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SL 4.10—X on y regression line - IB Questionbank | RevisionDojo

Practice SL 4.10—X on y regression line with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SLPaper 2

A researcher collects data on the hours spent practicing a musical instrument, $m$ , and the performance score, $p$ , out of 100 , for eight students.

$m$ (hours)	2	4	6	8	10	12	14	16
$p$ (score)	50	60	65	70	75	80	85	90

Let $L_{1}$ be the regression line of $m$ on $p$ , given by $m=a p+b$ . Let $L_{2}$ be the regression line of $p$ on $m$ .

Find the values of $a$ and $b$ .

[2]

Both lines intersect at the mean point ( $\bar{m}, \bar{p}$ ). Calculate $\bar{m}$ and $\bar{p}$ .

[2]

A student practiced for 9 hours. Estimate their performance score using an appropriate regression line. marks]

[2]

Question 2

SLPaper 2

A café records the daily temperature, $d{ }^{\circ} \mathrm{C}$ , and the number of coffees sold, $c$ , over seven days.

$d\left({ }^{\circ} \mathrm{C}\right)$	15	18	20	22	25	28	30
$c$	60	55	50	45	40	35	30

The regression line of $c$ on $d$ is $c=-2 d+85$ . Let $L_{1}$ be the regression line of $d$ on $c$ , given by $d=k c+m$ .

Find the values of $k$ and $m$ .

[2]

Estimate the temperature when 42 coffees are sold.

[2]

Question 3

SLPaper 2

A school records the time spent on homework, $t$ hours, and test scores, $s$ , for ten students. The regression line of $s$ on $t$ is $s=5 t+40$ . The regression line of $t$ on $s$ is $t=0.15 s-4.5$ .

Find the mean time spent on homework, $\bar{t}$ .

[3]

A student scores 72 on the test. Estimate their homework time using an appropriate regression line.

[2]

Comment on the validity of using the regression line of $s$ on $t$ to predict the score for a student who spent 12 hours on homework.

[2]

Question 4

SLPaper 2

A gym tracks the number of push-ups, $p$ , and the heart rate, $h$ beats per minute, of nine members after a workout.

The regression line of $h$ on $p$ is $h=2 p+80$ . The regression line of $p$ on $h$ is $p=0.4 h-28$ .

Estimate the heart rate for a member who does 38 push-ups.

[2]

Find the mean number of push-ups, $\bar{p}$ .

[3]

On the grid above, sketch the regression line of $p$ on $h$ .

[2]

Question 5

SLPaper 2

Three scatter diagrams ( $\mathrm{A}, \mathrm{B}, \mathrm{C}$ ) show relationships between variables $x, y$ , and $z$ over time in an experiment.

Identify which diagram shows (i) no correlation, (ii) strong positive correlation, (iii) strong negative correlation.

[3]

Given correlation coefficients: $0.95,-0.90,0.10,-0.05,1.20$ , assign the appropriate coefficient to each diagram and explain why 1.20 is rejected.

[4]

Question 6

SLPaper 2

The table below shows the number of hours, $h$ , a group of six students spent on homework and their corresponding test scores, $s$ , out of 100 .

$h$ (hours)	1	3	5	7	9	11
$s$ (score)	40	55	60	70	80	85

Let $L_{1}$ be the regression line of $h$ on $s$ , given by $h=a s+b$ .

Calculate the values of $a$ and $b$ .

[2]

Let $L_{2}$ be the regression line of $s$ on $h$ . Both lines intersect at the point $(\bar{h}, \bar{s})$ . Find the values of $\bar{h}$ and $\bar{s}$ .

[2]

Question 7

SLPaper 2

A researcher investigates the relationship between weekly screen time, $s$ hours, and academic performance, $p$ (GPA out of 4.0), for 12 university students. The data follows a bivariate normal distribution.

$s$ (hours)	10	15	20	25	30	35	40	45	50	12	18	28
$p$ (GPA)	3.8	3.5	3.2	3.0	2.8	2.5	2.2	2.0	1.8	3.6	3.4	2.9

Calculate Pearson's product moment correlation coefficient, $r$ , and interpret its value in context.

[2]

Find the equation of the regression line of $p$ on $s$ .

[2]

A stratified sample of 6 students is to be selected, proportional to screen time categories: low ( $<20$ hours), medium ( $20-35$ hours), and high ( $>35$ hours). Determine the number of students from each category.

[3]

Estimate the GPA of a student with 22 hours of screen time, and comment on the reliability of this estimate.

[2]

Question 8

SLPaper 2

A sports scientist studies the relationship between training hours per week, $t$ , and sprint times, $s$ seconds, for 10 athletes. The mean point is $M(15,11.5)$ .

Describe the relationship and mark the mean point $M$ .

[2]

The regression line of $s$ on $t$ passes through ( $0,13.5$ ). Draw this line.

[2]

Find the equation of the regression line of $t$ on $s$ .

[3]

Estimate the sprint time for 17 training hours and the training hours for a 11.3second sprint. Comment on the validity of each estimate.

[4]

Question 9

SLPaper 2

A study examines the relationship between daily water intake, $w$ liters, and energy levels, $e$ (rated 1-10), for nine individuals. The correlation coefficient is $r=0.85$ .

$w$ (liters)	1.5	2.0	2.5	3.0	3.5	2.2	2.8	1.8	3.2
$e$ (rating)	4	5	6	7	8	5	7	4	8

Find the equation of the regression line of $e$ on $w$ .

[2]

A person drinks 2.7 liters of water. Estimate their energy level.

[2]

Question 10

SLPaper 2

A teacher investigates the relationship between the number of revision hours, $h$ , and exam marks, $m$ , for seven students. The mean revision hours is 20 , and the mean exam mark is 65 .

Describe the relationship between $h$ and $m$ based on the scatter diagram.

[1]

Mark the mean point $M(20,65)$ on the scatter diagram.

[1]

The regression line of $m$ on $h$ is $m=1.5 h+35$ . Draw this line on the scatter diagram.

[2]

Estimate the exam mark for a student who revised for 19 hours using the regression line.

[1]

SL 4.10—X on y regression line Questionbank