Which type of regression tool is used when the response variable is continuous?

The choice of linear regression as the appropriate tool for modeling when the response variable is continuous is grounded in the fundamental principles of regression analysis. Linear regression aims to model the relationship between one or more independent variables and a continuous dependent variable. It does this by fitting a linear equation to observed data, allowing for predictions and interpretations of the relationship in terms of the coefficients.

In cases where the response variable is continuous, linear regression is particularly powerful because it can effectively capture linear relationships, making it straightforward to understand and implement. This method also provides insights into how changes in the independent variables affect the continuous outcome of interest.

The other options do not align with the characteristics of a continuous response variable. Logistic regression is primarily used for binary or categorical outcomes, while pseudoinverse regression is a mathematical technique that does not specifically pertain to regression analysis as it is traditionally understood. Multi-way regression, while it may seem related, often refers to multiple regression models that extend linear regression concepts, but without the specificity of focusing solely on a continuous response variable. Therefore, linear regression stands out as the correct and most suitable choice for this context.