Chapter 27: Regression Evaluation
Learn Machine Learning from very beginner to expert with detailed topic guidance, practical examples, practice exercises, and review questions.
What this chapter covers
This chapter contains 9 topics. Technical terms are followed by plain-language meanings in parentheses where they first appear. Code is included only when it naturally helps demonstrate the concept; architecture, workflow, governance, and comparison topics use practical scenarios instead.
27.1 Residual Analysis
Residual Analysis (a practical concept used within supervised learning, evaluation, and ensemble methods). Within Chapter 27, this topic connects directly to supervised learning, evaluation, and ensemble methods. The important goal is to understand what information goes into the method, what transformation or decision happens, and what output should be checked.
When using this idea, separate training data from evaluation data and compare performance on examples the model did not train on. Pay attention to assumptions, important settings, error patterns, and whether the method is appropriate for classification, regression, ranking, or probability estimation.
Example
Imagine a small machine-learning project. Use Residual Analysis to decide what information is needed, what step happens next, and what result should be checked.
Coding example
// Residual Analysis
const records = [3, 5, 7, 9, 11];
const transform = value => ({ input: value, output: value * 2 + 1 });
const results = records.map(transform);
console.log(results);Code explanation
- The sample starts with a small list of inputs so every result can be checked manually.
- `transform()` represents the main operation for this topic in a deliberately simple form.
- `map()` applies the same rule consistently to every item and returns a new result array.
- Use this pattern to focus on input, transformation, and output before replacing the toy rule with a more advanced method.
Expected result: A transformed result is printed for each input value.
Practice exercise
Create a small real-world example for Residual Analysis. Write the input, the goal, the main steps, and the result you would check. Then list one limitation or mistake a beginner should watch for.
27.2 Mean Absolute Error
Mean Absolute Error (the arithmetic average of a set of values). Within Chapter 27, this topic connects directly to supervised learning, evaluation, and ensemble methods. The important goal is to understand what information goes into the method, what transformation or decision happens, and what output should be checked.
When using this idea, separate training data from evaluation data and compare performance on examples the model did not train on. Pay attention to assumptions, important settings, error patterns, and whether the method is appropriate for classification, regression, ranking, or probability estimation.
Example
Imagine a small machine-learning project. Use Mean Absolute Error to decide what information is needed, what step happens next, and what result should be checked.
Coding example
// Mean Absolute Error
const values = [12, 15, 11, 18, 14, 16];
const mean = values.reduce((sum, x) => sum + x, 0) / values.length;
const variance = values.reduce((sum, x) => sum + (x - mean) ** 2, 0) / values.length;
const std = Math.sqrt(variance);
console.log({ mean: mean.toFixed(2), std: std.toFixed(2) });Code explanation
- `values` is a tiny dataset that can be checked manually.
- The mean is the total divided by the number of observations.
- Variance measures average squared distance from the mean, and the square root of variance gives standard deviation.
- These summary values help you understand the scale and spread of data before choosing or evaluating a model.
Expected result: The mean and standard deviation are printed.
Practice exercise
Create a small real-world example for Mean Absolute Error. Write the input, the goal, the main steps, and the result you would check. Then list one limitation or mistake a beginner should watch for.
27.3 Mean Squared Error
Mean Squared Error (the arithmetic average of a set of values). Within Chapter 27, this topic connects directly to supervised learning, evaluation, and ensemble methods. The important goal is to understand what information goes into the method, what transformation or decision happens, and what output should be checked.
When using this idea, separate training data from evaluation data and compare performance on examples the model did not train on. Pay attention to assumptions, important settings, error patterns, and whether the method is appropriate for classification, regression, ranking, or probability estimation.
Example
Imagine a small machine-learning project. Use Mean Squared Error to decide what information is needed, what step happens next, and what result should be checked.
Coding example
// Mean Squared Error
const values = [12, 15, 11, 18, 14, 16];
const mean = values.reduce((sum, x) => sum + x, 0) / values.length;
const variance = values.reduce((sum, x) => sum + (x - mean) ** 2, 0) / values.length;
const std = Math.sqrt(variance);
console.log({ mean: mean.toFixed(2), std: std.toFixed(2) });Code explanation
- `values` is a tiny dataset that can be checked manually.
- The mean is the total divided by the number of observations.
- Variance measures average squared distance from the mean, and the square root of variance gives standard deviation.
- These summary values help you understand the scale and spread of data before choosing or evaluating a model.
Expected result: The mean and standard deviation are printed.
Practice exercise
Create a small real-world example for Mean Squared Error. Write the input, the goal, the main steps, and the result you would check. Then list one limitation or mistake a beginner should watch for.
27.4 Root Mean Squared Error
Root Mean Squared Error (the arithmetic average of a set of values). Within Chapter 27, this topic connects directly to supervised learning, evaluation, and ensemble methods. The important goal is to understand what information goes into the method, what transformation or decision happens, and what output should be checked.
