Predicting Mobile Phone Prices

Recently a colleague of mine showed me a nauseating interactive scatterplot that plots mobile phones according to two dimensions of the user’s choice from a list of possible dimensions.  Although the interactive visualization was offensive to my tastes, the JSON data behind the visualization was intriguing.  It was easy enough to get the data behind it (see this link if you want an up to date copy and be sure to take out the “data=” from the start of the file! I pulled this data around noon on March 23rd.) so that I could start asking a simple question: Which of the available factors provided in the dataset were the most predictive of full mobile phone price?

I’ll present the graphs and then the predictive model first and then the code later on:

Price by OS and Brand:

Often when investigating a topic using data, we confirm things that we already knew to be true.  This is certainly the case here with price by OS and brand.  From the below boxplots we see that the bulk of iOS devices tend to be the most expensive, and that brand-wise Apple, Google, and Samsung seem to stick out.

Mobile Phone Price by Operating System

Mobile Phone Prices by Brand

Price by Storage Capacity, RAM, and SD Card Capacity:

Storage capacity is perhaps the least surprising to find as having such a sharply positive correlation with price. I think what is more surprising to me is that there aren’t more gradations of storage capacity in the higher range past 50 gigabytes.  I’m guessing this is because the bulk of these phones (bearing in mind roughly 90% of these phones are in fact smart phones) are catered towards lower income folks.  Can you guess which phones occupy the top-right-most position on the first graph?  If your answer involved the iPhone 6 then you’re right on two counts!

As you can see, the correlation between RAM and price is pretty linear (with phones costing $171.54 more for each additional gigabyte of RAM) and that between SD Card capacity and price is linear past the large group of phones with 0 SD Card capacity (with phones costing $3.64 more for each additional gigabyte of SD Card Capacity).

Price by Storage Capacity

Price by RAM

Price by SD Card

Price by Screen Size, Battery, and Weight:

The next factors that I think one would naturally think of when considering the price of a mobile phone are all related to how big the thing is. Smart phones these days have a lot of physical presence just by dint of their screen size alone. Add to the large screen size the batteries that are used to support such generous displays and you also get an impressive variety of weights to these phones.

In fact, for every additional inch of screen size to these phones, you can expect an additional .81504 ounces and 565.11 mAh of battery capacity. My own humble little smartphone (an HTC Desire 601) happens to be on the smaller and lighter side of the spectrum as far as screen size and weight goes (4.5 inches screen size, or 33rd percentile; 4.59 ounces or 26th percentile) but happens to have a pretty generous battery capacity all things considered (2100 mAh, or 56th percentile).

While positive correlations can be seen between Price and all these 3 factors, battery was the most correlated with Price, next to screen size and then weight.  There’s obviously a lot of variability in price when you look at the phones with the bigger screen sizes, as they probably tend to come packed with a variety of premium extra features that can be used to jack up the price.

Price by Screen Size

Price by Battery

Price by Weight

Putting it all together in a model:
Finally, let’s lump all of the factors provided in the data set into a model, and see how well it performs on a testing sample. I decided on an 80/20 training/testing split, and am of course using Max Kuhn’s fabulous caret package to do the dirty work. I ran a gbm model, shown below, and managed to get an R squared of 60.4% in the training sample, so not bad.

Stochastic Gradient Boosting 

257 samples
 23 predictors

No pre-processing
Resampling: Cross-Validated (10 fold) 

Summary of sample sizes: 173, 173, 171, 171, 172, 171, ... 

Resampling results across tuning parameters:

  interaction.depth  n.trees  RMSE      Rsquared   RMSE SD   Rsquared SD
  1                   50      150.1219  0.5441107  45.36781  0.1546993  
  1                  100      147.5400  0.5676971  46.03555  0.1528225  
  1                  150      146.3710  0.5803005  45.00296  0.1575795  
  2                   50      144.0657  0.5927624  45.46212  0.1736994  
  2                  100      143.7181  0.6036983  44.80662  0.1787351  
  2                  150      143.4850  0.6041207  45.57357  0.1760428  
  3                   50      148.4914  0.5729182  45.27579  0.1903465  
  3                  100      148.5363  0.5735842  43.41793  0.1746064  
  3                  150      148.8497  0.5785677  43.39338  0.1781990  

Tuning parameter 'shrinkage' was held constant at a value of 0.1
RMSE was used to select the optimal model using  the smallest value.
The final values used for the model were n.trees = 150, interaction.depth = 2 and shrinkage = 0.1.

