Question
Consider the following samples.
image
Which model accurately classifies the samples?
A.
image
B.
image
C.
image
D.
image
image
Which model accurately classifies the samples?
A.
image
B.
image
C.
image
D.
image
Answers
GPT-5 mini
I can’t see the images you attached. Please upload the problem images (the samples and the four candidate model diagrams) or paste the sample coordinates and the equations/diagrams of the four models.
While you upload, here’s a quick method you can use to decide which model is correct:
1. Extract the data
- Get the coordinates (x,y) and true class label for every sample point shown.
2. Encode each model’s decision rule
- For a linear boundary: use the line equation (ax+by+c=0) and compute s = ax+by+c. Predict class = sign(s) (or one side = class A, other = class B).
- For curved/nonlinear boundaries: implement the region test (e.g., inside/outside circle, above/below parabola).
- For tree-like piecewise classifiers: test each region rule.
3. Compute predictions and accuracy
- For each model, compute predicted labels for all samples and count mismatches.
- The model with the fewest mismatches (ideally zero) is the one that “accurately classifies the samples.”
4. (Optional) Quick Python check
- If you have coordinates and model equations, this snippet will test linear boundaries:
```python
import numpy as np
# points: list of (x,y,label) where label is +1 or -1
points = [(x1,y1,1),(x2,y2,-1), ... ]
# model: (a,b,c) for ax+by+c=0 with positive side = +1
def accuracy(model):
a,b,c = model
correct=0
for x,y,label in points:
pred = 1 if a*x + b*y + c > 0 else -1
if pred==label:
correct += 1
return correct/len(points)
models = [(a1,b1,c1),(a2,b2,c2),...]
for i,m in enumerate(models):
print(i+1, accuracy(m))
```
If you upload the images now I’ll check them and tell you which option (A–D) is correct.
While you upload, here’s a quick method you can use to decide which model is correct:
1. Extract the data
- Get the coordinates (x,y) and true class label for every sample point shown.
2. Encode each model’s decision rule
- For a linear boundary: use the line equation (ax+by+c=0) and compute s = ax+by+c. Predict class = sign(s) (or one side = class A, other = class B).
- For curved/nonlinear boundaries: implement the region test (e.g., inside/outside circle, above/below parabola).
- For tree-like piecewise classifiers: test each region rule.
3. Compute predictions and accuracy
- For each model, compute predicted labels for all samples and count mismatches.
- The model with the fewest mismatches (ideally zero) is the one that “accurately classifies the samples.”
4. (Optional) Quick Python check
- If you have coordinates and model equations, this snippet will test linear boundaries:
```python
import numpy as np
# points: list of (x,y,label) where label is +1 or -1
points = [(x1,y1,1),(x2,y2,-1), ... ]
# model: (a,b,c) for ax+by+c=0 with positive side = +1
def accuracy(model):
a,b,c = model
correct=0
for x,y,label in points:
pred = 1 if a*x + b*y + c > 0 else -1
if pred==label:
correct += 1
return correct/len(points)
models = [(a1,b1,c1),(a2,b2,c2),...]
for i,m in enumerate(models):
print(i+1, accuracy(m))
```
If you upload the images now I’ll check them and tell you which option (A–D) is correct.