What characteristic of a data set makes a linear regression model unreasonable?

A linear regression model becomes unreasonable when the relationship between the independent and dependent variables is non-linear. If the data exhibits a curvilinear pattern or contains significant outliers, the linear regression may not accurately capture the underlying trend. Additionally, if there are strong interactions among the predictors or if the residuals show a pattern rather than being randomly distributed, this also indicates that a linear model may not be appropriate.