IB Mathematics Analysis and Approaches Topic SL 4.10—X on y Regression Line Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 4.10—X on y Regression Line Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 4.10—X on y Regression Line with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 4.10—X on y Regression Line and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 2

A dataset records study time $x$ (hours) and test score $y$ (points) for eight students: $\begin{array}{c|cccccccc} x\,\text{(hours)} & 2&4&5&7&9&12&15&18\\ \hline y\,\text{(points)} & 30&28&25&21&20&17&14&12 \end{array}$

Using technology, find $r$ , the regression line $y = a x + b$ , and the regression line $x = cy + d$ .

[5]

Predict $y$ at $x = 10$ and find the residual for $(7, 21)$ .

[3]

Using $x$ on $y$ , estimate $x$ for $y = 16$ ; then invert $y = a x + b$ to estimate $x$ when $y = 16$ . Explain the difference.

[4]

Compute $r^{2}$ and interpret; comment on extrapolating to $x = 25$ .

[3]

Question 2

SLPaper 2

For a set of bivariate data, the regression line of $y$ on $x$ is given by $y = 0.85 x + 10.4$ , and the regression line of $x$ on $y$ is given by $x = 1.1 y - 8$ .

Both regression lines pass through the same point. State the significance of this point.

[1]

Find the coordinates of this point.

[4]

Question 3

SLPaper 1

A music teacher records the number of hours of practice, $t$ , and the score, $s$ , out of 100, of nine students in a performance assessment.

The regression line of $s$ on $t$ is $s = 5 t + 35$ . The regression line of $t$ on $s$ is $t = 0.1 s - 2$ .

Estimate the score for a student who practises for 7 hours.

[2]

Find the mean number of hours of practice, $\overset{ˉ}{t}$ .

[3]

Question 4

SLPaper 2

The marks of eight students on a science test ( $x$ ) and a maths test ( $y$ ) are recorded.

$x$	56	62	68	75	78	82	85	90
$y$	50	58	60	70	72	78	82	88

Find Pearson's product-moment correlation coefficient.

[2]

Find the equation of the regression line of $y$ on $x$ .

[2]

Find the equation of the regression line of $x$ on $y$ .

[2]

A student scored $72$ on the science test. Use an appropriate regression line to estimate their maths mark.

[1]

Question 5

SLPaper 2

A gym tracks the number of push-ups, $p$ , and the heart rate, $h$ , in 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, $\overset{p}{ˉ}$ .

[3]

IB Mathematics Analysis and Approaches SL 4.10—X on y Regression Line Questionbank

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IB Mathematics Analysis and Approaches SL 4.10—X on y Regression Line Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 4.10—X on y Regression Line Questionbank

Unlock all 9 questions with a free account