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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.

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  • $\begingroup$ 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. $\endgroup$ – conjugateprior Aug 20 '14 at 10:07
  • $\begingroup$ Whoops. That's correct! $\endgroup$ – Slim Aug 20 '14 at 11:36
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Sounds like you need an interaction term between walk_time and train_time. Certainly not three separate models.

If I've understood your setup right and if people tend to want to minimise or lower bound total travel time, then I would expect these two variables to be negatively related as people trade them off.

In SPSS I believe you have to construct interaction terms manually. The web is full of people who'll show you how to do that. Then you have to interpret the interaction properly. That will require a little reading, but any regression textbook should cover it.

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  • $\begingroup$ Thanks for your reply, but would it be possible to expand on it? I tried this (below) approach: 1. Creating dummy variables for the train_time, eg. Train_time_0_to_9 ... Train_time_40_to_49 2. Creating new variables for walk_time, eg. walk_time_0_to_9 ... walk_time_0_to_49. Each of these variables had the respective equation for walkt_time_0_9 = walk_timetrain_time_0_to_9 walkt_time_10_19 = walk_timetrain_time_10_to_19 etc. But the results didn't match the coefficients when I ran the regression individually for each train_time group. $\endgroup$ – Slim Aug 20 '14 at 15:35
  • $\begingroup$ 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. $\endgroup$ – conjugateprior Aug 20 '14 at 16:18
  • $\begingroup$ It strikes me that you should do little reading up on the theory and interpretation of interaction terms in regression models. This will help you make better sense of the SPSS output, I think. $\endgroup$ – conjugateprior Aug 20 '14 at 16:21
  • $\begingroup$ Did a full nights worth of reading and realise how wrong I was. Thanks for the heads up. Could I confirm my findings with you quickly? "y= m1x1 + m2x2+... + -6701*Train_time + -7740*Walk_time * 94*Train_time_x_Walk_time" With this result, would i be correct to say that for 2 houses at 10 mins train ride of the CBD, a HDB further by 1 min would be expected to be 5761 dollars less. While for 2 houses at 20 mins train ride of the CBD, a HDB further by 1 min would be expected to be 4821 dollars less. Hence, the further we are from CBD, the less one would value the walking distance from the MRT? $\endgroup$ – Slim Aug 21 '14 at 1:41
  • $\begingroup$ 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. $\endgroup$ – conjugateprior Aug 21 '14 at 9:09

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