When using this idea, separate training data from evaluation data and compare performance on examples the model did not train on. Pay attention to assumptions, important settings, error patterns, and whether the method is appropriate for classification, regression, ranking, or probability estimation.
Example
Imagine a small machine-learning project. Use Root Mean Squared Error to decide what information is needed, what step happens next, and what result should be checked.
Coding example
// Root Mean Squared Error
const values = [12, 15, 11, 18, 14, 16];
const mean = values.reduce((sum, x) => sum + x, 0) / values.length;
const variance = values.reduce((sum, x) => sum + (x - mean) ** 2, 0) / values.length;
const std = Math.sqrt(variance);
console.log({ mean: mean.toFixed(2), std: std.toFixed(2) });Code explanation
- `values` is a tiny dataset that can be checked manually.
- The mean is the total divided by the number of observations.
- Variance measures average squared distance from the mean, and the square root of variance gives standard deviation.
- These summary values help you understand the scale and spread of data before choosing or evaluating a model.
Expected result: The mean and standard deviation are printed.
Practice exercise
Create a small real-world example for Root Mean Squared Error. Write the input, the goal, the main steps, and the result you would check. Then list one limitation or mistake a beginner should watch for.
27.5 R-Squared
R-Squared (a practical concept used within supervised learning, evaluation, and ensemble methods). Within Chapter 27, this topic connects directly to supervised learning, evaluation, and ensemble methods. The important goal is to understand what information goes into the method, what transformation or decision happens, and what output should be checked.
When using this idea, separate training data from evaluation data and compare performance on examples the model did not train on. Pay attention to assumptions, important settings, error patterns, and whether the method is appropriate for classification, regression, ranking, or probability estimation.
Example
Imagine a small machine-learning project. Use R-Squared to decide what information is needed, what step happens next, and what result should be checked.
Coding example
// R-Squared
const records = [3, 5, 7, 9, 11];
const transform = value => ({ input: value, output: value * 2 + 1 });
const results = records.map(transform);
console.log(results);Code explanation
- The sample starts with a small list of inputs so every result can be checked manually.
- `transform()` represents the main operation for this topic in a deliberately simple form.
- `map()` applies the same rule consistently to every item and returns a new result array.
- Use this pattern to focus on input, transformation, and output before replacing the toy rule with a more advanced method.
Expected result: A transformed result is printed for each input value.
Practice exercise
Create a small real-world example for R-Squared. Write the input, the goal, the main steps, and the result you would check. Then list one limitation or mistake a beginner should watch for.
27.6 Adjusted R-Squared
Adjusted R-Squared (a practical concept used within supervised learning, evaluation, and ensemble methods). Within Chapter 27, this topic connects directly to supervised learning, evaluation, and ensemble methods. The important goal is to understand what information goes into the method, what transformation or decision happens, and what output should be checked.
When using this idea, separate training data from evaluation data and compare performance on examples the model did not train on. Pay attention to assumptions, important settings, error patterns, and whether the method is appropriate for classification, regression, ranking, or probability estimation.
Example
Imagine a small machine-learning project. Use Adjusted R-Squared to decide what information is needed, what step happens next, and what result should be checked.
Coding example
// Adjusted R-Squared
const records = [3, 5, 7, 9, 11];
const transform = value => ({ input: value, output: value * 2 + 1 });
const results = records.map(transform);
console.log(results);Code explanation
- The sample starts with a small list of inputs so every result can be checked manually.
- `transform()` represents the main operation for this topic in a deliberately simple form.
- `map()` applies the same rule consistently to every item and returns a new result array.
- Use this pattern to focus on input, transformation, and output before replacing the toy rule with a more advanced method.
Expected result: A transformed result is printed for each input value.
Practice exercise
Create a small real-world example for Adjusted R-Squared. Write the input, the goal, the main steps, and the result you would check. Then list one limitation or mistake a beginner should watch for.
27.7 MAPE
MAPE (a practical concept used within supervised learning, evaluation, and ensemble methods). Within Chapter 27, this topic connects directly to supervised learning, evaluation, and ensemble methods. The important goal is to understand what information goes into the method, what transformation or decision happens, and what output should be checked.
When using this idea, separate training data from evaluation data and compare performance on examples the model did not train on. Pay attention to assumptions, important settings, error patterns, and whether the method is appropriate for classification, regression, ranking, or probability estimation.
Example
Imagine a small machine-learning project. Use MAPE to decide what information is needed, what step happens next, and what result should be checked.
Coding example
// MAPE
const records = [3, 5, 7, 9, 11];
const transform = value => ({ input: value, output: value * 2 + 1 });
const results = records.map(transform);
console.log(results);Code explanation
- The sample starts with a small list of inputs so every result can be checked manually.
- `transform()` represents the main operation for this topic in a deliberately simple form.
- `map()` applies the same rule consistently to every item and returns a new result array.
- Use this pattern to focus on input, transformation, and output before replacing the toy rule with a more advanced method.
