The equation of a regression line linking the number of hours a student spends studying for a math exam ( $x$ ) and their final score out of 100 ( $y$ ) is given by $y = 5.2x + 34.5$ . Interpret the meaning of the parameter $5.2$ in the context of the question. Interpret the meaning of the parameter $34.5$ in the context of the question. A student concludes that "studying for exactly 10 hours causes your score to increase by 52 marks." Explain why this statement is statistically flawed.

$5.2$ is the gradient. It represents the estimated increase in the final score for every additional $1$ hour spent studying. A1 $34.5$ is the $y$ -intercept. It represents the estimated final score for a student who spends exactly $0$ hours studying. A1 Correlation does not imply causation. R1 While the data shows a trend linking study hours and higher scores, there may be confounding variables (e.g., natural ability, prior knowledge, paying attention in class) that contribute to the score. The line only predicts a trend, it does not guarantee a strict causal $52$ -mark increase. R1

Bivariate Data and Correlation Questions

What's examined in AA SL bivariate data and correlation

The question bank covers these bivariate data and correlation question types (number of questions in brackets):

Linear Regression Equation (21)
Pearson's Correlation Coefficient (15)
Regression Line Properties (13)

Key formulas

Mean of a data set: $\bar{x} = \frac{\sum f_{i} x_{i}}{n}, n = \sum f_{i}$

In the same notation as the IB formula booklet. All AA SL formulas →

Bivariate Data and Correlation worked examples

Worked example 1: Finding linear regression parameters · easy

Primary school children's ages $x$ and mean weights $y$ kg: $(6.25, 21.5), (7.35, 23.1), (8.50, 26.9), (9.25, 28.6), (10.75, 32.0)$ . The relationship is modelled by $y = a x + b$ . Find $a$ , $b$ and Pearson's $r$ .

Solution

6 steps · 1 to fill in

Examiner tip: Ensure "Diagnostics On" is enabled so

r

appears alongside

a

and

b

.

Worked example 2: Predicting values and reliability · medium

Regression line $y = 5.30 x + 34.9$ where the sample $x$ ranged $5.9$ to $9.4$ hours. Estimate the score for $x = 10.5$ hours and comment on reliability.

Solution

4 steps

Examiner tip: High

r

does NOT rescue extrapolated predictions. Any

x

outside the observed range makes the estimate unreliable.

Worked example 3: Reversing the regression lines · hard

Regression line $P$ on $D$ : $P = 0.088 D + 13.9$ ; regression line $D$ on $P$ : $D = 6.22 P + 116$ . A customer has budget $P = € 100$ . Predict the maximum distance.

Solution

4 steps

Examiner tip: Never rearrange the "

P

on

D

" line algebraically to predict

D

. Regression lines minimise vertical errors in one direction only.

Try these IB Maths AA SL bivariate data and correlation questions

Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area. One of them has its full worked solution here, open to everyone.

Question 1 · easy · 3 marks · Paper 2

The regression line of $y$ on $x$ for a bivariate dataset is given by $y = - 2.5 x + 10.4$ . The mean of the $x$ -values in the dataset is $3.2$ . Find the exact mean of the $y$ -values.

Attempt it and see the mark scheme →

Question 2 · medium · 4 marks · Paper 1

The equation of a regression line linking the number of hours a student spends studying for a math exam ( $x$ ) and their final score out of 100 ( $y$ ) is given by $y = 5.2 x + 34.5$ .

Interpret the meaning of the parameter $5.2$ in the context of the question.
Interpret the meaning of the parameter $34.5$ in the context of the question.
A student concludes that "studying for exactly 10 hours causes your score to increase by 52 marks." Explain why this statement is statistically flawed.

Full worked solution Free, no sign-in

$5.2$ is the gradient. It represents the estimated increase in the final score for every additional $1$ hour spent studying. A1
$34.5$ is the $y$ -intercept. It represents the estimated final score for a student who spends exactly $0$ hours studying. A1
Correlation does not imply causation. R1
While the data shows a trend linking study hours and higher scores, there may be confounding variables (e.g., natural ability, prior knowledge, paying attention in class) that contribute to the score. The line only predicts a trend, it does not guarantee a strict causal $52$ -mark increase. R1

Every question here has a full worked solution. See them all →

Question 3 · hard · 5 marks · Paper 1

For a dataset containing $n = 10$ pairs of bivariate data $(x, y)$ , the equation of the regression line of $y$ on $x$ is given by $y = 3.2 x - 14.5$ . Given that the sum of all the $x$ -values is $\sum x = 60$ :

Find the mean of $x$ , $\bar{x}$ .
Use the properties of the regression line to find $\bar{y}$ .
Hence, find the exact sum of all the $y$ -values, $\sum y$ .

Attempt it and see the mark scheme →

Free account — sign in to download Topic PDF: 7 questions with worked answers · 4 pages · 196 KB

All 49 bivariate data and correlation questions with mark schemes →

Revise bivariate data and correlation for the exam

FAQ

How many IB Maths AA SL bivariate data and correlation questions are there?

There are 49 exam-style bivariate data and correlation questions in the AA SL question bank (Paper 1: 15 · Paper 2: 34), graded 13 easy, 23 medium, 10 hard, 3 very hard. Every question has a full IB-style mark scheme (M, A and R marks).

Is bivariate data and correlation on Paper 1 or Paper 2?

Both. In the bank, Paper 1: 15 · Paper 2: 34. Paper 1 is non-calculator, so practise the exact-value algebra as well as the GDC methods.

Where can I get the mark schemes?

Open the AA SL Unit 4 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.

Teaching this topic?

Free ready-to-teach lesson (slides and teacher notes): Least-squares regression line.

IB Maths AA SL Bivariate Data and Correlation Questions

Try it first

What's examined in AA SL bivariate data and correlation

Key formulas

Bivariate Data and Correlation worked examples

Worked example 1: Finding linear regression parameters · easy

Solution

Worked example 2: Predicting values and reliability · medium

Solution

Worked example 3: Reversing the regression lines · hard

Solution

Try these IB Maths AA SL bivariate data and correlation questions

Question 1 · easy · 3 marks · Paper 2

Question 2 · medium · 4 marks · Paper 1

Full worked solution Free, no sign-in

Question 3 · hard · 5 marks · Paper 1

Revise bivariate data and correlation for the exam

FAQ

What else is free here

Teaching this topic?

More AA SL Unit 4 topics