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Fixing Multicollinearity
To fix Multicollinearity:
- If the Dataset is small, we can drop one independent variable. Or we can Transform them into One Variable (Eg. Average of two Variables)
- If the Dataset is large, we will use Ridge and Lasso Regression.
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Autocorrelation Detection
To detect autocorrelation
- Plot all points and check for patterns or
- Use Durbin - Watson test.
There is no remedy for Autocorrelation. Instead of linear regression, we can use
- Autoregressive Models.
- Moving Average Models.
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What is Ordinary Least Square Method?
Ordinary least squares, or linear least squares, estimates the parameters in a regression model by minimizing the sum of the squared residuals.
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Heteroscedasticity
In order to prevent Heteroscedasticity, we need to
- Look for Omitted Variable Bias.
- Look for Outliers.
- Apply log Transformation.
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Non-Linear Pattern
If the pattern doesn't looks like a Straight Line, then we need to apply
- A Non Linear Regression or
- Exponential Transformation or
- Log Transformation.
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2. No Endogeneity
- Technically, Endogeneity occurs when a predictor variable (x) in a regression model is correlated with the error term (e) in the model.
- This usually occurs due to the Omitted Variable Bias (when we forget to include a releva...
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3. Normality of Error Terms
- We need to consider that our Error Term is normally distributed.
- We only need Normal Distribution while making Statistical Inferences.
- T-tests and F-tests work because we have assumed normality.
- If Error Term isn't normally distribute...
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4. Zero Mean of Error Terms
- If the Mean of the Error Terms is not expected to be zero then the line is not the Best fitting one.
- Having an Intercept Solves the problem.
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5. Homoscedasticity
- Homoscedasticity means to have “Equal Variance”. The error terms should have equal variance with one another.
- When the error terms don’t have “Equal Variance”, then Heteroscedasticity happens.
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Assumptions for OLS
OLS Assumptions are the Conditions that we need to consider them before performing Regression Analysis.
Some OLS Assumptions are:
- Linearity
- No Endogeneity
- Normality
- Zero Mean of Error Terms
- Homoscedasticity
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6. No Autocorrelation
- Autocorrelation is a mathematical representation of the degree of similarity between a given time series and a lagged version of itself over successive time intervals.
- It is similar to the Correlation between two different Time Series but Autocorrela...
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1. Linearity
- A Linear Regression is Linear because the Equation is Linear.
- To verify the Linearity between Independent and Dependent Variable apply Scatter plot.
- If the Data points form a pattern that looks like a Straight Line then Linear Regression is Suitable.
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7. No Multicollinearity
- We observe Multicollinearity when two or more Independent Variables in a model are “Highly Correlated”.
- Correlation could be Positive (or) Negative.
- This will lead result in less reliable predictions.
- Multicollineari...
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IDEAS CURATED BY
These are some of the Assumptions to be pondered while Applying Ordinary Least Square Method and Performing Regression Analysis.
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Other curated ideas on this topic:
Polynomial regression
- Polynomials are algebraic expressions consisting of variables and coefficients.
- Polynomial regressions are the most used in machine learning.
Polynomial regression is a unique case of linear regression:
- You fit a polynomial equ...
Machine Learning Explained
Machine Learning is the process of letting your machine use the data to learn the relationship between predictor variables and the target variable. It is one of the first steps toward becoming a data scientist.
There are two kinds of Machine Learning: supervised, and unsupervised learning....
Autocorrelation Detection
To detect autocorrelation
- Plot all points and check for patterns or
- Use Durbin - Watson test.
There is no remedy for Autocorrelation. Instead of linear regression, we can use
- Autoregressive Models.
- Moving Average Models.
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