Residual plots:
Residual plots are graphical tools used to evaluate the performance and assumptions of regression models. They involve visualizing the differences between observed data points and the predictions made by the model. These plots help assess whether the model’s predictions exhibit patterns or systematic errors, and they can reveal issues such as heteroscedasticity, non-linearity, outliers, or violations of normality assumptions. Residual plots are crucial for diagnosing and improving regression models and ensuring the reliability of their predictions.
Residuals in a simple linear regression model can be calculated using the following formula:
Residual (εi) for the ith data point:
εi = Yi – (β0 + β1 * Xi)
Where:
(εi) is the residual for the ith data point.
-(Yi) is the observed or actual value of the dependent variable for the ith data point.
– (β0) is the intercept (constant) of the regression line.
– (β1) is the coefficient of the independent variable (slope) of the regression line.
– (Xi) is the value of the independent variable for the ith data point.
In this formula, calculate the difference between the observed value (Yi) and the predicted value (β0 + β1 * Xi) to obtain the residual for each data point in your dataset. These residuals represent the vertical distances between the actual data points and the points on the regression line, indicating how well the model fits the data.
- Calculate Residuals: First, you need to calculate the residuals for your model. Residuals are the differences between the actual (observed) values and the predicted values made by your model.
- Create the Plots: Depending on your programming environment and libraries, you can use various plotting functions to create residual plots. Common choices include scatterplots, histograms, and probability plots.
Residual Plot: Shows the differences between observed and predicted values, helping assess the model’s goodness-of-fit, linearity, and presence of patterns or outliers in the residuals.
Distribution Plot: Illustrates the data’s distribution, highlighting its shape, central tendency, and spread, aiding in understanding the data’s characteristics and adherence to assumptions.
Regression Plot: Displays the relationship between two variables, typically showing data points and a fitted regression line to visualize and evaluate the linear or nonlinear association between them.