🛣️ LSE DS202A 2025: Week 03 - Lab Roadmap

Author

The DS202 Team

Published

15 Sep 2025

🎯 Learning Outcomes

By the end of this lab, you will be able to:

  1. Distinguish between hypothesis testing and machine learning approaches - Understand the fundamental difference between using statistical models to test causal hypotheses versus building predictive models for accurate forecasting on unseen data.

  2. Implement proper machine learning workflow practices - Split datasets into training and test sets using tidymodels, build models on training data, and evaluate performance using appropriate metrics (R-squared, RMSE) on held-out test data.

  3. Apply and interpret penalized regression techniques - Use lasso regression with regularization penalties to perform automatic feature selection, understand how penalty parameters affect coefficient shrinkage, and compare model performance across different penalty values.

  4. Evaluate model performance and identify prediction errors - Create and interpret residual plots to diagnose model fit, calculate prediction errors, and systematically compare multiple modeling approaches to determine the most effective predictive strategy.

Loading libraries and functions

library("ggsci") # For pretty colour schemes
library("MASS") # For simulating data, note: always load before the tidyverse!
library("scales") # For number formatting in ggplot2
library("tidymodels") # For train / test splits
library("tidyverse") # For data wrangling / visualisation
library("colino")

Before we do anything more

  1. Download the lab’s .qmd notebook

Click on the link below to download the .qmd file for this lab. Save it in the DS202A folder you created in the first week. If you need a refresher on the setup, refer back to Part II of W01’s lab.

  1. Please create a data folder called data (in the DS202A folder) to store all the different data sets in this course.

Student Performance


students <- read_csv("data/students-data-cleaned.csv")

We start our machine learning journey with a student performance dataset (students), which contains information on students from two Portuguese schools. We have cleaned the data to only include statistically significant predictors. The columns include:

  • final_grade final grade from 0 to 20 (the outcome)
  • school student’s school (binary: ‘GP’ - Gabriel Pereira or ‘MS’ - Mousinho da Silveira, reference: GP)
  • sex student’s sex (binary: ‘F’ - female or ‘M’ - male, reference: female)
  • age student’s age (numeric: from 15 to 22 years)
  • studytime weekly study time (categorical: ‘<2hrs’, ‘2-5hrs’, ‘5-10hrs’, ‘>10hrs’, reference: <2hrs)
  • failures number of past class failures (categorical: ‘0’, ‘1’, ‘2’, ‘3’, ‘4+’, reference: 0 failures)
  • schoolsup extra educational support (binary: yes or no, reference: no)
  • higher wants to take higher education (binary: yes or no, reference: no)
  • goout going out with friends frequency (categorical: ‘VeryLow’, ‘Low’, ‘Average’, ‘High’, ‘VeryHigh’, reference: VeryLow)
  • dalc workday alcohol consumption (categorical: ‘VeryLow’, ‘Low’, ‘Average’, ‘High’, ‘VeryHigh’, reference: VeryLow)
  • health current health status (categorical: ‘VeryBad’, ‘Bad’, ‘Average’, ‘Good’, ‘VeryGood’, reference: VeryBad)
  • romantic in a romantic relationship (binary: yes or no, reference: no)

Understanding student performance: some exploratory data analysis (EDA) (10 minutes)

Now it’s your turn to explore the students dataset! Use this time to create visualizations and discover patterns in the data that might help explain what drives student success.

Some ideas to get you started:

  • How are final grades distributed? Are they normally distributed or skewed?
  • Do students who want higher education perform better than those who don’t?
  • Is there a relationship between study time and final grades?
  • How does past academic failure affect current performance?
  • Are there differences in performance between the two schools?
  • Does going out with friends impact academic performance?
  • What’s the relationship between health status and grades?
  • Do students receiving extra educational support perform differently?

Challenge yourself:

  • Can you find any surprising relationships in the data?
  • What patterns emerge when you look at combinations of variables?
  • Are there any outliers or interesting edge cases?

Share your most interesting findings on Slack! We’d love to see what patterns you discover and which visualizations tell the most compelling stories about student performance.

# Your EDA code here!
# Try different plot types: histograms, boxplots, scatter plots, bar charts
# Example starter code:

# students |>
#   ggplot(aes(x = final_grade)) +
#   geom_histogram()

Understanding student performance: the hypothesis-testing approach (5 minutes)

Why do some students perform better than others? This is one question that a quantitative social scientist might answer by exploring the magnitude and precision of a series of variables. Suppose we hypothesised that students who want to pursue higher education have better academic performance. We can estimate a linear regression model by using final_grade as the dependent variable and higher as the independent variable.