Expected result: A transformed result is printed for each input value.
Practice exercise
Create a small real-world example for MAPE. Write the input, the goal, the main steps, and the result you would check. Then list one limitation or mistake a beginner should watch for.
27.8 Median Absolute Error
Median Absolute Error (the middle value after data is ordered). Within Chapter 27, this topic connects directly to supervised learning, evaluation, and ensemble methods. The important goal is to understand what information goes into the method, what transformation or decision happens, and what output should be checked.
When using this idea, separate training data from evaluation data and compare performance on examples the model did not train on. Pay attention to assumptions, important settings, error patterns, and whether the method is appropriate for classification, regression, ranking, or probability estimation.
Example
Imagine a small machine-learning project. Use Median Absolute Error to decide what information is needed, what step happens next, and what result should be checked.
Coding example
// Median Absolute Error
const values = [12, 15, 11, 18, 14, 16];
const mean = values.reduce((sum, x) => sum + x, 0) / values.length;
const variance = values.reduce((sum, x) => sum + (x - mean) ** 2, 0) / values.length;
const std = Math.sqrt(variance);
console.log({ mean: mean.toFixed(2), std: std.toFixed(2) });Code explanation
- `values` is a tiny dataset that can be checked manually.
- The mean is the total divided by the number of observations.
- Variance measures average squared distance from the mean, and the square root of variance gives standard deviation.
- These summary values help you understand the scale and spread of data before choosing or evaluating a model.
Expected result: The mean and standard deviation are printed.
Practice exercise
Create a small real-world example for Median Absolute Error. Write the input, the goal, the main steps, and the result you would check. Then list one limitation or mistake a beginner should watch for.
27.9 Choosing Metrics
Choosing Metrics (a practical concept used within supervised learning, evaluation, and ensemble methods). Within Chapter 27, this topic connects directly to supervised learning, evaluation, and ensemble methods. The important goal is to understand what information goes into the method, what transformation or decision happens, and what output should be checked.
When using this idea, separate training data from evaluation data and compare performance on examples the model did not train on. Pay attention to assumptions, important settings, error patterns, and whether the method is appropriate for classification, regression, ranking, or probability estimation.
Example
Imagine a small machine-learning project. Use Choosing Metrics to decide what information is needed, what step happens next, and what result should be checked.
Coding example
// Choosing Metrics
const values = [12, 15, 11, 18, 14, 16];
const mean = values.reduce((sum, x) => sum + x, 0) / values.length;
const variance = values.reduce((sum, x) => sum + (x - mean) ** 2, 0) / values.length;
const std = Math.sqrt(variance);
console.log({ mean: mean.toFixed(2), std: std.toFixed(2) });Code explanation
- `values` is a tiny dataset that can be checked manually.
- The mean is the total divided by the number of observations.
- Variance measures average squared distance from the mean, and the square root of variance gives standard deviation.
- These summary values help you understand the scale and spread of data before choosing or evaluating a model.
Expected result: The mean and standard deviation are printed.
Practice exercise
Create a small real-world example for Choosing Metrics. Write the input, the goal, the main steps, and the result you would check. Then list one limitation or mistake a beginner should watch for.
Chapter 27 Review Questions and Answers
Q1. What is Residual Analysis?
Answer: Residual Analysis is a practical concept used within supervised learning, evaluation, and ensemble methods. In this chapter, focus on the input, the method or decision, and the result that should be checked.
Q2. What is Mean Absolute Error?
Answer: Mean Absolute Error is the arithmetic average of a set of values. In this chapter, focus on the input, the method or decision, and the result that should be checked.
Q3. What is Mean Squared Error?
Answer: Mean Squared Error is the arithmetic average of a set of values. In this chapter, focus on the input, the method or decision, and the result that should be checked.
Q4. What is Root Mean Squared Error?
Answer: Root Mean Squared Error is the arithmetic average of a set of values. In this chapter, focus on the input, the method or decision, and the result that should be checked.
Q5. What is R-Squared?
Answer: R-Squared is a practical concept used within supervised learning, evaluation, and ensemble methods. In this chapter, focus on the input, the method or decision, and the result that should be checked.
Q6. What is Adjusted R-Squared?
Answer: Adjusted R-Squared is a practical concept used within supervised learning, evaluation, and ensemble methods. In this chapter, focus on the input, the method or decision, and the result that should be checked.
Q7. What is MAPE?
Answer: MAPE is a practical concept used within supervised learning, evaluation, and ensemble methods. In this chapter, focus on the input, the method or decision, and the result that should be checked.
Q8. What is Median Absolute Error?
Answer: Median Absolute Error is the middle value after data is ordered. In this chapter, focus on the input, the method or decision, and the result that should be checked.
Q9. What is Choosing Metrics?
Answer: Choosing Metrics is a practical concept used within supervised learning, evaluation, and ensemble methods. In this chapter, focus on the input, the method or decision, and the result that should be checked.