Now let’s look at the terms that came out as the most significant in the chosen model.  Below we see some unsurprising findings! Storage, battery, weight, RAM, and whether or not the phone uses iOS as the top 5. I guess I’m surprised that screen size was not higher up in the priority list, but at least it got in 6th place!

gbm variable importance

  only 20 most important variables shown (out of 41)

att_storage      100.0000
att_battery_mah   59.7597
att_weight        46.5410
att_ram           27.5871
att_osiOS         26.9977
att_screen_size   21.1106
att_sd_card       20.1130
att_brandSamsung   9.1220

Finally, let’s look at how our model did in the testing sample. Below I’ve shown you a plot of actual versus predicted price values. The straight line is what we would expect to see if there were a perfect correlation between the two (obviously not!!) while the smoothed line is the trend that we actually do see in the scatter plot. Considering the high R squared in the testing sample of 57% (not too far off from the training sample) it’s of course a nice confirmation of the utility of this model to see the smooth line following that perfect prediction line, but I won’t call be calling up Rogers Wireless with the magical model just yet!

Price by Predicted Price

In fact, before I close off this post, it would be remiss of me not to investigate a couple of cases in this final graph that look like outliers. The one on the bottom right, and the one on the top left.

The one on the bottom right happens to be a Sony Xperia Z3v Black with 32GB of storage space. What I learned from checking into this is that since the pricing data on the source website is pulled from, sometimes instead of pulling the full regular price, it happens to pull the data on a day when a special sale or service agreement price is listed. When I pulled the data, the Xperia was listed at a price of $29.99. Today, on April 6th, the price that you would get if you looked it up through the source website is .99! Interestingly, my model had predicted a full price of $632.17, which was not very far off from the full price of $599.99 that you can see if you go on the listing on Not bad!

Now, how about the phone that cost so much but that the model said shouldn’t? This phone was none other than the Black LG 3960 Google Nexus 4 Unlocked GSM Phone with 16GB of Storage space. The price I pulled that day was a whopping $699.99 but the model only predicted a price of $241.86! Considering the specs on this phone, the only features that really seem to measure up are the storage (16GB is roughly in the 85th percentile for smart phones) and the RAM (2 GB is roughly in the 93rd percentile for smart phones). Overall though, the model can’t account for any other qualities that Google might have imbued into this phone that were not measured by the source website. Hence, this is a formidable model outlier!

If you take out the Sony Xperia that I mentioned first, the Adjusted R squared value goes up from 57% to 74%, and the Residual Standard Error decreases from $156 to $121. That’s a lot of influence for just one outlier that we found to be based on data quality alone. Wow!

Reflecting on this exercise, the one factor that I wished were collected is processor speed.  I’m curious how much that would factor into pricing decisions, but alas this information was unavailable.

Anyway, this was fun, and I hope not too boring for you, the readers. Thanks for reading!!

Data Until I Die: My blog title and statement of values

When I started keeping this Blog, my intent was to write about and keep helpful snippets of R code that I used in the line of work.  It was the start of my second job after grad school and I was really excited about getting to use R on a regular basis outside of academia!  Well, time went on and so did the number of posts I put on here.  After a while the posts related to work started to dip considerably.  Then, I found my third post grad-school job, which shifted the things I needed R for at work.  I still use R at work, but not for exactly the same things.

