# Assumptions of OLS Regression: Key Considerations for Valid Results

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## Key Takeaways

OLS assumptions are crucial for understanding and interpreting the results of linear regression models.

There are several key assumptions that need to be met for OLS to provide accurate and reliable estimates.

Violations of these assumptions can lead to biased and inefficient estimates, as well as incorrect inferences.

It is important to assess the assumptions before drawing conclusions from OLS regression results.

## Introduction

Ordinary Least Squares (OLS) regression is a widely used statistical technique for modeling the relationship between a dependent variable and one or more independent variables. It is based on a set of assumptions that need to be met for the estimates to be valid and reliable. In this article, we will explore the key assumptions of OLS regression and discuss their importance in interpreting the results.

## Linearity

The first assumption of OLS regression is linearity, which states that the relationship between the dependent variable and the independent variables is linear. This means that the effect of a one-unit change in an independent variable on the dependent variable is constant across all levels of the independent variable. Violations of this assumption can lead to biased estimates and incorrect inferences. To assess linearity, one can examine scatter plots of the dependent variable against each independent variable and look for any non-linear patterns.

## Independence

The second assumption of OLS regression is independence, which states that the observations are independent of each other. This means that the value of the dependent variable for one observation does not depend on the values of the dependent variable for other observations. Violations of this assumption can occur in cases of clustered or correlated data, such as when observations are taken from the same individual or when there is a time series structure. To assess independence, one can examine the residuals (the differences between the observed and predicted values) for any patterns or correlations.

## Homoscedasticity

The third assumption of OLS regression is homoscedasticity, which states that the variance of the residuals is constant across all levels of the independent variables. This means that the spread of the residuals should not systematically change as the values of the independent variables change. Violations of this assumption can lead to inefficient estimates and incorrect standard errors. To assess homoscedasticity, one can examine scatter plots of the residuals against the predicted values and look for any patterns or trends.

## Normality

The fourth assumption of OLS regression is normality, which states that the residuals are normally distributed. This means that the distribution of the residuals should resemble a bell-shaped curve. Violations of this assumption can lead to biased estimates and incorrect hypothesis tests. To assess normality, one can examine a histogram or a Q-Q plot of the residuals and look for any departures from normality.

## Conclusion

OLS assumptions are essential for ensuring the validity and reliability of the estimates obtained from linear regression models. Linearity, independence, homoscedasticity, and normality are the key assumptions that need to be met for OLS to provide accurate and meaningful results. Violations of these assumptions can lead to biased and inefficient estimates, as well as incorrect inferences. Therefore, it is crucial to assess these assumptions before drawing conclusions from OLS regression results. By understanding and addressing these assumptions, researchers can ensure the robustness and validity of their findings in the field of linear regression analysis.