1. Question 1

Each sample in predictor matrix X represents:

• ❌ A single feature

• ✅ One row of predictor variables

• ❌ Bias term

• ❌ All weights

Explanation:
Each row = one data sample containing all its features.

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2. Question 2

How is prediction y^\hat{y}y^​ computed?

• ❌ Sum of features

• ❌ Sigmoid

• ❌ Multiply bias

• ✅ Dot product $x\cdot w$ + bias

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3. Question 3

Correct dimension relationship:

• ✅ #columns in X must equal #rows in w

• ❌ Rows = columns

• ❌ Dimensions don’t matter

• ❌ Rows must match

Explanation:
Matrix multiplication rule:
(\text{n_samples} \times \text{n_features}) \cdot (\text{n_features} \times 1)

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4. Question 4

Role of criterion:

• ❌ Forward pass

• ✅ Compute loss between prediction and targets

• ❌ Initialize parameters

• ❌ Update weights

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5. Question 5

Gradient descent weight update:

• ❌ Multiply by gradient

• ❌ Set weights to gradient

• ❌ Add gradient

• ✅ Subtract gradient × learning rate

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6. Question 6

Main difference in multi-output regression:

• ❌ No bias

• ❌ More features

• ❌ Simpler cost

• ✅ Weights become a matrix instead of a vector

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7. Question 7

Purpose of creating a custom PyTorch module:

• ✅ Customize forward pass, add layers, add logic

• ❌ Simpler loss

• ❌ Increase features

• ❌ Manual backprop

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8. Question 8

Cost function measures:

• ❌ Average distance

• ❌ Number of samples

• ✅ Sum of squared distances (MSE)

• ❌ Parameter count

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9. Question 9

How are weights/bias updated?

• ❌ Random values

• ❌ Averaging

• ❌ Multiply by fixed factor

• ✅ Using gradients of cost w.r.t each weight & bias

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10. Question 10

Key difference in training multi-output regression:

• ❌ Optimizer changes

• ❌ Fewer epochs

• ❌ Single-output cost

• ✅ Adjust prediction matrix & weight matrix dimensions

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🧾 Summary Table

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