After I got my third job, I noticed that all my blog posts were for fun, and not for work.  That’s when I fiddled a little bit with my blog title to incorporate the concept of ‘fun’ in there.  Now that I’ve carried on these ‘for fun’ analyses which I’ve been posting every 1-2 months, I realize that it’s an obsession of mine that’s not going away.  Data, I realize, is a need of mine (probably more than sex, to be honest).  I work with data in the office, I play with data when I can find fun data sets every once in a while at home.

Data and data analysis are comfortably things that I can see myself doing for the rest of my life.  That’s why I decided to call this blog “Data Until I Die!”.  Sometimes I’ll post boring analyses, and sometimes I’ll post really interesting analyses.  The main thing is, this Blog is a good excuse to fuel my Data drive 🙂

Thanks for reading!

Who uses E-Bikes in Toronto? Fun with Recursive Partitioning Trees and Toronto Open Data

I found a fun survey released to the Toronto Open Data website that investigates the travel/commuting behaviour of Torontonians, but with a special focus on E-bikes.  When I opened up the file, I found various demographic information, in addition to a question asking people their most frequently used mode of transportation.  Exactly 2,238 people responded to this survey, of which 194 were frequent E-bike users.  I figured that’s enough to do some data mining and an especially fun opportunity to use recursive partitioning trees to do that data mining!

Following is the code I used (notice in the model statements that I focus specifically on E-bike users versus everyone else):

Here is the first tree based on Sex, Health, and Age (Remember that the factor levels shown are not the only ones.  When you look on the “no” side of the tree, it means that you are examining the proportion of ebike users who are described by factor levels not shown):

Health and Age Tree
As you can see, only Health and Age came out as significantly discriminating between E-bike users and everyone else.  What this tree is telling us is that it’s in fact those people who are not in “Excellent, Good, Very good” health who are likely to use E-bikes, but rather an un-shown part of the Health spectrum: “Other,Fairly good,Poor”.  That’s interesting in and of itself.  It seems that of those people who are in Excellent or Very Good health, they are more likely (44%) to be riding Bicycles than people in other levels of health (23%).  That makes sense!  You’re not going to choose something effortful if your health isn’t great.

We also see a very interesting finding that it is in fact the 50 – 64 year olds (whose health isn’t great) who are more likely to be riding an E-bike compared to people of all other age groups!

Here’s the second tree based on Education and Income:

Education and Income Tree
Here we see that it is in fact not the university educated ones more likely to ride E-bikes, but in fact people with “College or trade school diploma,High school diploma”.  Interesting!!  Further, we see that amongst those who aren’t university educated, it’s those who say they make lower than $80,000 in income who are more likely to ride E-bikes.

So now we have an interesting picture emerging, with two parallel descriptions of who is most likely to ride E-bikes:

1) 50 – 64 year olds in not the greatest of health
2) Non University educated folks with lower than $80,000 income.

Toronto, these are your E-bike users!

Estimating Ages from First Names Part 2 – Using Some Morbid Test Data

In my last post, I wrote about how I compiled a US Social Security Agency data set into something usable in R, and mentioned some issues scaling it up to be usable for bigger datasets.  I also mentioned the need for data to test out the accuracy of my estimates.  First, I’ll show you how I prepped the dataset that it became more scalable (for the code that got us here, see my last post):

name_data_wavgpop_unisex = ddply(name_data, .(Name), function (x) sum(x$Rel_Pop*as.numeric(x$Year))/sum(x$Rel_Pop))
name_data_wavgpop_unisex$V1 = round(name_data_wavgpop_unisex$V1,0)

Above I’ve taken a different tactic to predicting expected year of birth according to name than I started out with in my last post. Here I’m using the relative popularity of the names in each year as weights for each year value. Multiplying them by the years, I get a weighted average of Year that gives me predicted year of birth. Then I round off the predictions to the nearest integer and continue on my way. Also, because test data doesn’t seem to come packaged with gender info, I’ve constructed the weighted averages using all relative popularity values for each name, regardless of whether or not that name has been used for both sexes (a.k.a. “Jordan”).

