline

> HKSYU_ADS370.exe --module MODEL_BUILDING_I --week 12

┌────────────────────────────────────────────────────────────────────┐
│  LOADING MODULES FOR ADS370 WEEK 12 ...                            │
├─────────────────────────────────────────────┬──────────────────────┤
│  MODULE                                     │  DURATION            │
├─────────────────────────────────────────────┼──────────────────────┤
│  [§1] DEFINING MODELS                       │  ~30 min             │
│       What is a model?  RMSD  lm()          │                      │
├─────────────────────────────────────────────┼──────────────────────┤
│  [§2] MODEL FAMILIES         ◄── CORE TODAY │  ~35 min             │
│       Model matrix  Categorical  Interaction│                      │
│       Transformations  Splines              │                      │
├─────────────────────────────────────────────┼──────────────────────┤
│  [§3] PRACTICAL EXAMPLES                    │  ~25 min             │
│       Diamonds paradox  NYC Flights         │                      │
├─────────────────────────────────────────────┼──────────────────────┤
│  [§4] AT2 IN-CLASS EXERCISE                 │  60 min              │
│       Implementing Models                   │                      │
└─────────────────────────────────────────────┴──────────────────────┘

Readings: Wickham & Grolemund (2017) Ch. 18–19 | Mailund (2017) Ch. 6–7

§ SECTION 01 / 05 ────────────────────────────

DEFINING MODELS

What is a model? · RMSD · lm() · Optimization

What Is a Model?

A model provides a simple, low-dimensional summary of a dataset. It partitions data into:

• Pattern — the structure captured by the model
• Residuals — what the model does not explain

The key insight:

Models do not reveal truth. They provide useful approximations.

DATA = PATTERN + RESIDUAL
         ↑            ↑
      (model)    (signal left over)

“All models are wrong, but some are useful.” — Box (1976)

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23, p. 345. | Box, G. E. P. (1976). Science and statistics. Journal of the American Statistical Association, 71(356), 791–799. https://doi.org/10.1080/01621459.1976.10480949

The Two Parts of Every Model

① Family of Models

A family is a generic pattern expressed as an equation with free parameters.

Examples:

Family	Equation
Linear	(y = a_1 + a_2 x)
Power law	(y = a_1 x^{a_2})
Polynomial	(y = a_1 + a_2 x + a_3 x^2)

② Fitted Model

The fitted model is the specific member of the family closest to your data.

Example:

\[y = \underbrace{4.22}_{\hat{a}_1} + \underbrace{2.05}_{\hat{a}_2} \cdot x\]

Parameters (_1, _2) are estimated from data.

Analogy: Family = blueprint template. Fitted model = the specific building constructed from it.

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.1, pp. 345–346.

From 250 Lines to One: Visualising the Search

Start with random candidate models from the family (y = a_1 + a_2 x):

library(tidyverse)
library(modelr)

# 250 random (intercept, slope) pairs
models <- tibble(
  a1 = runif(250, -20, 40),  # intercept
  a2 = runif(250, -5, 5)     # slope
)

Most are poor fits — but this shows the space we are searching.

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.2, pp. 347–348.

Measuring Fit: Root-Mean-Squared Deviation

How do we decide which model is “best”?

RMSD — Root-Mean-Squared Deviation

\(\text{RMSD} = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{y}_i)^2}\)

• \((y_i)\) = observed value
  
• \((\hat{y}_i)\) = predicted value from model
  
• Smaller RMSD → better fit

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.2, p. 349.

Grid Search: Brute-Force Parameter Exploration

What grid search reveals:

• 25 × 25 = 625 candidate models evaluated
• Minimum RMSD found at approximately a1 ≈ 4.2, a2 ≈ 2.0
• Still only an approximation — the true optimum lies between grid points

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.2, pp. 350–351.

Newton-Raphson Optimisation with optim()

# Numerical minimisation — finds exact minimum
best <- optim(
  par  = c(0, 0),              # initial guess: a1=0, a2=0
  fn   = measure_distance,
  data = sim1
)

best$par   # ➜ [1] 4.222248  2.051204

optim() uses Newton-Raphson / gradient descent internally. It iteratively steps in the direction of decreasing RMSD until it converges.