To run a linear regression, we can use the lm function, which requires two things:

  • A model formula (a.k.a. equation)
  • The data used to estimate the model

Let’s do this now. We can call the summary function to get information on the coefficient estimate for higher.


lm(final_grade ~ higher, data = students) |>
  summary()

Call:
lm(formula = final_grade ~ higher, data = students)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.2759  -1.2759  -0.2759   1.7241   6.7241 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   8.7971     0.3671  23.962   <2e-16 ***
higheryes     3.4788     0.3883   8.958   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.05 on 647 degrees of freedom
Multiple R-squared:  0.1103,    Adjusted R-squared:  0.109 
F-statistic: 80.24 on 1 and 647 DF,  p-value: < 2.2e-16

We see that students who want to pursue higher education have a positive and statistically significant (p < 0.001) increase in final grades of about 3.5 points.

👉 NOTE: The process of hypothesis testing is obviously more involved when using observational data than is portrayed by this simple example. Control variables will almost always be incorporated and, increasingly, identification strategies will be used to uncover causal effects. The end result, however, will involve as rigorous an attempt at falsifying a hypothesis as can be provided with the data.

For an example of how multivariate regression is used, we can run the following code.


lm(final_grade ~ ., data = students) |>
  summary()
Call:
lm(formula = final_grade ~ higher, data = students)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.2759  -1.2759  -0.2759   1.7241   6.7241 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   8.7971     0.3671  23.962   <2e-16 ***
higheryes     3.4788     0.3883   8.958   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.05 on 647 degrees of freedom
Multiple R-squared:  0.1103,    Adjusted R-squared:  0.109 
F-statistic: 80.24 on 1 and 647 DF,  p-value: < 2.2e-16

> lm(final_grade ~ ., data = students) |>
+   summary()

Call:
lm(formula = final_grade ~ ., data = students)

