A five-position vector by hand
A vector is an ordered list of numbers. Each position must have the same meaning for every student.
Training scores [60,60,80,80] have mean 70 and population SD 10. Training logins [2,2,6,6] have median 4, mean 4 and population SD 2. Keep category order [CS,Economics,Psychology].
For a future student with score 78, missing logins and programmeCS: impute logins 4; score_z=(78-70)/10=0.8; logins_z=(4-4)/2=0; encodeCS=[1,0,0]. Final vector: [0.8,0,1,0,0], meaning score_z, logins_z, CS, Economics, Psychology. No parameter is fitted from this student. This example prepares inputs; without a fitted prediction rule and labels, the vector alone is not a withdrawal prediction.
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.
The lab uses three scaled numbers followed by three programme indicators. This fixed layout tells the distance calculation what to compare.
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.
Saved score mean=70, SD=10. What is the transformed score 78?
Score 78, missing logins filled with 4, CS, and saved login mean=4/SD=2 produce what vector?
2. Application
Apply the concept to a case or calculation.
A new student has missing logins. The training median is 4. What value is used before scaling?
Filled logins=4, saved mean=4, SD=2. What is logins_z?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
Does [0.8,0,1,0,0] alone tell us a withdrawal label?
If the last three positions are CS, Economics, Psychology, what does [0,1,0] mean?
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 first is the scaled score. The second is the scaled login total. The last three are indicators for CS, Economics and Psychology, in that order.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
The saved login mean is also 4, so (4−4)/2=0. This numerical result does not mean the original value was observed or that the student had zero logins.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?