How can you interpret regression coefficients in a meaningful way?

Before diving into interpretation, ensure you're familiar with the basics of regression analysis. In BI, regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. The regression coefficient is a numerical value representing the type of relationship—positive or negative—between these variables. A positive coefficient indicates that as the independent variable increases, the dependent variable also increases, while a negative coefficient suggests an inverse relationship.

To build a solid foundation in regression analysis, it's also important to understand the assumptions underlying the model. These include linearity, independence, homoscedasticity, and normality of residuals.

The size of a regression coefficient is as important as its sign. It shows the magnitude of the impact on the dependent variable. A larger absolute value indicates a stronger relationship. For instance, in sales data analysis, if the coefficient for marketing spend is 2, it suggests that for every additional dollar spent on marketing, sales increase by two dollars. However, be mindful of the units of measurement, as comparing coefficients directly is only valid when they are on the same scale. In one of my projects, understanding the coefficient sizes helped us prioritize budget allocation effectively.

When interpreting coefficient size, it's also helpful to look at standardized coefficients. These allow you to compare the relative impact of different variables on the dependent variable, as they are all measured on the same scale. This can be particularly useful when dealing with variables that have different units of measurement.

To deepen your understanding of the p-value, consider its role in hypothesis testing within regression analysis. The p-value helps determine whether the observed relationship between variables is statistically significant or likely due to random chance. A lower p-value indicates stronger evidence against the null hypothesis, which posits no effect or relationship.

If the multicollinearity presents regression coefficients are determinate but poses large standard errors hence we have much wider CIs and small t ratios. Hence results are conservative. Although sighns of the regression coefficients might change. Therefore we should detect the problem multicollinearity. Suitable measure is VIF.