What graphical representation is used to check the validity of assumptions made about a regression model?

A residual plot is used to check the validity of assumptions made about a regression model. This plot displays the residuals on the vertical axis and the fitted values (or independent variable) on the horizontal axis. Analyzing the residuals helps in assessing whether the assumptions of linearity, independence, and homoscedasticity (constant variance of errors) are met.

In a well-fitted regression model, the residuals should be randomly scattered around zero, forming a cloud-like shape without any discernible pattern. If the residuals show patterns, it indicates potential problems with the model, such as non-linearity or heteroscedasticity, which can lead to misleading conclusions about the relationships between the variables.

This makes the residual plot a critical tool for validating the underlying assumptions of the regression model. Other graphical representations, such as scatter plots or regression plots, help visualize the relationship between variables but do not directly assist in checking the assumptions of the regression analysis.