Limitations:

• Finds local minimum (not always global)
• Only practical for non-linear families
• For linear models: use lm() → exact global minimum via linear algebra

OPTIMISER LOG:
iteration  1 → dist: 3.12
iteration  8 → dist: 2.18
iteration 24 → dist: 2.07
iteration 51 → CONVERGED
a1 = 4.222  a2 = 2.051

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.2, pp. 351–352.

The lm() Function: Linear Models in R

lm(formula, data) — fits a linear model using ordinary least squares (OLS) via linear algebra. Faster and exact.

Anatomy of output:

Term	Value	Meaning
(Intercept)	4.22	(_1) — value when x=0
x	2.05	(_2) — slope

Generate predictions:

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.2, pp. 352–353. | R Core Team. (2024). R: A language and environment for statistical computing (Version 4.4). R Foundation for Statistical Computing. https://www.R-project.org/

Residuals: What Your Model Missed

Computing residuals:

What to look for in residuals:

• Random scatter around 0 → good fit
• Systematic pattern → model is missing something
• Outliers → unusual observations

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.3, pp. 354–355.

▶ QUICK CHECK — §1 DEFINING MODELS

Write the lm() call that fits mpg as a function of wt from the mtcars dataset.

Interpretation: For every 1,000 lb increase in weight, fuel efficiency decreases by approximately 5.3 mpg.

Dataset: Henderson, H. V., & Velleman, P. F. (1981). Building multiple regression models interactively. Biometrics, 37(2), 391–411. https://doi.org/10.2307/2530428

§ SECTION 02 / 05 ────────────────────────────

MODEL FAMILIES

Model Matrix · Categorical · Interactions · Transformations · Splines

What Is a Model Family?

A model family is a class of equations sharing the same structural form, differentiated only by their parameters.

Common families in data science:

Family	Formula	R function
Linear	(y = a_0 + a_1 x)	lm()
Polynomial	(y = a_0 + a_1 x + a_2 x^2)	lm() + I()
Natural spline	flexible nonlinear	lm() + ns()
Logistic	( = X)	glm(..., binomial)
Robust linear	downweights outliers	MASS::rlm()

Choosing a family is a design decision:

• Start simple — linear first
• Let residuals guide you to more complex families
• Avoid overfitting: more parameters ≠ better model

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.4, pp. 355–356. | Mailund, T. (2017). Beginning data science in R. Apress. Ch. 6, pp. 125–136.

The Model Matrix: Under the Hood

model_matrix(data, formula) translates a formula into a design matrix (X). Each column in (X) becomes a coefficient in the model.

df <- tribble(
  ~y, ~x1, ~x2,
   4,   2,   5,
   5,   1,   6
)

model_matrix(df, y ~ x1)
#   (Intercept) x1
# 1           1  2
# 2           1  1

model_matrix(df, y ~ x1 + x2)
#   (Intercept) x1 x2
# 1           1  2  5
# 2           1  1  6

# Remove intercept with -1:
model_matrix(df, y ~ x1 - 1)
#   x1
# 1  2
# 2  1

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.4.1, p. 356. | Mailund, T. (2017). Beginning data science in R. Apress. Ch. 6, p. 136.

The Model Matrix: Continuous Predictor

From formula to matrix — the linear model:

\[y = a_1 \cdot \underbrace{1}_{\text{intercept col}} + a_2 \cdot \underbrace{x_1}_{\text{predictor col}}\]

model_matrix(df, y ~ x1 + x2)

(Intercept)	x1	x2
1	2	5
1	1	6

Each row = one observation. Each column = one model term.

Rule: The number of columns = the number of estimated parameters.

Key formula notation:

R syntax	Meaning
y ~ x	(y = a_0 + a_1 x)
y ~ x - 1	(y = a_1 x) (no intercept)
y ~ x1 + x2	two predictors
y ~ x1 * x2	interaction
y ~ I(x^2)	quadratic term

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.4.1, pp. 356–357.

Categorical Variables: Dummy Encoding

R automatically converts a categorical variable into dummy (indicator) variables. One level is dropped to avoid perfect multicollinearity (reference category).

df_cat <- tribble(
  ~sex,     ~response,
  "male",   1,
  "female", 2,
  "male",   1
)

model_matrix(df_cat, response ~ sex)
#   (Intercept) sexmale
# 1           1       1    ← male = 1
# 2           1       0    ← female = 0 (reference)
# 3           1       1

Model equation: \[\text{response} = a_0 + a_1 \cdot \text{sexmale}\]

• When sex = "female": sexmale = 0 → response = (a_0)
• When sex = "male": sexmale = 1 → response = (a_0 + a_1)

Why drop one level?
If we had both sexfemale and sexmale, then sexfemale = 1 - sexmale always → perfect collinearity → matrix is singular → lm() fails.

