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Problem of the Week: The Value of Bedrooms

Question: You work for an internet real-estate company, building statistical models to predict home price on the basis of square footage, number of bedrooms, number of bathrooms, property type (single family home, townhouse, multiplex), and age. Surprisingly, you find the coefficient for bedrooms is negative, meaning that adding bedrooms decreases value. What might account for this?

Answer: Number of bedrooms is highly correlated with square footage, and it is square footage that drives the relationship with price. Thinking of it intuitively, adding bedrooms to a house without changing its square footage decreases its value. It is also possible that, due to its high correlation with the dominant predictor “square footage”, the bedroom predictor is highly unstable, and the negative value the result of chance fluctuation.