Residuals:
     Min       1Q   Median       3Q      Max 
-11.7275  -1.3732   0.1009   1.5526   7.3862 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)          7.30785    2.54277   2.874 0.004202 ** 
schoolMS            -1.11221    0.27336  -4.069 5.39e-05 ***
sexM                -0.72456    0.24955  -2.904 0.003831 ** 
age                  0.20145    0.10269   1.962 0.050275 .  
addressU             0.40454    0.26203   1.544 0.123168    
famsizeLE3           0.29420    0.24433   1.204 0.229045    
pstatusT             0.28615    0.34907   0.820 0.412702    
meduPrimary          0.25719    1.15015   0.224 0.823137    
medu5th-9th          0.02378    1.15816   0.021 0.983624    
meduSecondary        0.17393    1.17222   0.148 0.882098    
meduHigher           0.36932    1.20668   0.306 0.759670    
feduPrimary         -1.16578    1.07170  -1.088 0.277140    
fedu5th-9th         -0.70044    1.08083  -0.648 0.517205    
feduSecondary       -0.72657    1.10120  -0.660 0.509643    
feduHigher          -0.35673    1.13248  -0.315 0.752874    
mjobhealth           0.70046    0.54668   1.281 0.200602    
mjobother            0.02909    0.30317   0.096 0.923583    
mjobservices         0.48291    0.37275   1.296 0.195652    
mjobteacher          0.15798    0.52398   0.301 0.763147    
fjobhealth          -0.65551    0.75511  -0.868 0.385698    
fjobother            0.01680    0.45963   0.037 0.970861    
fjobservices        -0.42321    0.48310  -0.876 0.381381    
fjobteacher          0.64758    0.69123   0.937 0.349223    
reasonhome          -0.11480    0.28321  -0.405 0.685363    
reasonother         -0.57702    0.36240  -1.592 0.111880    
reasonreputation     0.05013    0.29638   0.169 0.865753    
guardianmother      -0.35945    0.26535  -1.355 0.176073    
guardianother        0.24572    0.53496   0.459 0.646173    
traveltime15-30min   0.09210    0.24772   0.372 0.710193    
traveltime30min-1hr  0.60224    0.42640   1.412 0.158380    
traveltime>1hr      -0.51974    0.72346  -0.718 0.472792    
studytime2-5hrs      0.32059    0.26629   1.204 0.229117    
studytime5-10hrs     0.92405    0.36509   2.531 0.011638 *  
studytime>10hrs      0.97285    0.51866   1.876 0.061198 .  
failures1           -2.64004    0.37785  -6.987 7.74e-12 ***
failures2           -3.04327    0.73865  -4.120 4.34e-05 ***
failures3           -2.98888    0.76691  -3.897 0.000109 ***
schoolsupyes        -1.14529    0.36452  -3.142 0.001764 ** 
famsupyes           -0.12318    0.22828  -0.540 0.589683    
paidyes             -0.26061    0.45938  -0.567 0.570725    
activitiesyes        0.18262    0.22327   0.818 0.413741    
nurseryyes          -0.09086    0.27264  -0.333 0.739053    
higheryes            1.55928    0.38493   4.051 5.80e-05 ***
internetyes          0.29038    0.27702   1.048 0.294973    
romanticyes         -0.35903    0.23038  -1.558 0.119688    
famrelBad            0.27599    0.78502   0.352 0.725286    
famrelAverage        0.51891    0.66642   0.779 0.436504    
famrelGood           1.06771    0.62457   1.710 0.087892 .  
famrelExcellent      0.64974    0.63744   1.019 0.308493    
freetimeLow          0.45627    0.48805   0.935 0.350242    
freetimeAverage     -0.20749    0.44806  -0.463 0.643484    
freetimeHigh        -0.06067    0.47752  -0.127 0.898943    
freetimeVeryHigh    -0.16014    0.55132  -0.290 0.771565    
gooutLow             1.51599    0.45708   3.317 0.000968 ***
gooutAverage         1.08580    0.44860   2.420 0.015809 *  
gooutHigh            0.92551    0.47878   1.933 0.053714 .  
gooutVeryHigh        0.48026    0.50828   0.945 0.345121    
dalcLow             -0.34567    0.32278  -1.071 0.284640    
dalcAverage          0.29935    0.51598   0.580 0.562035    
dalcHigh            -2.18846    0.72651  -3.012 0.002706 ** 
dalcVeryHigh        -0.46026    0.84155  -0.547 0.584646    
walcLow             -0.11154    0.29771  -0.375 0.708055    
walcAverage         -0.26810    0.34007  -0.788 0.430801    
walcHigh            -0.37326    0.42431  -0.880 0.379389    
walcVeryHigh         0.11392    0.63865   0.178 0.858492    
healthBad           -0.27317    0.42497  -0.643 0.520605    
healthAverage       -0.76200    0.38083  -2.001 0.045870 *  
healthGood          -0.32390    0.39305  -0.824 0.410239    
healthVeryGood      -0.97409    0.34813  -2.798 0.005311 ** 
absences            -0.02242    0.02478  -0.905 0.365952    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.593 on 579 degrees of freedom
Multiple R-squared:  0.4244,    Adjusted R-squared:  0.3558 
F-statistic: 6.188 on 69 and 579 DF,  p-value: < 2.2e-16

The . placeholder indicates that we want to use all other variables in the data set. We can see that the coefficient estimate for higher approximately halves in size yet remains positive and highly significant (p < 0.001), suggesting this relationship holds even when controlling for other factors like study time, past failures, and demographic characteristics.

👉 NOTE: p-values are useful to machine learning scientists as they indicate which variables may yield a significant increase in model performance. However, p-hacking where researchers manipulate data to find results that support their hypothesis make it hard to tell whether or not a relationship held up after honest attempts at falsification. This can range from using a specific modelling approach that produces statistically significant (while failing to report others that do not) findings to outright manipulation of the data. For a recent egregious case of the latter, we recommend the Data Falsificada series.

Predicting student grades: the machine learning approach (30 minutes)

Machine learning scientists take a different approach. Our aim, in this context, is to build a model that can be used to accurately predict how happy a person is using a mixture of features and, for some models, hyperparameters (which we will address in Lab 5).

Thus, rather than attempting to falsify the effects of causes, we are more concerned about the fit of the model in the aggregate when applied to unforeseen data.

To achieve this, we do the following:

  • Split the data into training and test sets
  • Build a model using the training set
  • Evaluate the model on the test set

Let’s look at each of these in turn.

Split the data into training and test sets

It is worth considering what a training and test set is and why we might split the data this way.

A training set is data that we use to build (or “train”) a model. In the case of multivariate linear regression, we are using the training data to estimate a series of coefficients. Here is a made-up multivariate linear model with three coefficients derived from (non-existent) data to illustrate things.


sim_model_preds <- function(x1, x2, x3) {
  y <- 1.1 * x1 + 2.2 * x2 + 3.3 * x3
  y
}

A test set is data that the model has not yet seen. We then apply the model to this data set and use an evaluation metric to find out how accurate our predictions are. For example, suppose we had a new observation where x1 = 10, x2 = 20 and x3 = 30 and y = 150. We can use the above model to develop a prediction.


sim_model_preds(10, 20, 30)

We get a prediction of 154 points!

