Moving averages in ML Python - Model Metrics & Evaluation

Metrics & Evaluation - Moving averages

Which metric matters for Moving Averages and WHY

Moving averages smooth data to show trends clearly. The key metric is Mean Squared Error (MSE) or Mean Absolute Error (MAE) between the smoothed values and the original data. These metrics tell us how close the moving average is to the actual data points.

Lower error means the moving average follows the data well without too much noise. This helps in forecasting and spotting trends.

Confusion Matrix or Equivalent Visualization

Moving averages do not use confusion matrices because they are not classification models. Instead, we visualize the smoothing effect by plotting:

Original Data:  10, 12, 15, 14, 13, 16, 18, 20
Moving Average:  - , 12.33, 13.67, 14, 14, 14.33, 15.67, 18

This shows how the moving average smooths sudden changes.

Tradeoff: Smoothness vs Responsiveness

Using a longer window in moving averages smooths data more but reacts slower to changes. A shorter window reacts quickly but can be noisy.

Example:

• Short window (3 points): Captures quick changes but may show false ups and downs.
• Long window (7 points): Shows overall trend but misses sudden shifts.

Choosing the right window balances smoothness and responsiveness based on your goal.

Good vs Bad Metric Values for Moving Averages

Good: Low MSE or MAE means the moving average closely follows the data trend without too much noise.

Bad: High error means the moving average either misses important changes (too smooth) or is too noisy (too responsive).

For example, an MAE near zero is excellent, while a large MAE compared to data range means poor smoothing.

Common Pitfalls in Moving Average Metrics

• Ignoring window size: Using a window too large or too small can mislead interpretation.
• Over-smoothing: Losing important data patterns by averaging too much.
• Under-smoothing: Not reducing noise enough, leading to confusing trends.
• Comparing errors without context: Error size depends on data scale; always compare relative to data range.

Self Check

Your moving average model has a low MSE but reacts very slowly to sudden changes. Is it good?

Answer: It depends on your goal. If you want to see overall trends, this is good. But if you need to catch quick changes, it is not good because it is too smooth and slow.

Key Result

Mean Squared Error (MSE) or Mean Absolute Error (MAE) measure how well moving averages smooth data by balancing noise reduction and trend responsiveness.

Practice

1. What is the main purpose of using a moving average in data analysis?

easy

A. To smooth out short-term fluctuations and highlight longer-term trends

B. To increase the number of data points in a dataset

C. To remove all noise from the data completely

D. To predict exact future values without error

Solution

1. Step 1: Understand the role of moving averages

   Moving averages smooth data by averaging nearby points, reducing short-term ups and downs.

2. Step 2: Identify the main goal

   The goal is to reveal longer-term trends by reducing noise, not to remove noise completely or predict exact values.

3. Final Answer:

   To smooth out short-term fluctuations and highlight longer-term trends -> Option A

4. Quick Check:

   Moving average = smoothing trends [OK]

Hint: Moving averages smooth data to show trends clearly [OK]

Common Mistakes:

• Thinking moving averages increase data points
• Believing moving averages remove all noise
• Assuming moving averages predict exact future values

2. Which of the following Python code snippets correctly computes a simple moving average with window size 3 for a list data?

easy

A. [data[i] / 3 for i in range(len(data))]

B. [sum(data[i:i+3]) for i in range(len(data)-3)]

C. [sum(data[i:i+3]) / 3 for i in range(len(data)-3)]

D. [(data[i] + data[i+1] + data[i+2]) / 3 for i in range(len(data)-2)]

Solution

1. Step 1: Understand moving average calculation

   A simple moving average with window 3 averages each group of 3 consecutive elements.

2. Step 2: Check each option's correctness

   [(data[i] + data[i+1] + data[i+2]) / 3 for i in range(len(data)-2)] correctly sums three consecutive elements and divides by 3, iterating till len(data)-2.
   [sum(data[i:i+3]) for i in range(len(data)-3)] sums but does not divide by 3.
   [sum(data[i:i+3]) / 3 for i in range(len(data)-3)] divides but uses range(len(data)-3), which is too short.
   [data[i] / 3 for i in range(len(data))] divides single elements by 3, not averaging groups.

