Regress New York house prices on area and number of bathrooms: what signs do you expect, will the fit agree, and how do you handle multicollinearity?

You model New York house prices with a linear regression on two variables: total area and number of bathrooms. What sign do you expect each coefficient to have? When you actually run the regression, will the signs come out as you expect, and why or why not? How would you deal with multicollinearity, and what does regularisation do here?