Using a multiple regression model for my cost estimation Disclaimer: not a statistics student, I am a civil engineering undergrad currently writing my thesis. And, I have never done a multiple regression analysis before.
Half of my study is cost estimation of a retrofitting project. I have a data set to use, albeit with just about 35 data points. My main adviser told me to use a simple linear regression using the total floor building area only to predict the cost. All good, and very simple especially since you only need to plug in the building area, and ta-da you get the cost.
However, I feel like this is very one-dimensional. All the cost estimation models I read online relating to my study are using multiple variables. I came to realize this when I was presenting my regression model, one panelist pointed out that some data points are clustered together, which might indicate that there is some hidden variable that could be affecting the regression model. I have not asked my adviser about this yet.
The data set given to me has other variables to consider:

*

*total building floor area (which I used)

*number of floors

*year of construction

*proximity to fault line

*liquefaction potential (qualitative: safe, low, high, moderate)

Do I need to use multiple regression here? Does my data set have enough points for it?
 A: I would agree with your supervisor.  That's good enough for the data you have and your knowledge.
However, its easy enough to run a multiple linear regression (even in excel if you enable/download the analysis toolpak)
then you would check for the significance of each coefficient (but would have to do some multiple testing adjustment eg Bonferroni  (divide the test criterion value eg p=0.05 by the number of coefficient tests, 5)
you could review whether the sign of the coefficients made sense.
one of the issues you are facing is that the data is observational rather than from an experiment, so there are likely to be lots of hidden correlations which might make the meaning of the coefficients suspect. eg perhaps more recent buildings are larger, being closer to a fault line is actually associated with an omitted variable like property prices.
A: One small tip here: Two of your variables (total floor area and number of floors) have a direct causal relationship that will make them strongly correlated.  In order to reduce this collinearity I recommend you change the first variable to look at average area per floor instead of total area.  This change in the input variables will allow you to decompose the effects of the number of floors and the area-per-floor more easily and will make the output of your model easier to interpret.  You can also add an interaction term between these variables and if you do it will decompose the relationships more sensibly.
