Nearest-student reasoning by hand
A nearest-neighbour rule compares a new record with training records and uses the closest one's known label. How values are represented affects “closest”.
Past A: score 70, minutes 60, Stay. Past B: score 80, minutes 180, Withdraw. NEW: score 79, minutes 100.
Using score alone, the absolute gaps are 9 and 1, so the nearest student is B and the copied prediction is Withdraw.
Using Euclidean distance on both raw numbers, distance to A = sqrt(9^2+40^2) = 41. Distance to B = sqrt(1^2+80^2), about 80.006. A is now closest, producing Stay. The minutes differences dominate the squared distance. Changing minutes to seconds would multiply those differences by 60 and their squared contribution by 3,600.
Scaling makes an explicit choice about feature representation and weighting. It does not reveal a uniquely correct distance or guarantee that prediction improves.
Sources: W4 PDF pp. 2-42; L4 Tasks 1-7. All fixed worked values here were recalculated from the supplied examples. These toy rules are teaching devices, not deployable student-support recommendations.
Use all six feature positions to calculate distance to training students. Choose the smallest distance, then take that training student's label.
Practice problems
Supplementary study questions on the lecture concepts — not verbatim exam questions. Each answer counts toward spaced review.
1. Conceptual understanding
Definitions and distinctions.
Why can raw Euclidean distance be dominated by minutes?
For A=(70,60), B=(80,180), NEW=(79,100), which is closest in raw distance?
2. Application
Apply the concept to a case or calculation.
Using score only, NEW=79 is closer to A=70 or B=80?
Differences in two coordinates are 3 and 4. What is Euclidean distance?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
Which records may act as neighbours in the specified method?
Minutes dominate a raw distance calculation. Does this show they are the strongest cause of withdrawal?
Explain it in writing
Self-checked, not marked. Write a few sentences, then compare with the example answer. Your writing is saved as you type.
Show an example answer
The differences are 9 and 40. Square and add: 81+1600=1681. The square root is 41.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
Scaling changes the relative contribution of coordinates to distance. If the nearest training record changes and its label differs, the prediction can change too.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?