Now enter the test data. I’ve discovered that the easiest way of getting real names and ages off the internet is by looking for lists of victims of some horrible tragedy. The biggest such list of victims I could find was a list of 9/11 victims.  It’s not exactly formatted for easy analysis, and I was too lazy to get the data programatically, so I just copy-pasted into LibreOffice Calc the names and ages from the first 4 lists on the page (all from either American Airlines, or United Airlines) for a total of 285 observations.  I then extracted the first names, and then imported the first names and ages into R.

worldtrade = read.csv("world trade.csv")
worldtrade.ages = sqldf("SELECT a.*, b.V1 as Year FROM [worldtrade] AS a LEFT JOIN name_data_wavgpop_unisex AS b on a.Name == b.Name")
worldtrade.ages$Pred.Age = 2001 - as.numeric(worldtrade.ages$Year)

As you can see, I opted to use sqldf to append the appropriate predicted birth years for each name on the list I imported. I then got the predicted ages by subtracting each predicted birth year from 2001. Finally, let’s have a look at the resulting model fit (showing how close each predicted age was to the real age of the victim at the time of death):

Predicted vs Real Ages for 911 Victims




As you can see, it’s not a tight prediction in the least bit.  According to model fit statistics, there’s an adjusted r-squared of 14.6% and a residual standard error of 15.58 years.  You can also see from the scatter plot that the prediction doesn’t become reasonably linear until about age 30 and onwards.  Overall, I’d say it’s not too impressive, and I’d imagine it’s even worse for predicting who’s under 10 years old!

Well, this was fun (if only a little disappointing).  That’s statistics for you – sometimes it confirms, and sometimes it humbles you.  If you think you can show me a better way of using this name trending data to better predict ages than what I’ve done here, feel free to show me!

Which Torontonians Want a Casino? Survey Analysis Part 2

In my last post I said that I would try to investigate the question of who actually does want a casino, and whether place of residence is a factor in where they want the casino to be built.  So, here goes something:

The first line of attack in this blog post is to distinguish between people based on their responses to the third question on the survey, the one asking people to rate the importance of a long list of issues.  When I looked at this list originally, I knew that I would want to reduce the dimensionality using PCA.

issues.pca = principal(casino[,8:23], 3, rotate="varimax",scores=TRUE)

The PCA resulted in the 3 components listed in the table below.  The first component had variables loading on to it that seemed to relate to the casino being a big attraction with lots of features, so I named it “Go big or Go Home”.  On the second component there seemed to be variables loading on to it that related to technical details, while the third component seemed to have variables loading on to it that dealt with social or environmental issues.

Go Big or Go Home Concerned with Technical Details Concerned with Social/Environmental Issues or not Issue/Concern
Q3_A 0.181 0.751 Design of the facility
Q3_B 0.366 0.738 Employment Opportunities
Q3_C 0.44 0.659 Entertainment and cultural activities
Q3_D 0.695 0.361 Expanded convention facilities
Q3_E 0.701 0.346 Integration with surrounding areas
Q3_F 0.808 0.266 New hotel accommodations
Q3_G -0.117 0.885 Problem gambling & health concerns
Q3_H 0.904 Public safety and social concerns
Q3_I 0.254 0.716 Public space
Q3_J 0.864 0.218 Restaurants
Q3_K 0.877 0.157 Retail
Q3_L 0.423 0.676 -0.1 Revenue for the city
Q3_M 0.218 0.703 0.227 Support for local businesses
Q3_N 0.647 0.487 -0.221 Tourist attraction
Q3_O 0.118 0.731 Traffic concerns
Q3_P 0.497 0.536 0.124 Training and career development

Once I was satisfied that I had a decent understanding of what the PCA was telling me, I loaded the component scores into the original dataframe.

casino[,110:112] = issues.pca$scores
names(casino)[110:112] = c("GoBigorGoHome","TechnicalDetails","Soc.Env.Issues")

In order to investigate the question of who wants a casino and where, I decided to use question 6 as a dependent variable (the one asking where they would want it built, if one were to be built) and the PCA components as independent variables.  This is a good question to use, because the answer options, if you remember, are “Toronto”, “Adjacent Municipality” and “Neither”.  My approach was to model each response individually using logistic regression.

