Interpreting the values of slope and intercept coefficients using the CLRM

[1daj]

Hello there,
I'm given the following population regression equation:
PRICE(i) = β(0) + β(1)SQFT(i) + u(i) where the things in brackets are subscripts and SQFT represents the square footage.
A sample of houses is then given with their cooresponding prices and square footage.
I have solved such that β(1) = 108.7832 and β(0) = 11984.83
My question is how exactly to word the interpretation of the slope coefficient B(1) and the intercept coefficient β(0).
What I believe to be the answer is:
β1 means that a unit change in the sample living area of a house, measured in square feet, will result in an estimated $108.78 change in the price of the house and β0 represents the estimated price of the house that is not attributed to the living area size.

Is it accurate to be refer to an individual house in interpretation, as I have done, or should I be referring to houses collectively and refer to the mean sample living area and mean price.

Any help would be greatly appreciated. Thanks

 

[winterfors]

What you're doing is calculating a rough estimate of how the price of a house depends on the square footage, in a population.

The equation you're using is supposing that it is reasonable to have a non-zero price for a non existing (zero square footage) house, whether this is reasonable or not is up to you to tell - if all prices include the terrain they are standing on it should be ok.

β(1) is the average price per square foot (measured in $/ft²),
β(0) corresponds to the average price of an empty plot. It may however be quite inaccurate, since it is an extrapolation using a model that might not be very accurate.

 

[ssd]

β(0) corresponds to the average price of an empty plot.

In my opinion it sounds better to describe β(0) as the overhead cost. The term avarage is not applicable for both the eatimates of β(0) and β(1). Think that two different regression lines possible (shall that imply two avarages of the same variable from the same sample?)

These are the values which minimizes the error of the assumed model.