3. Final Answer:

   [(data[i] + data[i+1] + data[i+2]) / 3 for i in range(len(data)-2)] -> Option D

4. Quick Check:

   Sum 3 elements / 3, range correct = [(data[i] + data[i+1] + data[i+2]) / 3 for i in range(len(data)-2)] [OK]

Hint: Sum 3 elements and divide by 3, loop till len-2 [OK]

Common Mistakes:

• Forgetting to divide by window size
• Using wrong range length causing index errors
• Averaging single elements instead of groups

3. Given the code below, what is the output?

data = [2, 4, 6, 8, 10]
window = 2
moving_avg = [sum(data[i:i+window]) / window for i in range(len(data) - window + 1)]
print(moving_avg)

medium

A. [2.0, 4.0, 6.0, 8.0, 10.0]

B. [3.0, 5.0, 7.0]

C. [3.0, 5.0, 7.0, 9.0]

D. [6.0, 8.0, 10.0]

Solution

1. Step 1: Calculate moving averages manually

   Window size is 2, so average pairs:
   (2+4)/2=3.0
   (4+6)/2=5.0
   (6+8)/2=7.0
   (8+10)/2=9.0

2. Step 2: Confirm output list length and values

   Length is len(data)-window+1 = 5-2+1=4, matching 4 values above.

3. Final Answer:

   [3.0, 5.0, 7.0, 9.0] -> Option C

4. Quick Check:

   Pairs averaged = [3.0, 5.0, 7.0, 9.0] [OK]

Hint: Average pairs sliding by one, length = len - window + 1 [OK]

Common Mistakes:

• Confusing window size with output length
• Calculating sums but forgetting to divide
• Off-by-one errors in range length

4. The following code is intended to compute a moving average with window size 3, but it misses the last window. What is the problem?

data = [1, 2, 3, 4, 5]
window = 3
moving_avg = [sum(data[i:i+window]) / window for i in range(len(data)-window)]
print(moving_avg)

medium

A. The range should be len(data) - window + 1 to include the last window

B. The window size is too large for the data list

C. sum() cannot be used on list slices

D. Division by window size should be outside the list comprehension

Solution

1. Step 1: Analyze the range length

   Range is len(data)-window = 5-3=2, but to cover all windows it should be len(data)-window+1 = 3.

2. Step 2: Understand impact of incorrect range

   Using len(data)-window misses the last valid window slice, causing incomplete results.

3. Final Answer:

   The range should be len(data) - window + 1 to include the last window -> Option A

4. Quick Check:

   Range length = len - window + 1 [OK]

Hint: Use range(len(data) - window + 1) for full coverage [OK]

Common Mistakes:

• Using len(data) - window instead of +1
• Thinking sum() can't handle slices
• Misplacing division outside comprehension

5. You have daily sales data for 10 days: [10, 12, 11, 14, 13, 15, 16, 14, 13, 12]. You want to smooth this data using a moving average with window size 4 but only want to keep averages where the window's average is greater than 13. Which Python code correctly computes this filtered moving average?

hard

A. [sum(data[i:i+4])/4 for i in range(len(data)-4) if sum(data[i:i+4])/4 > 13]

B. [avg for i in range(len(data)-3) if (avg := sum(data[i:i+4])/4) > 13]

C. [sum(data[i:i+4])/4 for i in range(len(data)-3) if sum(data[i:i+4]) > 13]

D. [sum(data[i:i+4])/4 for i in range(len(data)-3) if sum(data[i:i+4])/4 < 13]

Solution

1. Step 1: Understand window size and range

   Window size 4 means averaging groups of 4 elements, so range is len(data)-3 = 10-3=7.

2. Step 2: Filter averages greater than 13

   [avg for i in range(len(data)-3) if (avg := sum(data[i:i+4])/4) > 13] uses assignment expression to compute average once and filter if > 13.
   [sum(data[i:i+4])/4 for i in range(len(data)-4) if sum(data[i:i+4])/4 > 13] uses wrong range (len(data)-4=6), missing last window.
   [sum(data[i:i+4])/4 for i in range(len(data)-3) if sum(data[i:i+4]) > 13] filters sum > 13, not average > 13.
   [sum(data[i:i+4])/4 for i in range(len(data)-3) if sum(data[i:i+4])/4 < 13] filters averages less than 13, opposite condition.

3. Final Answer:

   [avg for i in range(len(data)-3) if (avg := sum(data[i:i+4])/4) > 13] -> Option B

4. Quick Check:

   Use assignment expression to filter averages > 13 [OK]

Hint: Use assignment expression (walrus) to filter averages [OK]

Common Mistakes:

• Using wrong range length missing last windows
• Filtering sum instead of average
• Using wrong comparison operator