Which characteristic of a data set makes a linear regression model unreasonable?
Answer: A correlation coefficient close to zero makes a linear regression model unreasonable.
If the correlation between the two variable is close to zero, we can not expect one variable explaining the variation in other variable. For a linear regression model to be reasonable, the most important check is to see whether the two variables are correlated. If there is correlation between the two variable, we can think of regression analysis and if there is no correlation between the two variable, it does not make sense to apply regression analysis.
Therefore, if the correlation coefficient is close to zero, the linear regression model would be unreasonable.