casino$Q6[casino$Q6 == ""] = NA
casino$Q6 = factor(casino$Q6, levels=c("Adjacent Municipality","City of Toronto","Neither"))

adj.mun = glm(casino$Q6 == "Adjacent Municipality" ~ GoBigorGoHome + TechnicalDetails + Soc.Env.Issues, data=casino, family=binomial(logit))
toronto = glm(casino$Q6 == "City of Toronto" ~ GoBigorGoHome + TechnicalDetails + Soc.Env.Issues, data=casino, family=binomial(logit))
neither = glm(casino$Q6 == "Neither" ~ GoBigorGoHome + TechnicalDetails + Soc.Env.Issues, data=casino, family=binomial(logit))

Following are the summaries of each GLM:

Adjacent municipality:

Neither location:

And here is a quick summary of the above GLM information:
Summary of Casino GLMs

Judging from these results, it looks like those who want a casino in Toronto don’t focus on the big social/environmental issues surrounding the casino, but do focus on the flashy and non-flashy details and benefits alike.  Those who want a casino outside of Toronto do care about the social/environmental issues, don’t care as much about the flashy details, but do have a focus on some of the non-flashy details.  Finally, those not wanting a casino in either location care about the social/environmental issues, but don’t care about any of the details.

Here’s where the issue of location comes into play.  When I look at the summary for the GLM that predicts who wants a casino in an adjacent municipality, I get the feeling that it’s picking up people living in the down-town core who just don’t think the area can handle a casino.  In other words, I think there might be a “not in my backyard!” effect.

The first inkling that this might be the case comes from an article from the Martin Prosperity Institute (MPI), who analyzed the same data set, and managed to get a very nice looking heat map-map of the responses to the first question on the survey, asking people how they feel about having a new casino in Toronto.  From this map, it does look like people in Downtown Toronto are feeling pretty negative about a new casino, whereas those in the far east and west of Toronto are feeling better about it.

My next evidence comes from the cities uncovered by geocoding the responses in the data set.  I decided to create a very simple indicator variable, distinguishing those for whom the “City” is Toronto, and those for whom the city is anything else.  I like this better than the MPI analysis, because it looks at peoples’ attitudes towards a casino both inside and outside of Toronto (rather than towards the concept of a new Casino in Toronto).  If there really is a “not in my backyard!” effect, I would expect to see evidence that those in Toronto are more disposed towards a casino in an adjacent municipality, and that those from outside of Toronto are more disposed towards a casino inside Toronto!  Here we go:

Where located by city of residenceAs you can see here, those from the outside of Toronto are more likely to suggest building a casino in Toronto compared with those from the inside, and less likely to suggest building a casino in an adjacent municipality (with the reverse being true about those from the inside of Toronto).

That being said, when you do the comparison within city of residence (instead of across it like I just did), those from the inside of Toronto seem equally likely to suggest that the casino be built in our outside of the city, whereas those outside are much more likely to suggest building the casino inside Toronto than outside.  So, depending on how you view this graph, you might only say there’s evidence for a “not in my backyard!” effect for those living outside of Toronto.

As a final note, I’ll remind you that although these analyses point to which Torontonians do want a new casino, the fact from this survey remains that about 71% of respondents are unsupportive of a casino in Toronto, and 53% don’t want a casino built in either Toronto or and adjacent municipality.  I really have to wonder if they’re still going to go ahead with it!

