Worked solution
Transform both variables without changing correlation
After a school physical fitness test, ten pupils have the following masses (kg) and overall scores .
| Pupil | ||
|---|---|---|
| A | 38.6 | 60 |
| B | 41.8 | 58 |
| C | 38.6 | 72 |
| D | 54.1 | 59 |
| E | 44.9 | 62 |
| F | 32.1 | 94 |
| G | 38.4 | 86 |
| H | 41.4 | 62 |
| I | 30.2 | 81 |
| J | 52.4 | 54 |
(i) Calculate the product moment correlation coefficient between and for this sample.
(ii) Given and , calculate the product moment correlation coefficient between and for this sample.
CJC · Lecture · Example 9
(i) Correlate mass and score
Answer
(3 s.f.).
Enter masses in L1 and scores in L2. Use STAT → CALC → 8:LinReg(a+bx) with Xlist=L1, Ylist=L2, then Calculate. The source screen gives , , , . The requested result is the printed to 3 s.f.
(ii) Generate and pair the transformed lists
Answer
(3 s.f.).
Highlight the L3 heading, press ENTER, enter L3=10(L1−30), then ENTER. Highlight L4, press ENTER, enter L4=L2−50, then ENTER. The source screenshots retain all transformed values:
| Pupil | ||
|---|---|---|
| A | 86 | 10 |
| B | 118 | 8 |
| C | 86 | 22 |
| D | 241 | 9 |
| E | 149 | 12 |
| F | 21 | 44 |
| G | 84 | 36 |
| H | 114 | 12 |
| I | 2 | 31 |
| J | 224 | 4 |
Use 8:LinReg(a+bx) with Xlist=L3, Ylist=L4. Calculator x now means , and calculator y means . The printed output is , , , . Both scale factors are positive, so translation and rescaling leave unchanged. This is not a general rule for a single negative scale factor.
Solution notes
Both complete original/transformed tables, calculator workflows and numerical screen outputs retained. The source’s general transformation statement is qualified in the lesson: a single negative scaling reverses the sign, and a zero scaling makes correlation undefined. No printed marks.