<Data preprocessing>

Aggregation: Combine multiple samples or features (reduce sample size, convert scale, more stable)
Sampling: taking a sample
Dimensionality reduction: representing samples in position space (PCA, SVD)
Feature selection: select important features (Lasso)
Feature Creation: Reconstructing Useful Features (Fouter Transformation)
discretization
- The process of converting continuous attributes into discrete attributes
- Commonly used for classification
dualization
- Map continuous or categorical attributes to one or more binary variables
- Correlation Analysis
- Convert continuous attributes into categorical attributes and convert categorical attributes into a set of binary variables
variable transformation
- Converts the value of a given attribute
- Linear transformation method (simple function)
Standardize
- min-max normalization (normalization)
- z-score normalization (zero-mean normalization)
- Decimal scaling normalization

<sklearn machine learning platform>

MLlib learning library:

Algorithms covered: classification algorithms, clustering algorithms, regression algorithms, dimensionality reduction algorithms
Scikit-learn main usage:
- Symbol tags: training data, training set labels, test data, test set labels, complete data, labeled data
- Data partition:
  - train_test_split(x,y,random)
  - shuffle = True
- Data preprocessing
- Supervised learning algorithms (classification,
  - logistic regression
  - Support Vector Machines
  - Naive Bayes

Chapter 3 Regression Analysis

3.1 Basic concepts of regression analysis

regression analysis
Divided by the number of variables involved: single regression, multiple regression analysis
Divided according to the number of dependent variables: simple regression analysis, multiple regression analysis
Divided according to the type of relationship between independent variables and dependent variables: linear regression analysis, nonlinear regression analysis.
Problems solved by regression analysis:
- Correlation between variables: deterministic relationship, non-deterministic relationship
- Predict or control the value of a variable(s)
Regression analysis steps
- Determine variables: related influencing factors (independent variables), main influencing factors
- Building a predictive model: Calculation of historical statistics for independent and dependent variables
- Conduct correlation analysis: the degree of correlation between variables and predicted objects
- Calculate prediction error: can it be used for actual predictions
- Determine the predicted value: conduct a comprehensive analysis of the predicted value

F test, T test

Y = a + bX + ε
Model features:
- Y is a linear function of X plus an error term
- The linear part reflects changes in Y due to changes in X
- The error chosen ε is a random variable
- For a given value of X, the expected value of Y is E(Y) = a+bX
Regression equation:
Regression equation solving and model testing:
- Least Squares (Equation Solving), Residual Sum of Squares
- Goodness of fit test (model test)
- Significance test of linear relationship: Significance level test regression equation (significance test of regression parameters), ESS, RSS
- Univariate linear regression example
- Evaluation criteria r ²

Y = a + b₁X₁ + b₂X₂ + … + b_nX_n
Model features:
- Y has a linear relationship with X ₁ X ₂ X ₃ …X ₄
- Each observation value Y _i (i=1,2,3,…) is independent of each other
- Random error ε~N(0,q ² )
Solving polynomial regression equations using least squares method
Goodness of fit test
Significance test of regression parameters
Multiple linear regression example

Polynomial regression equation (nonlinear → linear)
Polynomial regression equation example
- Solving polynomial regression equations
- Regression equation F test
- Polynomial regression equation t-test