I was an appraiser (although I've not renewed my licensing). Â My dad still is one and trains appraisers all over the country. Â :) Â You've pretty much nailed it.
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They are looking at square footage, number of bedrooms, bathrooms, whether there's a basement, what kind of basement, what other rooms there are, how many bathrooms, whether you have a garage, whether the major mechanical systems function (usually, they just check the water and if it's cold--that the heat is running or if it's hot and you have central air--if the air is operable). Â They will also look to see how outdated your home is. Â How any of this affects value really depends on how it compares to other homes in your neighborhood. Â They'll look at your landscaping, fencing, what kind of lot you're on and how the location of your lot may make it more or less attractive to own (like if it is on a busy road vs. a cul de sac, etc.)
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That's what they'll look at in your house. Â They will often only look at the cleanliness of your home in terms of what they'll think about it being maintained well; but unless they find an actual problem--that won't matter a whole lot.