Linear regression analysis is frequently employed by researchers to investigate the impact of independent variables on dependent variables. The Ordinary Least Squares (OLS) method is a popular choice among scholars for estimating parameters in linear regression models. The OLS technique aims to minimize the squared differences between observed and predicted values.

**Prerequisites Assumptions in OLS Linear Regression**

Testing the prerequisites in OLS linear regression ensures that you attain the Best Linear Unbiased Estimator. Assumption tests in linear regression analysis include tests for linearity, normality, homoscedasticity, and multicollinearity. For time series data, autocorrelation tests are essential.

A crucial test in OLS linear regression is the linearity test. This ensures that the relationship between independent and dependent variables follows a linear pattern. In a linear equation, any rise or drop in the independent variable leads to a consistent change in the dependent variable.

Normality tests ensure the model’s residuals follow a normal distribution. This is vital as it determines the validity of the linear regression equation.

Homoscedasticity tests ensure that the variance of residuals remains constant across all levels of the independent variable. If the variance is inconsistent across observation levels, this is called heteroscedasticity, which can complicate statistical inference.

Multicollinearity tests are vital for multiple linear regression analysis. Their purpose is to ensure that two or more independent variables in the regression model aren’t perfectly or near-perfectly correlated. For robust and interpretable analysis results, it’s essential to prevent multicollinearity in the model.

**Understanding Interval and Ratio Data Scales**

In statistical analysis, variable selection is crucial. It’s vital for researchers to understand the data measurement scales of observed variables. The interval and ratio scales are most commonly used in OLS linear regression.

Interval scales refer to data with a clear order or interval, but the difference between each value isn’t always consistent, e.g., temperature scales.

Ratio scales add an absolute zero point to interval scale characteristics. This means data values can reach zero and have genuine meaning, like weight or income.

In the context of linear regression, variables on a ratio scale tend to be more potent and more straightforward to interpret due to the clear linear relationship compared to other data scales.

**How to Choose the Right Variables**

In linear regression analysis, variable selection is pivotal. One primary consideration is theoretical relevance. Chosen variables should have a solid theoretical foundation, ensuring logical grounding and strengthening the study’s conceptual framework.

Furthermore, empirical considerations from previous research are vital. Referring to past studies offers valuable insights into which variables might significantly relate to the dependent variable. Understanding previous findings allows researchers to hypothesize more effectively.

**Specifying the Regression Equation**

When constructing the regression equation, it’s essential to ensure an accurate model. Researchers should clearly identify dependent and independent variables based on literature, previous studies, or strong theoretical considerations.

It’s also crucial to determine the relationship form between variables, whether linear or non-linear. When formulating a regression model, considering potential interactions between independent variables is key. Addressing all these aspects will enhance the model’s ability to depict and predict the studied phenomenon.

**Formulating Equations Based on Theory and Previous Studies**

Several essential steps can enhance model quality by understanding models from previous research. Researchers can gain valuable insights into the best approach for their research problem or question.

Moreover, referring to the literature can prevent potential mistakes encountered in past studies. Using relevant theory as a foundation can aid in selecting crucial variables for the model.

A robust theory ensures the chosen variables have substantive relevance, not just statistical significance. Adapting models to data and research context ensures results truly reflect the studied reality.

OLS linear regression is excellent for understanding variable relationships. By choosing the right variables and ensuring all assumptions are met, the analysis becomes more accurate. Well, that’s what I can share for now. Stay tuned for updates from Kanda Data next week!