We can also calculate the amount of error we make by calculating residuals (actual value - predicted value).


# Code here

How many points off is our model?

Why do we evaluate our models using different data? Because, as stated earlier, machine learning scientists care about the applicability of a model to unforeseen data. If we were to evaluate the model using the training data, we obviously cannot do this to begin with. Furthermore, we cannot ascertain whether the model we have built can generalise to other data sets or if the model has simply learned the idiosyncrasies of the data it was used to train on. We will discuss the concept of overfitting throughout this course.

We can use the rsample package in the tidymodels ecosystem to split the data into training and test sets.

# Set a seed for reproducibility

set.seed(123)

# Split the data with 75% being used to train the model

students_split <- initial_split(students, prop = 0.75)

# Create tibbles of the training and test set

students_train <- training(students_split)
students_test <- testing(students_split)

👉 NOTE: Our data are purely cross-sectional, so we can use this approach. However, when working with more complex data structures (e.g. time series cross sectional), different approaches to splitting the data will need to be used.

Build a model using the training set

This is remarkably simple. We will use almost exactly the same code we used to build a multivariate linear model, but with one exception. Instead of using the whole of the data, we will only use students_train. We will also only create a model object (mv_model, short for multivariate model).


mv_model <- lm(final_grade ~ ., data = students_train)

Evaluate the model using the test set

Now that we have trained a model, we can then evaluate its performance on the test set. We will look at two evaluation metrics:

  • R-squared: the proportion of variance in the outcome explained by the model.
  • Root mean squared error (RMSE): the amount of error a typical observation parameterised as the units used in the initial measurement.

reg_metrics <- metric_set(rsq, rmse)

mv_model |>
  augment(new_data = students_test) |>
  reg_metrics(truth = final_grade, estimate = .fitted)

🗣️ CLASSROOM DISCUSSION:

How can we interpret these results?

Graphically exploring where we make errors

We are going to build some residual scatter plots which look at the relationship between the values fitted by the model for each observation and the residuals (actual - predicted values). Before we do this for our data, let’s take a look at an example where there is a near perfect relationship between two variables. As this very rarely exists in the social world, we will rely upon simulated data.

We adapted this code from here.

# Set a seed for reproducibility

set.seed(123)

# Create the variance covariance matrix

sigma <- rbind(c(1, 0.99), c(0.99, 1))

# Create the mean vector

mu <- c(10, 5)

# Generate a multivariate normal distribution using 1,000 samples

sim_data <-
  mvrnorm(n = 1000, mu = mu, Sigma = sigma) |>
  as.data.frame() |>
  as_tibble()

Plot the correlation


# Code here

Residual plots


# Build a linear model and plot the fitted versus residual values

lm(V2 ~ V1, data = sim_data) |>
  augment() |>
  ggplot(aes(.fitted, .resid)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  geom_point() +
  theme_scatter() +
  labs(x = "Fitted values", y = "Residuals")

Now let’s run this code for our model.


# Code here

🎯 ACTION POINTS why does the graph of the simulated data illustrate a more well-fitting model when compared to our actual data?

Challenge: Experiment with Filter Methods (30 minutes)

🎯 YOUR CHALLENGE: Experiment with different filter methods for automatic feature selection using the colino package!

Your Mission

You started with this code that selects categorical features using ANOVA:

library("colino")

recipe(final_grade ~ ., data = students_train) |>
  step_select_aov(all_nominal(), -all_outcomes(), outcome = "final_grade", top_p = 5) |> 
  prep() |> 
  bake(new_data = NULL) |> 
  glimpse()

Rows: 486
Columns: 8
$ school      <fct> GP, MS, GP, MS, GP, GP, GP, GP, GP, GP, GP, MS…
$ sex         <fct> F, F, M, M, M, M, F, F, F, M, F, F, F, F, F, F…
$ age         <int> 20, 15, 17, 17, 16, 16, 17, 17, 17, 15, 17, 18…
$ medu        <fct> Primary, Primary, Primary, Higher, Higher, Sec…
$ studytime   <fct> 5-10hrs, 2-5hrs, 2-5hrs, 5-10hrs, 2-5hrs, <2hr…
$ failures    <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ absences    <int> 8, 0, 0, 0, 4, 6, 2, 6, 0, 0, 0, 4, 0, 2, 0, 2…
$ final_grade <int> 15, 14, 8, 16, 11, 15, 12, 11, 16, 13, 10, 10,…

Now explore what other filter methods are available!

