第三章-数据分析方法

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6.2.1 Describe the Linear Regression Model
Regression Models:
• 1. Answer ‘What Is the Relationship Between the Variables?’
• 2. Equation Used
– 1 Numerical Dependent (Response) Variable – 1 or More Numerical or Categorical Independent
1
Linear normalization:
(6.1)
x'iX'm in (X'm aX X xm 'm a)i x X n(m xi in Xm)in
Ratio normalization:
(6.2)
x 'i
| xi |
n
| xi |
i 1
Z-score normalization:
(6.3)
Chapter 4 The Methods of Data Analysis
6.1 Data normalization
Data normalization is the basis for comparing experiments within large series when experimental conditions may not be identical.
various options to standardize data and to adjust
background levels and correct gradients. The commonly
used normalization functio编n辑s版apprte as follows:
(Explanatory) Variables
• 3. Used Mainly for Prediction & Estimation
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Types of Regression Models
Regression Models
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Types of Regression Models
S 编辑版ppt
(xi x)2 n
3
6.2 Simple Linear Regression
Learning Objectives: •1. Describe the Linear Regression Model •2. Explain Ordinary Least Squares •3. Compute Regression Coefficients •4. Evaluate the linear regression model •5. Predict Response Variable
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Types of Regression Models
1 Explanatory Variable
Regression Models
2+ Explanatory Variable
Simple
Multiple
Linear
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Types of Regression Models
1 Explanatory Variable
Regression Models
Simple
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Types of Regression Models
1 Explanatory Variable
Regression 2+ Explanatory
Models
Variables
Simple
Multiple
deviation) and leads to incorrect pattern recogwenku.baidu.comition.
σ Is population standard deviation, in general, it can be approximated by sample standard deviation (S)
Multiple
Linear
NonLinear
Linear
1 Explanatory Variable
Regression 2+ Explanatory Models Variable
Simple
Multiple
Linear
NonLinear
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Types of Regression Models
1 Explanatory Variable
Regression 2+ Explanatory
Normalization ensures that the experimental quality
of the data is comparable and, sound mathematical
algorithms have been employed. Normalization includes
Models
Variable
Simple
Multiple
Linear
NonLinear
Linear
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Types of Regression Models
1 Explanatory Variable
Regression 2+ Explanatory
Models
Variable
Simple
➢ Z-score assumes xi obeys Gaussian distribution. If xi has a different distribution, then the normalization will twist the
pattern (variance will be far away from the standard
x'i
(xi
x)
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➢ Generally, linear normalization is recommended (if
X’max = 1 and X’min = 0, x’i is normalized in percentage by formula (6.1)).
➢ After Ratio normalization, the sum of normalized variables will be equal to 1.