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.4.2, pp. 358–359.

Categorical Predictor: sim2 Example

Key insight: For a categorical-only model, lm() predicts the group mean for each level.

⚠ Warning: New factor levels not seen during training → prediction error.
"Error: factor x has new level e"

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.4.2, pp. 359–360.

Interactions (1): Continuous + Categorical

+ operator — estimates effects independently (parallel slopes).
* operator — estimates effects with interaction (different slopes per group).

Comparing predictions:

grid <- sim3 |>
  data_grid(x1, x2) |>
  gather_predictions(mod1, mod2)   # ← stacks predictions from both models

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.4.3, pp. 360–363.

Interactions (2): Two Continuous Variables

# sim4: both x1 and x2 are continuous
mod1 <- lm(y ~ x1 + x2,      data = sim4)   # additive
mod2 <- lm(y ~ x1 * x2,      data = sim4)   # interaction surface

# Fine-grained prediction grid
grid <- sim4 |>
  data_grid(
    x1 = seq_range(x1, 5),    # 5 evenly spaced x1 values
    x2 = seq_range(x2, 5)     # 5 evenly spaced x2 values
  ) |>
  gather_predictions(mod1, mod2)

With two continuous predictors and interaction, the model surface is a tilted plane (additive) or a warped surface (interaction). You must visualise both variables simultaneously.

seq_range() tips: pretty=TRUE → human-readable steps · trim=0.1 → exclude tails · expand=0.1 → extend range

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.4.4, pp. 363–366.

Transformations Inside Formulas

R formulas support transformations directly — but be careful with operator precedence.

df_t <- tribble(~y, ~x, 1,1, 2,2, 3,3)

# ⚠ WRONG — x^2 is parsed as x*x = x
model_matrix(df_t, y ~ x^2 + x)
#   (Intercept)  x   ← only ONE x column!

# ✅ CORRECT — use I() to protect
model_matrix(df_t, y ~ I(x^2) + x)
#   (Intercept)  I(x^2)  x

# Log transform
model_matrix(df_t, y ~ log(x))

# Square root
model_matrix(df_t, y ~ sqrt(x))

Why I() is needed:

In formula notation: - + means “add predictor” - * means “interaction” - ^ means “crossing to degree n”

I() wraps an expression so R treats it as arithmetic, not formula syntax.

Syntax	Result
y ~ x^2	just x
y ~ I(x^2)	(x^2) term ✓

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.4.5, pp. 366–367.

Natural Splines: A Flexible Family

Natural splines (ns(x, df)) fit piecewise polynomials joined smoothly at knots. They are safer than polynomials for extrapolation.

library(splines)

# sim5: y = 4*sin(x) + noise
# Fit models with 1 to 5 degrees of freedom
mod1 <- lm(y ~ ns(x, 1), data = sim5)
mod2 <- lm(y ~ ns(x, 2), data = sim5)
mod3 <- lm(y ~ ns(x, 3), data = sim5)
mod4 <- lm(y ~ ns(x, 4), data = sim5)
mod5 <- lm(y ~ ns(x, 5), data = sim5)

grid <- sim5 |>
  data_grid(x = seq_range(x, n = 50)) |>
  gather_predictions(mod1, mod2,
                     mod3, mod4, mod5)

Warning: Higher df fits training data well but may extrapolate poorly outside ([0, 3.5]).

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.4.5, pp. 367–368.

Supervised Learning: Specifying Models (Mailund Ch. 6)

Mailund’s perspective: formulas in R are first-class objects with associated environments. lm(y ~ x, data = df) looks up variables in df first, then the formula’s environment.

# Formulas capture their defining environment (like closures)
make_formula <- function() {
  x <- rnorm(5); y <- rnorm(5)
  y ~ x   # formula carries x and y from THIS function's scope
}

f <- make_formula()
lm(f)     # uses x and y from the closure, not global scope

Three model specification components (Mailund):

Component	What it does
model.frame()	Extracts response + predictor data
model.matrix()	Builds design matrix (X)
model.response()	Extracts target vector (y)

Mailund, T. (2017). Beginning data science in R: Data analysis, visualization, and modelling for the data scientist. Apress. Ch. 6, pp. 128–138.

