Residual analysis in ML Python - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate residuals from actual and predicted values.

ML Python

residuals = actual - [1]

Drag options to blanks, or click blank then click option'

Amedian

Bactual

Cmean

Dpredicted

Attempts:

3 left

💡 Hint

Common Mistakes

Subtracting actual from predicted instead of predicted from actual.

Using mean or median instead of predicted values.

The residual is the difference between the actual value and the predicted value.

2fill in blank

medium

Complete the code to plot residuals against predicted values using matplotlib.

ML Python

plt.scatter([1], residuals)
plt.axhline(y=0, color='r', linestyle='--')
plt.xlabel('Predicted Values')
plt.ylabel('Residuals')
plt.show()

Drag options to blanks, or click blank then click option'

Aactual

Bpredicted

Cresiduals

Dmean

Attempts:

3 left

💡 Hint

Common Mistakes

Plotting residuals against actual values instead of predicted.

Plotting residuals against residuals.

Plotting residuals against predicted values helps check for patterns in errors.

3fill in blank

hard

Fix the error in the code to compute residuals correctly.

ML Python

residuals = [1] - predicted

Drag options to blanks, or click blank then click option'

Aactual

Bmean

Cpredicted

Dmedian

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping actual and predicted in subtraction.

Using mean or median instead of actual values.

Residuals are actual minus predicted, so actual must be first.

4fill in blank

hard

Fill both blanks to create a dictionary of residuals for each data point where residual is positive.

ML Python

positive_residuals = {i: residuals[i] for i in range(len(residuals)) if residuals[i] [1] 0 and residuals[i] [2] 0}

Drag options to blanks, or click blank then click option'

A>

B<

C==

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using < 0 or == 0 instead of > 0.

Using != 0 which includes negative residuals.

We want residuals greater than zero, so both conditions use > 0.

5fill in blank

hard

Fill all three blanks to compute mean squared error (MSE) from residuals.

ML Python

mse = sum([1]**2 for [2] in residuals) / [3]

Drag options to blanks, or click blank then click option'

Aresidual

Bresiduals

Clen(residuals)

Drange(len(residuals))

Attempts:

3 left

💡 Hint

Common Mistakes

Using residuals instead of residual in the loop.

Dividing by range instead of length.

Not squaring residuals.

MSE is average of squared residuals. We square each residual and divide by count.

Practice

1. What does a residual represent in machine learning?

easy

A. The difference between the actual and predicted values

B. The predicted value itself

C. The average of all predicted values

D. The sum of all actual values

Solution

1. Step 1: Understand residual definition

   A residual is the error between what the model predicts and what actually happened.

2. Step 2: Match with options

   The difference between the actual and predicted values correctly states this difference, while others describe unrelated concepts.

3. Final Answer:

   The difference between the actual and predicted values -> Option A

4. Quick Check:

   Residual = Actual - Predicted [OK]

Hint: Residuals = Actual minus Predicted values [OK]

Common Mistakes:

• Confusing residual with predicted value
• Thinking residual is the average error
• Mixing residual with total sum of values

2. Which of the following is the correct formula to calculate a residual for a data point?

easy

A. Residual = Actual value + Predicted value

B. Residual = Predicted value - Actual value

C. Residual = Actual value - Predicted value

D. Residual = Predicted value / Actual value

Solution

1. Step 1: Recall residual calculation formula

   Residual is calculated as Actual value minus Predicted value.

2. Step 2: Identify correct option

   Residual = Actual value - Predicted value matches the formula exactly; others are incorrect operations.

3. Final Answer:

   Residual = Actual value - Predicted value -> Option C

4. Quick Check:

   Residual = Actual - Predicted [OK]

Hint: Subtract predicted from actual to get residual [OK]

Common Mistakes:

• Reversing the subtraction order
• Adding values instead of subtracting
• Dividing values instead of subtracting

3. Given the actual values [3, 5, 7] and predicted values [2, 5, 8], what is the residual for the third data point?

medium

A. 1

B. -1

C. 0

D. 2

Solution

1. Step 1: Identify actual and predicted values for third point

   Actual = 7, Predicted = 8 for the third data point.

2. Step 2: Calculate residual

   Residual = Actual - Predicted = 7 - 8 = -1.

3. Final Answer:

   -1 -> Option B

4. Quick Check:

   7 - 8 = -1 [OK]

Hint: Subtract predicted from actual for the point [OK]

Common Mistakes:

• Mixing up actual and predicted values
• Calculating predicted minus actual
• Using wrong index for data point

4. You have a residuals list: [2, -3, 4, -1]. Which code snippet correctly calculates the mean squared error (MSE)?

medium

A. mse = sum([r**2 for r in residuals]) / len(residuals)

B. mse = sum([abs(r) for r in residuals]) / len(residuals)

C. mse = max(residuals) - min(residuals)

D. mse = sum(residuals) / len(residuals)

Solution

1. Step 1: Understand MSE formula

   MSE is the average of squared residuals, so square each residual and average them.

2. Step 2: Match code to formula

   mse = sum([r**2 for r in residuals]) / len(residuals) squares each residual and divides by count, matching MSE calculation.

3. Final Answer:

   mse = sum([r**2 for r in residuals]) / len(residuals) -> Option A

4. Quick Check:

   MSE = average of squared residuals [OK]

Hint: Square residuals then average for MSE [OK]

Common Mistakes:

• Using sum instead of sum of squares
• Calculating mean absolute error instead
• Using max-min difference instead of average

5. A model's residual plot shows a clear curve pattern instead of random scatter. What does this indicate about the model?

hard

A. The model fits the data perfectly

B. The model has no bias

C. The residuals are normally distributed

D. The model misses a non-linear pattern in data

Solution

1. Step 1: Interpret residual plot pattern

   A curve pattern in residuals suggests systematic error, meaning the model misses some pattern.

2. Step 2: Identify what pattern means

   This usually means the model is too simple and misses non-linear relationships.

3. Final Answer:

   The model misses a non-linear pattern in data -> Option D

4. Quick Check:

   Curved residuals = missed non-linear pattern [OK]

Hint: Curved residuals mean model misses pattern [OK]

Common Mistakes:

• Assuming perfect fit from residual pattern
• Confusing residual distribution with residual pattern
• Ignoring bias presence in model