Redefining Multivariable Linear Regression in R: Your Ultimate Guide!

  • Multivariable models provide a more accurate representation of reality than univariable models, allowing for a deeper understanding of complex relationships.
  • Use the wage data set in the ISLR package to determine which factors affect salary, and use the LM function to build a multivariable linear model.
  • It is essential to check model assumptions visually rather than relying solely on statistical tests, as they can sometimes yield significant results even when assumptions are not met.
  • Visualize model predictions using the GG effect function and interpret the statistical significance of salary differences using the table regression function from the GT summary package.
  • Multivariable models differ from univariable models, and it is important to compare the importance of predictors using effect size and interpretation functions.
  • Assess model fit using the adjusted R squared and AIC to determine the relative quality of statistical models.
  • Interactions between variables are crucial for creating more realistic models and should be thoroughly understood for better data analysis.

Multivariable Linear Regression in R: Everything You Need to Know!

Key Takeaways

  • Multivariable models provide a more accurate representation of reality.
  • Check model function from the performance package is intuitive and helpful for checking assumptions.
  • Visualizing model predictions can be done using the GG effect and plot function.
  • Table regression function from GT summary package can display pairwise comparisons for categorical predictors and correct P values for multiple comparisons.
  • Extract function from the Equatic package can convert the model to LaTeX for easier inclusion of equations in documents.
  • Education is the most important predictor of salary, followed by age and profession choice.
  • Adjusted R squared is a more appropriate indicator of model fit for multivariable models.
  • Interactions between variables should be considered for a more realistic model.

πŸ“Š Overview

In this article, we will be discussing multivariable linear regression in R. We will cover the importance of multivariable models, how to effectively visualize model results, how to interpret them correctly, and much more.

πŸ“ˆ Building the Model

To build a multivariable linear model in R, we will use the LM function with two arguments: the formula and the data. The formula has two sides, the left side is for our outcome variable, and the right side is for our predictors. We will select only two numeric and categorical predictors to learn how to correctly interpret complex models.

πŸ“Š Checking Assumptions

Before interpreting our model results, we must check the assumptions. The Check Model function from the performance package is intuitive and helpful for this. We can check for linearity, homoscedasticity, absence of outliers, and multicollinearity. If all assumptions are satisfied, we can move on to interpreting our model.

πŸ“ˆ Visualizing Model Predictions

We can use the GG effect and plot function to visualize model predictions. We can plot estimated averages of all predictors separately and combine them into a multiplot. This allows us to create a fancy plot in the format, quality, and size of our choice that tells us a compelling story. However, we need to check if these salaries are statistically significant. To do this, we can create a fancy table with P values alongside our fancy plot using the table regression function from the GT summary package.

πŸ“Š Interpreting Model Results

To interpret our model results, we can use the extract function from the Equatic package to convert the model to LaTeX for easier inclusion of equations in documents. We interpret the beta as the average change in wage for a one unit change in any of the predictors while holding all other predictors constant. Education is the most important predictor of salary, followed by age and profession choice.

πŸ“ˆ Considering Interactions

It is important to consider interactions between variables for a more realistic model. Interactions will make our models way more realistic, but we need to understand how to easily handle them between any kind of variables, numeric or categorical.

πŸ“Š Model Performance

To assess model performance, we can use two commonly used metrics: coefficient of determination (R squared) and the AK information criterion (AIC). Adjusted R squared is a more appropriate indicator of model fit for multivariable models. The lower the AIC, the better the fit, as less information is lost due to model complexity.

πŸ“ˆ Conclusion

Multivariable linear regression in R is a powerful tool for predicting outcomes based on multiple variables. By checking assumptions, visualizing model predictions, interpreting model results, and considering interactions, we can create more realistic models that accurately represent reality.

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