IB Mathematics SL 4.1 Concepts of population, sample AA SL Paper 2- Exam Style Questions- New Syllabus
Question
The following table displays the weekly duration, in hours, spent on physical activity, \( x \), and on rest, \( y \), for a sample of six children.
| Activity time (\( x \)) | 11 | 13 | 14 | 17 | 22 | 24 |
| Rest time (\( y \)) | 62 | 65 | 68 | 75 | 84 | 87 |
The least squares regression line of \( y \) on \( x \) for this dataset is expressed as \( y = ax + b \).
(a) Determine the values of \( a \) and \( b \).
(b) Using the regression equation, predict the weekly rest time for a child whose activity time is 20 hours.
Most-appropriate topic codes (IB Mathematics AA SL 2021):
• SL 4.4: Linear correlation and regression — parts (a), (b)
• SL 4.1: Concepts of sample, data and reliability — context
• SL 4.1: Concepts of sample, data and reliability — context
▶️ Answer/Explanation
(a)
Using a GDC to perform linear regression on the given bivariate data yields the regression line parameters.
\( a = 1.98 \), \( b = 40.2 \) (or more precisely: \( a \approx 1.97651, b \approx 40.2286 \))
Therefore, the regression line is approximately \( y = 1.98x + 40.2 \).
(b)
Substitute \( x = 20 \) into the regression equation:
\( y = 1.97651 \times 20 + 40.2286 = 79.7589… \)
\( \boxed{79.8} \) hours (to 3 significant figures).