Split, Apply, and Combine for ffdf

Call me incompetent, but I just can’t get ffdfdply to work with my ffdf dataframes.  I’ve tried repeatedly and it just doesn’t seem to work!  I’ve seen numerous examples on stackoverflow, but maybe I’m applying them incorrectly.  Wanting to do some split-apply-combine on an ffdf, yet again, I finally broke down and made my own function that seems to do the job! It’s still crude, I think, and it will probably break down when there are NA values in the vector that you want to split, but here it is:

mtapply = function (dvar, ivar, funlist) {
  lenlist = length(funlist)
  outtable = matrix(NA, dim(table(ivar)), lenlist, dimnames=list(names(table(ivar)), funlist))
  c = 1
  for (f in funlist) {
    outtable[,c] = as.matrix(tapply(dvar, ivar, eval(parse(text=f))))
    c = c + 1
  return (outtable)}

As you can see, I’ve made it so that the result is a bunch of tapply vectors inserted into a matrix.  “dvar”, unsurprisingly, is your dependent variable.  “ivar”, your independent variable.  “funlist” is a vector of function names typed in as strings (e.g. c(“median”,”mean”,”mode”).  I’ve wasted so much of my time trying to get ddply or ffdfdply to work on an ffdf, that I’m happy that I now have anything that does the job for me.

Now that I think about it, this will fall short if you ask it to output more than one quantile for each of your split levels.  If you can improve this function, please be my guest!

Finding Patterns Amongst Binary Variables with the homals Package

It’s survey analysis season for me at work!  When analyzing survey data, the one kind of analysis I have realized that I’m not used to doing is finding patterns in binary data.  In other words, if I have a question to which multiple, non-mutually exclusive (checkbox) answers apply, how do I find the patterns in peoples’ responses to this question?

I tried apply PCA and Factor Analysis alternately, but they really don’t seem well suited to the analysis of data consisting of only binary columns (1s and 0s). In searching for something that works, I came across the homals package.  While the main function is described as a “homogeneity analysis”, its one ability that interests me is called “non-linear PCA”.  This is supposed to be able to reduce the dimensionality of your dataset even when the variables are all binary.

Well, here’s an example using some real survey data (with masked variable names).  First we start off with the purpose of the data and some simple summary stats:

It’s a group of 6 variables (answer choices) showing peoples check-box responses to a question asking them why they donated to a particular charity.  Following are the numbers of responses to each answer choice:

mapply(whydonate, FUN=sum, 1)
 V1  V2  V3  V4  V5  V6 
201  79 183 117 288 199

With the possible exception of answer choice V2, there are some pretty healthy numbers in each answer choice.  Next, let’s load up the homals package and run our non-linear PCA on the data.

fit = homals(whydonate)

Call: homals(data = whydonate)

Loss: 0.0003248596 

    D1     D2 
0.0267 0.0156 

Variable Loadings:
           D1          D2
V1 0.28440348 -0.10010355
V2 0.07512143 -0.10188037
V3 0.09897585  0.32713745
V4 0.20464762  0.21866432
V5 0.26782837 -0.09600215
V6 0.33198532 -0.04843107

As you can see, it extracts 2 dimensions by default (it can be changed using the “ndim” argument in the function), and it gives you what looks very much like a regular PCA loadings table.

Reading it naively, the pattern I see in the first dimension goes something like this: People tended to answer affirmatively to answer choices 1,4,5, and 6 as a group (obviously not all the time and altogether though!), but those answers didn’t tend to be used alongside choices 2 and 3.

In the second  dimension I see: People tended to answer affirmatively to answer choices 3 and 4 as a group.  Okay, now as a simple check, let’s look at the correlation matrix for these binary variables:


           V1            V2            V3         V4          V5         V6
V1 1.00000000  0.0943477325  0.0205241732 0.16409945 0.254854574 0.45612458
V2 0.09434773  1.0000000000 -0.0008474402 0.01941461 0.038161091 0.08661938
V3 0.02052417 -0.0008474402  1.0000000000 0.21479291 0.007465142 0.11416164
V4 0.16409945  0.0194146144  0.2147929137 1.00000000 0.158325383 0.22777471
V5 0.25485457  0.0381610906  0.0074651417 0.15832538 1.000000000 0.41749064
V6 0.45612458  0.0866193754  0.1141616374 0.22777471 0.417490642 1.00000000

The first dimension is easy to spot in the “V1” column above. Also, we can see the second dimension in the “V3” column above – both check out! I find that neat and easy. Does anyone use anything else to find patterns in binary data like this? Feel free to tell me in the comments!