Question: Consider a multiple regression of Y (gas mileage) on two predictor variables \({{X}_{1}}\) (vehicle weight) and \({{X}_{2}}\) (engine type). Suppose \({{X}_{2}}\) is an indicator variable that takes the value +1, if the engine is fueled by gasoline and 0, if the engine is fueled diesel. Is there some numeric value for variable \({{X}_{1}}\) such that if \({{X}_{1}}\) is less than this value the mean fuel economy for gasoline vehicles will be lower than the mean fuel economy of the diesel vehicles, but if \({{X}_{1}}\) is greater than this value, the mean fuel economy for gasoline vehicles will be higher than the mean fuel economy of the diesel vehicles.

Yes, there is such a value.

No, no such value exists.

The question depends on the sign of the slope parameter for variable

You can only answer this question for a specific regression on a specific data set.

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