CORRELATION
&
REGRESSION
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Correlation and Regression: Understanding the Relationship between Variables, Slides of Mathematical Statistics
An overview of correlation and regression analysis, including definitions, types, methods, and examples. Correlation analysis measures the degree and direction of the relationship between variables, while regression analysis defines the functional relationship between two variables. Learn about positive and negative correlations, simple and multiple correlations, and the advantages and disadvantages of scatter diagrams and Pearson's and Spearman's correlation coefficients.
What you will learn
- What is the difference between Pearson's and Spearman's correlation coefficients?
- What are the different types of correlation?
- How is Pearson's correlation coefficient calculated?
- What is correlation analysis and how is it used?
- What is regression analysis and how is it used to find regression lines?
Typology: Slides
2019/2020
1 / 45
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CORRELATION
REGRESSION
Flow of Presentation
- Correlation
- Definition
- Types of correlation
- Method of studying correlation (Scatter Diagram, Karl Pearson’s correlation and Spearman’s rank correlation)
- Regression
- Definition
- Regression lines
- Methods to find regression lines (Scatter diagram and Least square method)
Types of Correlation
Type I: Direction of the Correlation
Correlation
Positive Correlation Negative Correlation
Examples:
- Positive relationships
water consumption
and temperature
study time and grades
- Negative relationships alcohol consumption and driving ability Price & crops
Type III: Relationship assumed
Correlation LINEAR NON LINEAR
Methods of Studying Correlation
- Scatter Diagram
- Karl Pearson’s Coefficient of Correlation
- Spearman’s Rank Correlation Coefficient
A perfect positive correlation Height Weight Height of A Weight of A Height of B Weight of B
A linear
relationship
High Degree of positive correlation
- Positive relationship Height Weight r = +.
Degree of correlation
- Moderate Negative Correlation Exam score Use of Mobile per week r = -.
Degree of correlation
- Perfect Negative Correlation Exam score Use of Mobile per week r = - 1.
Degree of correlation
- No Correlation (horizontal line) Height IQ r = 0.
Advantages and Disadvantage of Scatter Diagram
Advantages:
- Simple & Non Mathematical method
- Not influenced by the size of extreme item
- First step in investing the relationship between two variables Disadvantage:
- Can not adopt an exact degree of correlation
2 2 2 2 2 2 cov( , ) ( ) ( ) x y x y r x x y y x x y y n xy x y n x x n y y
Interpretation of Correlation Coefficient (r)
- If r = +1, then the correlation between the two
variables is said to be perfect and positive
- If r = - 1 , then the correlation between the two
variables is said to be perfect and negative
- If r = 0, then there exists no correlation between
the variables
- If 0<r<1, then the correlation between the two
variables is said to be partial and positive
- If - 1<r<0, then the correlation between the two