H2 Maths Correlation & Regression Formula Sheet | PMCC & Lines

Q: What does H2 Maths Notes (JC 1-2): 6.6) Correlation and Linear Regression cover?
A: Product-moment correlation, least-squares lines, residual interpretation, and prediction limits for H2 Maths.

Download: Get the H2 Maths Correlation and Regression formula sheet (PDF) for quick revision, or the complete notes (PDF) for the full walkthrough.

Before you revise
Revisit scatter diagram basics and variance formulas so the transition to algebraic PMCC and regression is smooth. Keep a graphing calculator (GC) or spreadsheet handy to compute $r$ and regression coefficients quickly.

The core idea is simple: Correlation measures association, not cause.

Use it as a working check: Regression predicts one variable from another, so decide which variable is the input before calculating.

Then go one layer deeper: Reliable prediction stays near the observed data range. Example: use Physics score to predict Maths score only if the Physics score is inside the original data range.

Concrete example: A strong link between Physics and Maths scores can help predict one from the other, but it does not prove that one subject caused the other score.

Status: SEAB's current H2 Mathematics (9758) syllabus PDF is labelled for 2026. Topic 6.6 is assessed in Paper 2 Section B (Probability and Statistics, 60 marks) and excludes hypothesis tests.

Formulas at a glance

Every result the 9758 syllabus expects you to recall, on one screen. The GC computes $r$ and the regression coefficients directly - focus your memorisation on what each result means and when to use the correct regression direction. Worked examples for each appear in the sections below.

Correlation coefficient

Regression lines

Residuals and interpretation

Core Definitions

• Product-moment correlation coefficient $r$ measures linear association between $x$ and $y$; $-1 \leq r \leq 1$.
• $r > 0$

PMCC interpretation checkpoint

When a question asks you to comment on $r$, build the sentence in four parts instead of quoting the number alone.

Worked check: if $r = -0.86$ for revision hours missed and test score, write "There is a strong negative linear association between revision hours missed and test score." Do not write that missing revision caused the lower score unless the question gives causal evidence.

Misconception check: the sign tells you direction, while the distance from zero tells you strength. A negative value can still describe a strong association.

Computing $r$

For paired data $(x_i, y_i)$, $r = \dfrac{\sum (x_i - \bar{x})(y_i - \bar{y})}{(n - 1) S_x S_y}$

Example -- Physics vs Maths scores

Data $\left(\text{Physics}, \text{Maths}\right)$ for $6$ students: $(68, 72), (74, 75), (65, 69), (80, 83), (70, 73), (78, 81)$

1. Enter into GC lists and run LinReg(ax+b).
2. Output (rounded): $r = 0.984$, $\bar{x} = 72.5$, $\bar{y} = 75.5$

Regression Line and Prediction

Using the same data, the regression line of $y$ on $x$ (Maths on Physics) is

• $y = 0.913x + 9.34$ (3 s.f.).
• To predict Maths score when Physics = 76: substitute $x = 76$, obtaining $y \approx 78.7$ (nearest whole number 79).
• Only predict within the range of observed $x$

Prediction reliability checkpoint

For prediction questions, the arithmetic is only half the answer. Check whether the input value belongs to the data range before deciding how confidently to use the regression line.

define x and y
  -> check observed x-range
  -> substitute into the correct line
  -> qualify the prediction

Worked check: if the Physics scores used to fit the model range from 65 to 80, predicting Maths score for Physics = 76 is interpolation. Predicting Maths score for Physics = 95 is extrapolation, so the numerical answer should be accompanied by a warning about reliability.

Misconception check: a high $r$ value does not make every prediction safe. Regression reliability depends on the data range and whether a straight-line model is suitable.

Decision map - choose the regression direction first

Before pressing LinReg, translate the question sentence into input and output variables. The output is the variable you want to predict.

Misconception check: swapping the variables is not the same as rearranging the first regression equation. The least-squares line for predicting Maths from Physics minimises vertical errors in Maths. The line for predicting Physics from Maths is fitted again with the roles reversed.

Residuals and Coefficient of Determination

• Residual: $e_i = y_i - \hat{y_i}$

Example -- Interpretation

If $r = 0.82$, then $r^2 = 0.6724$. State: “About 67% of the variation in Maths marks is explained by Physics marks via the fitted linear model.”

$r^2$ interpretation checkpoint

When interpreting $r^2$, name the response variable and keep the statement tied to the fitted linear model.

