mathematics

Scree plot

Scree plot is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Scree plot rather than just read about it. In short: In multivariate statistics, a scree plot is a line plot of the eigenvalues of factors or principal components in an analysis. The scree plot is used to determine the number of factors to retain in an exploratory factor analysis (FA) or principal components to keep in a principal component analysis (PCA).

Key takeaways

Scree plot belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Scree plot to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Scree plot from memory before moving on to harder problems.

Reference excerpt

In multivariate statistics, a scree plot is a line plot of the eigenvalues of factors or principal components in an analysis. The scree plot is used to determine the number of factors to retain in an exploratory factor analysis (FA) or principal components to keep in a principal component analysis (PCA). The procedure of finding statistically significant factors or components using a scree plot is also known as a scree test. Raymond B. Cattell introduced the scree plot in 1966. A scree plot always displays the eigenvalues in a downward curve, ordering the eigenvalues from largest to smallest. According to the scree test, the "elbow" of the graph where the eigenvalues seem to level off is found, and factors or components to the left of this point should be retained as significant. As the "elbow" point has been defined as point of maximum curvature, this property has led to the creation of the Kneedle algorithm.

Etymology

The scree plot is named after the elbow's resemblance to a scree in nature.

Criticism This test is sometimes criticized for its subjectivity. Scree plots can have multiple "elbows" that make it difficult to know the correct number of factors or components to retain, making the test unreliable. There is also no standard for the scaling of the x and y axes, which means that different statistical programs can produce different plots from the same data. The test has also been criticized for producing too few factors or components for factor retention.

Illustrations

Worked examples

Example 1 — a first encounter with Scree plot

Start with the simplest possible case. Write down what Scree plot claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Scree plot before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Scree plot ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Scree plot

In research: Scree plot appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Scree plot in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Scree plot is common in secondary-school and first-year university syllabi. It links to neighbouring topics Factor analysis, Statistical charts and diagrams, so understanding it makes those chapters shorter.
In everyday life: Look for Scree plot outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Scree plot” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Scree plot in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Scree plot means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Scree plot out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Scree plot in simple terms?

Why does Scree plot matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Scree plot?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Scree plot.