Regression and Correlation Analysis
Kifayat Ullah
Zoology BS
Bio-Statistics
Department of Zoology University of Chitral
August 9, 2022
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Regression and Correlation Analysis
Regression Analysis
Class Overview
1 Introduction to regression
2 Deterministic Vs Probabilistic Model
3 Simple linear Regression Model
4 Formula and derivation
5 Standard Deviation of Regression Estimate
6 Example
7 Correlation definition
8 Example
9 Conclusion
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Regression and Correlation Analysis
Introduction
Introduction
Regression analysis is the analysis of relationship between dependent
and independent variable as it depicts how dependent variable will
change when one or more independent variable changes due to factors.
Regression is a statistical tool to predict the dependent variable with
the help of one or more than one independent variable. While running
a regression analysis, the main purpose of the researcher is to find out
the relationship between the dependent variable and the independent
variable.
In order to predict the dependent variable, one or multiple
independent variables are chosen, which can help in predicting the
dependent variable. It helps in the process of validating whether the
predictor variables are good enough to help in predicting the
dependent variable.
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Regression and Correlation Analysis
Introduction
Introduction
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Introduction
Introduction
Figure 2: Regression Variables
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Regression and Correlation Analysis
Introduction
General Regression Formula
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Regression and Correlation Analysis
Introduction
Explanation
While running a regression, the main purpose of the researcher is to
find out the relationship between the dependent variable and the
independent variable.
In order to predict the dependent variable, one or multiple
independent variables are chosen, which can help in predicting the
dependent variable.
Regression analysis helps in the process of validating whether the
predictor variables are good enough to help in predicting the
dependent variable.
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Regression and Correlation Analysis
Introduction
Introduction
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Regression and Correlation Analysis
Introduction
Introduction
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Introduction
Introduction
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Regression and Correlation Analysis
Introduction
Introduction
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Regression and Correlation Analysis
Introduction
Introduction
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Regression and Correlation Analysis
Introduction
Introduction
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Regression and Correlation Analysis
Deterministic vs Probabilistic Model
Deterministic
A deterministic model does not include elements of randomness.
Every time you run the model with the same initial conditions you will
get the same results.
Most simple mathematical models of everyday situations are
deterministic, for example, the height (h) in metres of an apple
dropped from a hot air balloon at 300m could be modelled by h = -
5t2 + 300, where t is the time in seconds since the apple was
dropped.
Some things we know for certain. For example, water freezes at 0
degrees Celsius and boils at 100 degrees Celsius. Some relationships
we know for certain as well. If we know the temperature in degrees
Celsius, we can convert that value to the temperature in degrees
Fahrenheit using this formula:
F = (9/5 ∗ C ) + 32 (1)
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Regression
Deterministic Model
This mathematical formula is actually a model of the relationship
between two different temperature scales. It is a deterministic model,
as the relationship between the variables is known exactly. A
deterministic model is one in which there is no error in the prediction
of one variable from the others.
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Regression
Probabilistic Model
A probabilistic model includes elements of randomness. Every time
you run the model, you are likely to get different results, even with
the same initial conditions. A probabilistic model is one which
incorporates some aspect of random variation.
Probabilistic models are statistical models that include one or more
probability distributions in the model to account for these additional
factors.
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Introduction to Correlation
Figure 9: Regression Variables
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Introduction to Correlation
Figure 10: Regression Variables
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Regression
Example of Correlation
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Example of Correlation
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Example of Correlation
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Example of Correlation
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