Linear regression is appropriate for what type of dependent variable?

Linear regression is designed to model the relationship between a dependent variable and one or more independent variables. When we discuss the type of dependent variable suitable for linear regression, the ideal scenario involves a continuous dependent variable that is measured on a ratio scale and is normally distributed.

A ratio scale contains meaningful zero points and allows for a comparison of quantities. This means that both the differences between values and the ratios of values are interpretable, which is essential for assessing linear relationships. For linear regression to be valid, the residuals (the differences between observed and predicted values) should also be normally distributed, supporting the assumption of normality that underlies many of the statistical tests used in regression analysis.

This approach diverges from the other options. Count data may be better suited for Poisson regression or negative binomial regression due to its non-continuous nature. Dichotomous dependent variables, which involve two possible categories, are typically analyzed using logistic regression. Polytomous variables, having more than two categories, also require specialized approaches such as multinomial logistic regression. Therefore, linear regression's effectiveness hinges on using a dependent variable that is continuous, ideally on a ratio scale and approximately normally distributed.