In the given scenarios:
1. A linear regression can work with a continuous independent variable and a continuous dependent variable. This is a common scenario where linear regression is used to establish a relationship between the independent and dependent variables through a straight line.
2. A linear regression cannot work with a binary independent variable and a continuous dependent variable. In this case, the independent variable being binary (having only two possible values) doesn't allow for a linear relationship with the continuous dependent variable. An alternative model like logistic regression would be more suitable for this scenario.
3. A linear regression can work with a continuous independent variable and a binary dependent variable. In this case, the continuous independent variable can still be used to predict the binary outcome by fitting a linear regression model.
Therefore, the scenario where a linear regression cannot work is when there is a binary independent variable and a continuous dependent variable due to the nature of the variables not being conducive to a linear relationship in this context.