Linear Regression Anatomy: summary(lm())

mod <- lm(y ~ x, data = sim1)
summary(mod)

Call: lm(formula = y ~ x, data = sim1)
Residuals:
   Min      1Q    Median    3Q     Max
 -3.046  -0.913   0.068   0.837   3.219

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  4.2208     0.2735   15.44   <2e-16 ***
x            2.0515     0.0483   42.49   <2e-16 ***

Residual standard error: 1.308 on 28 degrees of freedom
Multiple R-squared:  0.9846,  Adjusted R-squared:  0.9840
F-statistic: 1805 on 1 and 28 DF,  p-value: < 2.2e-16

• Estimate — coefficient value
• Std. Error — uncertainty
• p-value — significance

• R² — proportion of variance explained
• F-statistic — overall model significance

Mailund, T. (2017). Beginning data science in R. Apress. Ch. 6, pp. 128–133. | Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 23.2, p. 353.

Logistic Regression: Binary Outcomes

When the outcome (y {0, 1}), use logistic regression:

\[\log\frac{p}{1-p} = \beta_0 + \beta_1 x_1 + \cdots + \beta_k x_k\]

where (p = P(Y=1 | X)). Use glm() with family = binomial.

# Example: predict survival (binary)
mod_logit <- glm(
  survived ~ age + fare,
  data   = titanic_data,    # illustrative
  family = binomial         # link = logit
)

# Predicted probabilities
titanic_data |>
  add_predictions(mod_logit,
                  type = "response") |>
  head(3)

Mailund, T. (2017). Beginning data science in R. Apress. Ch. 6, pp. 133–136.

Model Matrices and Formulas: Mailund’s View

Mailund shows how to build your own lm()-like function using model matrices directly — demystifying R’s internals.

# OLS solution: β = (X'X)^{-1} X'y
linmo <- function(form, data = NULL) {
  mf     <- model.frame(form, data)
  y      <- model.response(mf, "numeric")
  X      <- model.matrix(form, data)
  # Solve normal equations
  weights <- solve(t(X) %*% X, t(X) %*% y)
  structure(
    list(weights = weights, formula = form, data = data),
    class = "linear_model"
  )
}

# Test it
m <- linmo(y ~ x, data = sim1)
m$weights
#              [,1]
# (Intercept)  4.221
# x            2.052

Mailund, T. (2017). Beginning data science in R. Apress. Ch. 6, pp. 136–140.

▶ QUICK CHECK — §2 MODEL FAMILIES

Using sim3 from modelr:

Discuss with your neighbour: Does the interaction model improve the fit? How can you tell from the residuals?

§ SECTION 03 / 05 ────────────────────────────

PRACTICAL EXAMPLES

Diamonds Paradox · NYC Flights · Iterative Model Building

Why Model Building? The Iterative Workflow

Model building is iterative, not a one-shot process.

┌─────────────────────────────────────────────────────────┐
│                                                         │
│  1 VISUALISE data → spot a pattern                      │
│            ↓                                            │
│  2 FIT a model → make the pattern concrete              │
│            ↓                                            │
│  3 COMPUTE residuals → what's left over?                │
│            ↓                                            │
│  4 VISUALISE residuals → find the next pattern          │
│            ↑_________________________________________↑  │
│                     REPEAT                              │
└─────────────────────────────────────────────────────────┘

Prerequisites for this section:

library(tidyverse); library(modelr)
library(nycflights13); library(lubridate)
options(na.action = na.warn)

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 24.1, p. 415.

Case 1: The Diamond Paradox 💎

Paradox: Lower-quality diamonds (worse cut, colour, clarity) tend to have higher prices. Why?

Worst colour: J (slightly yellow)
Worst clarity: I1 (inclusions visible)
Yet both show higher median prices…

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 24.2, pp. 416–417.

Diamonds: The Confounding Variable — Carat

The hidden variable is carat (diamond weight). Low-quality diamonds tend to be larger, and larger diamonds command higher prices regardless of quality.

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 24.2.1, pp. 417–419.