🔍 Your Resource

Read this page: https://tidymodels.aml4td.org/chapters/feature-selection.html#sec-automatic-selection

Look for different step_select_* functions and try them out!

🧪 Experiments to Try

Experiment 1: Different Selection Functions

Find and try 2-3 different step_select_* functions from the documentation:

🎯 What to Report

For each method you try, record:

  1. Function name: step_select_???()
  2. What it does: What statistical test/method does it use?
  3. Variable types: Does it work with categorical, numerical, or both?
  4. Features selected: Which features did it choose?
  5. How many: How many features were selected?

Create a simple comparison table!

💡 Questions to Explore

  • Do different methods select different features?
  • Which methods work with which variable types?
  • What happens when you change the selection criteria (top_p vs threshold)?
  • Do any methods surprise you with their selections?

🎪 Bonus Challenges

  • Can you combine multiple selection methods in one recipe?
  • What happens if you select features first, then transform them?
  • Can you extract the actual statistical scores each method calculated?

📢 Share Your Findings

Post on Slack:

  • Which filter methods did you discover and try?
  • Which method selected the most interesting features for predicting student grades?
  • Any surprising differences between methods?

Keep it simple - just experiment and see what you discover!

Using penalised linear regression to perform feature selection (20 minutes)

We are now going to experiment with a lasso regression which, in this case, is a linear regression that uses a so-called hyperparameter - a “dial” built into a given model that can be experimented with to improve model performance. The hyperparameter in this case is a regularisation penalty which takes the value of a non-negative number. This penalty can shrink the magnitude of coefficients down to zero and the larger the penalty, the more shrinkage occurs.

Step 1: Create a lasso model

Run the following code. This builds a lasso model with the penalty parameter set to 0.01.


lasso_model <-
  linear_reg(penalty = 0.01, mixture = 1) |>
  set_engine("glmnet") |>
  fit(final_grade ~ ., data = students_train)

Step 2: Extract lasso coefficients

Use the tidy function on the lasso model to get the coefficients.


# Code here

🎯 ACTION POINTS What is the output? Which coefficients have been shrunk to zero? What is the most important feature?

Step 3: Create a bar plot


# Code here

Step 4: Evaluate on the test set

Although a different model is used, the code for evaluating the model on the test set is exactly the same as earlier.


# Code here

🗣️ CLASSROOM DISCUSSION:

Does this model represent an improvement on the linear model?

(Bonus) Step 5: Experiment with different penalties

This is your chance to try out different penalties. Can you find a penalty that improves test set performance?

Let’s employ a nested tibbles approach to find better penalty values.


# Code here

Which penalty value gives you the lowest RMSE? How do the coefficients change as you increase the penalty?

👉 NOTE: In labs 4 and 5, we are going to use a method called k-fold cross validation to systematically test different combinations of hyperparameters for models such as the lasso.

(Bonus) Challenge: Running multiple univariate regressions efficiently

🎯 YOUR CHALLENGE: Can you figure out how to run a univariate model for all features in the student dataset without creating 11 separate model objects?

Remember our univariate model earlier where we looked at final_grade ~ higher? Now we want to do the same thing for ALL features to see which individual variables are the strongest predictors of student performance.

The naive approach would be to copy-paste code 11 times and create 11 different model objects, but that’s inefficient and error-prone. Your job is to find a more elegant solution!

Your mission:

Figure out how to systematically run univariate regressions for each predictor variable and compare their performance.

Some things to think about:

  • How can you automate the process of fitting multiple models?
  • How will you store and compare the results?
  • What’s the best way to visualize which features are most predictive?

Work in pairs and brainstorm different approaches!

You might consider:

  • Loops (for loops, while loops)
  • Functional programming (map functions)
  • Advanced tidyverse techniques (nested tibbles)
  • Or something completely different!

Questions to explore:

  • Which single variable is the strongest predictor of student performance?
  • Are there any surprisingly weak predictors?
  • How do these univariate results compare to what you found significant in the multivariate model?
  • Do the “best” univariate predictors match what you’d expect from theory?

Get creative and experiment!

There’s no single “right” way to solve this problem. Try different approaches, see what works, and don’t be afraid to ask for help when you get stuck.

Share your approach and findings on Slack! We want to see the different methods you came up with and which features you found most predictive.


# Code here