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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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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
- No Autocorrelation
- No Multicollinearity

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- 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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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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- 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 relevant variable in the Model). - As
*the thing that**we don’t explain with our model goes into the error*, the error would be correlated to the variable that we have omitted. - Omitted Variable Bias is hard to find. When in doubt, include the Variable in the model and try it yourself.

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- 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 distributed then we can use
**Central Limit Theorem**.

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- 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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- 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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In order to prevent Heteroscedasticity, we need to

- Look for Omitted Variable Bias.
- Look for
**Outliers**. - Apply log Transformation.

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**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 Autocorrelation uses same time series twice. - One is
**Original form**and other one is**Lagged**version of Original form.

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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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- 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.
- Multicollinearity can be noticed easily by finding the correlation between each two pairs of Independent Variables.

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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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IDEAS CURATED BY

CURATOR'S NOTE

These are some of the Assumptions to be pondered while Applying Ordinary Least Square Method and Performing Regression Analysis.

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