Introduction to linear model.

1. Introduction to Linear
Models
Linear models are a fundamental part of statistical learning and machine
learning. They provide a simple and efficient way to understand
relationships between input variables and the output, making predictions
based on those relationships.
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2. Regression with Linear Models
1 Basic Principles
Linear regression is used to model the relationship between a dependent
variable and one or more independent variables. It assumes a linear
relationship between the input and output variables.
2 Model Evaluation
Evaluating the performance of a linear regression model involves examining
how well the model fits the data and if the assumptions of linear regression
are met.
3 Applications
Linear regression is widely used in various fields, including economics,
finance, and social sciences to analyze and predict trends and future values.

3. Types of Regression Problems
1 Simple Linear Regression
When there is only one independent
variable.
2 Multiple Linear Regression
When there are several independent
variables.
3 Polynomial Regression
Used when the relationship between the
independent and dependent variables isn't
linear.
4 Ridge Regression
Addresses multicollinearity and overfitting
in multiple regression.

4. Linear Regression Assumptions
Linearity
The relationship between the independent
and dependent variables is linear.
Independence
The residuals are independent of each other.
Homoscedasticity
The variance of residual errors is constant
across all levels of the independent variables.
Normality
The residuals are normally distributed.

5. Classification with Linear Models
Binary Classification
Classifying instances into
one of two classes.
Multi-Class
Classification
Classifying instances into
one of three or more classes.
Probabilistic
Interpretation
Logistic regression provides
the probability of a certain
class.

6. Logistic Regression
2
Classification
Logistic regression is used for classification
problems.
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Interpretability
It provides insights into the influence of each
feature on the classification.

7. Types of Classification Problems
Binary Classification
Problems with two classes,
e.g., spam detection.
Multi-Class
Classification
Problems with three or more
classes, e.g., digit
recognition.
Multilabel Classification
Instances can belong to
multiple classes, e.g.,
tagging.

8. Linear vs. Logistic Regression
Model Type Linear Regression Logistic Regression
Suitable for Continuous output Binary or Multiclass
classification
Output Numeric Probabilities