Diamonds: Fit, Predict, Back-Transform

Key technique: fit the model on the transformed scale, then back-transform predictions to the original scale for interpretation.

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 24.2.1, pp. 419–420.

Diamonds: Residuals Restore the Truth

Interpretation of log₂ residuals:

Residual	Meaning
−1	Half the predicted price
0	Exactly as predicted
+1	Twice the predicted price

After removing carat’s effect: better cut/colour/clarity → higher residual. Paradox resolved.

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 24.2.1, pp. 420–422.

Diamonds: A Richer Model

# Multi-predictor model
mod_diamond2 <- lm(
  lprice ~ lcarat + color + cut + clarity,
  data = diamonds2
)

# Grid using .model to fill in median values
grid <- diamonds2 |>
  data_grid(cut, .model = mod_diamond2) |>
  add_predictions(mod_diamond2)

ggplot(grid, aes(cut, pred)) +
  geom_point(colour = "#39ff14", size = 3)

# Check large residuals (potential pricing errors)
diamonds2 |>
  add_residuals(mod_diamond2, "lresid2") |>
  filter(abs(lresid2) > 1) |>
  select(price, carat, cut, color, clarity) |>
  arrange(price)

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 24.2.2, pp. 422–424.

Case 2: NYC Flights — Daily Counts

Question: What affects the number of daily flights from New York City airports in 2013?

Data: 365 rows × 2 columns

date	n
2013-01-01	842
2013-01-02	943
…	…

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 24.3, pp. 424–425.

Flights: Day-of-Week Model

Pattern: Fewer flights on weekends — especially Saturdays (business travel dominates). The model captures this day-of-week effect cleanly.

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 24.3.1, pp. 425–427.

Flights: Residuals Expose More Patterns

daily <- daily |>
  add_residuals(mod)

ggplot(daily, aes(date, resid)) +
  geom_ref_line(h = 0) +
  geom_line(colour = "#39ff14")

Three remaining patterns in residuals:

① June anomaly — strong regular pattern the model misses

② Saturday seasonality — more flights in summer, fewer in fall

③ Holiday outliers — large negative residuals on: 2013-01-01, 2013-07-04, 2013-09-01, 2013-11-28, 2013-12-25

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 24.3.1, pp. 427–429.

Flights: Seasonal Saturday Effect & Robust Model

# Define academic terms as season proxy
term <- function(date) {
  cut(date,
    breaks = ymd(20130101, 20130605, 20130825, 20140101),
    labels = c("spring", "summer", "fall")
  )
}

daily <- daily |> mutate(term = term(date))

# Model with interaction: wday × term
mod2 <- lm(n ~ wday * term, data = daily)

# Robust model: downweights holiday outliers
mod3 <- MASS::rlm(n ~ wday * term, data = daily)

# Compare residuals
daily |>
  gather_residuals(basic = mod, with_term = mod2) |>
  ggplot(aes(date, resid, colour = model)) +
  geom_line(alpha = 0.75)

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 24.3.2–24.3.4, pp. 429–434. | Venables, W. N., & Ripley, B. D. (2002). Modern applied statistics with S (4th ed.). Springer. https://doi.org/10.1007/978-0-387-21706-2

Key Takeaways from Model Building

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  WEEK 12 CORE PRINCIPLES — MODEL BUILDING (I)
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① Start simple
Linear model first. Complexity only when residuals demand it.

② Transformations linearise
log(), sqrt(), I(x^2), ns() — make non-linear patterns tractable.

③ Residuals are your compass
Every pattern in residuals = next modelling opportunity.

④ Confounders hide truth
Always ask: what third variable could explain this relationship?

⑤ Know when to stop
More parameters → overfitting. Use rlm() for robustness.

⑥ Combine visualisation + model
add_predictions() + add_residuals() + ggplot2 = your standard workflow.

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 24.4, pp. 434–435. | Mailund, T. (2017). Beginning data science in R. Apress. Ch. 6–7.

§ SECTION 04 / 05 ────────────────────────────

AT2 — IN-CLASS EXERCISE

Implementing Models · 60 minutes

AT2: Implementing Models — Task Brief

▶ AT2 — WEEK 12 IN-CLASS EXERCISE · IMPLEMENTING MODELS

Dataset: Use mpg from ggplot2 (or your own dataset with instructor approval)

Tasks (complete all four):

1. EDA — Visualise the relationship between hwy (highway mpg) and at least two predictors. Identify a non-linear pattern.