Worked check: if $r = -0.70$ for hours of sleep and reaction time, then $r^2 = 0.49$. A careful sentence is: "About 49% of the variation in reaction time is explained by the fitted linear relationship with hours of sleep." The negative sign belongs in the direction of association, not in the percentage explained.

Misconception check: $r^2$ does not say that $49\%$ of reaction time is caused by sleep. It describes how much variation in the response variable is accounted for by the fitted straight-line model.

Residual plot checkpoint

After fitting a regression line, use the residual plot to check whether the linear model is still sensible.

Worked check: if residuals are mostly positive for small and large $x$, but negative near the middle, the fitted straight line is missing a curved trend. The problem is not arithmetic; the model shape is wrong for the data.

Calculator Workflows

• TI: LinReg(ax+b) returns $a$ (gradient), $b$ (intercept), $r$, and $r^2$ when diagnostics are on.
• Casio: REG mode $\rightarrow$ LR $\rightarrow$

Exam Watch Points

• Label axes and highlight whether you are predicting $y$ from $x$ or vice versa. The regression line of $x$ on $y$ is different.
• Interpret $r$ in words (“strong/weak, positive/negative”) and link back to context.
• Check units: regression line must retain units of $y$

Practice Quiz

Test your correlation interpretation and regression modelling in one sitting.

Quick Revision Checklist

• Compute $r$ and regression coefficients quickly with calculator support.
• Write regression equations in the form $y = ax + b$ and perform predictions.
• Interpret $r^2$ and residual plots qualitatively.
• Explain interpolation vs extrapolation and avoid causal claims.

Want weekly guided practice on Correlation and Regression? Our H2 Maths tuition programme builds fluency in this topic through structured problem sets and exam-style drills.

Common exam mistakes

• Confusing the two regression lines: The line of $y$ on $x$ minimises vertical residuals; the line of $x$ on $y$ minimises horizontal residuals. Using the wrong line to make a prediction loses accuracy marks.
• Claiming causation from correlation: Stating that a high $r$ value means one variable causes the other is incorrect. Always describe the relationship as an association.
• Extrapolating outside the data range: Predictions are reliable only for $x$

Frequently asked questions

Is there a formula sheet for H2 Maths correlation and regression?
Yes - the "Formulas at a glance" section near the top of this page collects every result you need: the PMCC formula, both regression line equations and the $(\bar{x}, \bar{y})$ fixed point, and the interpolation vs extrapolation rule. Note that the GC computes $r$ and the regression coefficients ($a$ and $b$

Is correlation and regression in Paper 1 or Paper 2?
Topic 6.6 is assessed in Paper 2 Section B (Probability & Statistics, 60 marks). Paper 1 is Pure Mathematics only.

Can I use the GC to find $r$ and the regression equation?
Yes - GC is expected. Use LinReg (TI) or REG → LR → AX+B (Casio) to obtain $a$, $b$, and $r$ directly. You must still define variables, state the regression equation clearly, and interpret results in context.

Are correlation hypothesis tests included in the 2026 syllabus?
No. The 2026 H2 Maths (9758) syllabus explicitly excludes hypothesis tests on the correlation coefficient. Focus only on computing, interpreting, and applying PMCC and the least-squares regression line.

Other H2 Maths formula sheets

Revising more than one topic? Grab the matching one-page formula sheet:

• Functions & graphs: Functions · Graphs & Transformations · Equations & Inequalities
• Sequences & series: Sequences & Series
• Vectors: Vectors
• Calculus: Differentiation · Maclaurin Series · Integration Techniques · Definite Integrals · Differential Equations
• Statistics: Probability · Discrete Random Variables · Normal Distribution · Sampling · Hypothesis Testing · Correlation & Regression (this page)

For the official SEAB reference booklet, see the H2 Maths MF27 formula list.

Sources

• SEAB H2 Mathematics syllabus (9758), examinations from 2026 - Topic 6 Probability and statistics sub-topic 6.6 Correlation and regression (PMCC, least-squares line of $y$ on $x$, interpretation of $r$ and $r^2$; excludes hypothesis tests): https://isomer-user-content.by.gov.sg/334/f27e37f7-f0ec-4a35-b1e8-3a5e88ae2f81/9758_y26_sy.pdf

Next steps: Keep the H2 Maths notes hub on standby for mixed-paper practice that blends this regression module with sampling (6.4) and hypothesis testing (6.5).