# SPSS: Comparing Regression Coefficient for 2 Models

Hope you guys could help me with a question I've been stuck on for a while.

I'm currently writing my thesis on how MRT (the railway system in Singapore) accessibility affects prices of public housings (HDBs). So far I've gotten quite far but have reached a wall. I have collected 11,000 HDB transactions, all which are within walking distance of MRT station (<750m to the nearest MRT Station or <10min walk to the nearest MRT Station). Apart from the usual structural variables:

• Age
• Floor
• Size

I also managed to obtain locational variables such as:

• Time taken to walk to nearest railway station (time_walk)
• Time taken to commute, via train, from the nearest station to the CBD station (time_train)
• Total Traveling Time, time_walk + time_train (TTT)

With these variables, I ran a multiple regression with Price as the DV and Age, Floor, Size, time_walk, and time_train as the IVs. This then produced regression coefficients for the DV. With these coefficient it allowed me to analyse the quantitative impact that, with everything else constant, (i) each additional walking minute, and (ii) each additional commuting minute on the MRT, had on the pricing of HDB.

However, what I would like to investigate is, do residents living at different distances from the CBD value time_walk differently?

I understand that I can't create 3 models (shown below), each containing only the relevant details (eg. 0-9 mins train time, 10-19 mins train time ...etc) as the n number would be different, thus, comparing the coefficient estimates wouldn't be fair

Model A: (0-9 mins time_train): How would Walking_Time affects house pricing?

Model B: (10-19 mins time_train): How would Walking_Time affects house pricing?

Model C: (20-29 mins time_train): How would Walking_Time affects house pricing?

Any advice would be greatly appreciated.

• Do you perhaps mean "I ran a multiple regression with Price as the DV and Age, Floor, Size, time_walk, and time_train as the IVs." It seems that what you should mean, in any case. – conjugateprior Aug 20 '14 at 10:07
• Whoops. That's correct! – Slim Aug 20 '14 at 11:36

Sounds like you need an interaction term between walk_time and train_time. Certainly not three separate models.
• First, why not just construct walk_time multiplied by train_time as your interaction term to start with, if they're both continuous. You can discretise later (and when you do, don't forget to leave a level out of each of them). Second, you wouldn't expect your new model to give the same parameter estimates as the separate models: different cases lead to different results! Your first task should be to build a single model with all the cases and interaction that you can interpret in a way that asnwers your question. – conjugateprior Aug 20 '14 at 16:18
• First the coefficients: Set tt=-6701, wt=-7740, and ttxwt=94 as above. Set train_time=10 and compare walk_time=10 and walk_time=11 (if the model is linear it doesn't matter what the absolute value of walk_time is). Then (tt * 10 + wt * 10 + ttxwt * (10 * 10)) minus (tt * 10 + wt * 11 + ttxwt * (10 * 11)) = 6800. That's the expected reduction in price for being the same train time away but 1 more minute longer walk. I'm not sure where the 5761 came from. – conjugateprior Aug 21 '14 at 9:09