2. Model fitting — Fit at least two models from different families (e.g., additive vs. interaction, or linear vs. spline). Use lm() or glm().

3. Predictions — Generate prediction grids using data_grid() and add_predictions(). Plot predictions against observed values.

4. Residual analysis — Compute residuals with add_residuals(). Visualise and interpret. Does any pattern remain?

Submission: R script (.R) or R markdown document (.rmd) with plots and a brief written interpretation (≤ 200 words).

AT2 assessment: In-class Exercises (20% total; only best 5 contribute). Assessment details in ADS370 course outline (Niu, R., 2026).

AT2: Step-by-Step Code Scaffold

AT2: Submission & Grading Reminder

▶ AT2 LOGISTICS & RUBRIC

Submission requirements:

• ✅ Working R script or .rmd file
• ✅ At least 2 ggplot2 visualisations
• ✅ All four tasks attempted
• ✅ Written interpretation (≤ 200 words)
• ✅ Submit via Moodle before class ends

Grading focus:

Criterion	Weight
Correct lm()/glm() usage	30%
Prediction visualisation	25%
Residual interpretation	25%
Code clarity & comments	20%

AT2 Assessment Overview:

• 20% of final grade
• Only your best 5 of all weekly exercises count
• Missing this week = one fewer chance at a top-5 score
• Each exercise = equal weight

PROGRESS TRACKER:
■ Week 1  ■ Week 2  ■ Week 3
■ Week 4  ■ Week 5  ■ Week 6
■ Week 7  ■ Week 9  ■ Week 10
■ Week 11 ▶ Week 12 □ Week 13
□ Week 14

§ SECTION 05 / 05 ────────────────────────────

CLOSING

Next Week Preview · References

Next Week Preview — Week 13

> PRELOADING WEEK_13_MODULES ...

Week 13 — Model Building (II)

• List-columns — store models, data frames, and arbitrary objects inside a tibble
• broom package — tidy statistical model outputs into data frames
  • tidy() → coefficients table
  • glance() → model-level statistics
  • augment() → observation-level statistics
• Many models at once — fit hundreds of models simultaneously using purrr::map()
• Quiz 2 — covers Weeks 9–12 content

Readings:

• Wickham & Grolemund (2017), Ch. 20 — Many Models
• Mailund (2017), Ch. 8 — More R Programming

Wickham, H., & Grolemund, G. (2017). R for data science. O’Reilly Media. Ch. 20. | Mailund, T. (2017). Beginning data science in R. Apress. Ch. 8.

References

Box, G. E. P. (1976). Science and statistics. Journal of the American Statistical Association, 71(356), 791–799. https://doi.org/10.1080/01621459.1976.10480949

Henderson, H. V., & Velleman, P. F. (1981). Building multiple regression models interactively. Biometrics, 37(2), 391–411. https://doi.org/10.2307/2530428

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2021). An introduction to statistical learning: With applications in R (2nd ed.). Springer. https://doi.org/10.1007/978-1-0716-1418-1

Mailund, T. (2017). Beginning data science in R: Data analysis, visualization, and modelling for the data scientist. Apress. https://doi.org/10.1007/978-1-4842-2671-1

Niu, R. (2026). ADS370 R for data science: Course outline [Unpublished course document]. Department of Applied Data Science, Hong Kong Shue Yan University.

R Core Team. (2024). R: A language and environment for statistical computing (Version 4.4). R Foundation for Statistical Computing. https://www.R-project.org/

Venables, W. N., & Ripley, B. D. (2002). Modern applied statistics with S (4th ed.). Springer. https://doi.org/10.1007/978-0-387-21706-2

Wickham, H. (2016). ggplot2: Elegant graphics for data analysis (2nd ed.). Springer. https://doi.org/10.1007/978-3-319-24277-4

Wickham, H., & Grolemund, G. (2017). R for data science: Import, tidy, transform, visualize, and model data. O’Reilly Media. https://r4ds.had.co.nz

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ADS370 · Week 12 · Lecture Complete
        END OF TRANSMISSION
        MODEL BUILDING (I)
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SEE YOU NEXT WEEK

Dr. Ruiwu Niu · Department of Applied Data Science
Hong Kong Shue Yan University