Write down the correlation coefficient.
About this question
Question 1.2 of Mathematics Grade 12 Paper 2, NSC Examination (DBE, November 2024). It tests the Term 3 ATP topic Statistics (Regression and Correlation).
- TermTerm 3
- ATP topicStatistics (Regression and Correlation)
- PaperPaper 2
- Marks1 mark for the method (formula and substitution) and the correct final answer
At the start of a season a rugby coach recorded the weight (in kg) of the 15 players in a junior boys' team and the number of push-ups each player could do in one minute. The least squares regression line is drawn on the scatter plot.
| Weight in kg (\(x\)) | 34 | 32 | 40 | 27 | 33 | 28 | 27 | 55 | 39 | 44 | 30 | 57 | 28 | 32 | 31 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Push-ups per minute (\(y\)) | 26 | 21 | 6 | 20 | 16 | 26 | 23 | 7 | 18 | 14 | 17 | 8 | 28 | 25 | 20 |
Diagram: a scatter plot with weight (0 to 60 kg) on the horizontal axis and push-ups per minute (0 to 30) on the vertical axis. The points slope downwards from left to right and a straight regression line runs through them. One point, \((40\,;\,6)\), lies far below the line.
From the calculator:
\[r = -0{,}797\ldots\]\(r = -0{,}80\)
More Questions On Statistics (Regression and Correlation)
About \(22{,}35\) push-ups (so about 22 push-ups)
This player scored far more runs than the other players who faced a similar number of balls (about 90 to 100 balls gave about 145 to 160 runs).
\(n = 92\), so the median is at a cumulative frequency of:
\[\frac{92}{2} = 46\]Read across from 46 to the curve and down to the \(x\)-axis.
\(\text{Median} \approx 54\%\)
Find the frequency of each class by subtracting consecutive cumulative frequencies:
\(0 \lt t \leq 20\): \(16\); \(20 \lt t \leq 40\): \(40 - 16 = 24\); \(40 \lt t \leq 60\): \(59 - 40 = 19\); \(60 \lt t \leq 80\): \(67 - 59 = 8\); \(80 \lt t \leq 100\): \(70 - 67 = 3\)
Draw bars with no gaps: \(x\)-axis Time, \(t\) (minutes) marked 0, 20, 40, 60, 80, 100; \(y\)-axis Number of people.
Bar heights 16, 24, 19, 8, 3 for the five classes, bars touching.
Enter the data in the calculator in STAT mode (A + BX), with \(x\) = age and \(y\) = price.
\[a = 331\,397{,}20\]\[b = -22\,988{,}32\]\(\hat{y} = 331\,397{,}20 - 22\,988{,}32x\)