Summer 2016 License Plate Game Report
by Mark Kloha
© 2016
The Hypothesis
The probability, frequency, and difficulty of finding a
license plate from any given state is related to three variables – population,
distance, and per capita income for that state.
The number of license plates that I find from any given state will be
highly correlated to a combination of these three variables.
Background
This is the second summer where I’ve tracked license plates
from Memorial Day weekend through Labor Day weekend. It was a fun game that I played as a kid, and
now my wife and kids are playing along.
I did this last summer and put together an extensive report, and now
here is the Summer 2016 License Plate Game Report.
Methodology
Timing –
I began on Wednesday, May 25, and went through Tuesday,
September 6 (Memorial Day Weekend through Labor Day Weekend). For the purposes of this research, each
‘week’ began on Wednesday and ended on the following Tuesday. This timing allows the weekends to be grouped
together including the Mondays of holiday weekends such as Memorial Day weekend
and Labor Day weekend.
Tools –
When tracking license plates, I will be using an iphone app
to track where and when I see a license plate.
The app I am using is “License Plate Zone”. This app allows me to log any state and any
license plate multiple times. Most
license plate apps will only let me log a state once. This app lets me log multiple license plates
for each state.
Trish does most of the driving on the weekends and in the
evenings. I will be able to log the
license plates quite effectively. If I
am driving and see an out-of-state license plate, I can press a button on my
iphone to talk to Siri through a Bluetooth-hands-free connection and have Siri
make a note of what license plate I just saw.
Then I can enter the information into the app later on.
How I’m Counting
I am only counting the official 50 States in the United
States of America.
I do not track the District of Columbia or any other US
territories.
I am only counting the license plate if it is on the back of
the car. Some states require a license
plate on the front and back. Some states
only require a license plate on the back of the car. It is possible for a car to have two
different plates from two different states.
This can happen if a person lived in say Hawaii for a while, brought
their license plate back (or even their car) to a state that only requires a
license plate on the back, and then they kept the license plate on the
front. I have seen a number of Hawaii
license plates on the front of a car with a different plate on the back – while
these front Hawaii plates are rare in of themselves, these front license plates
will not be counted. I cannot make an
exception for Hawaii because then I would need to make an exception for all
front license plates. Technically, counting
the front license plate would increase the population of that state to anyone
who had ever lived there and just happened to keep their license plate as a
memento. I have no way of adjusting the
population factor to accommodate these front license plates.
License plates from semi-trucks, U-Hauls, etc. do not
count. Depending on the state laws, it
is more beneficial for certain types of truck companies to be registered in
various states. I’ve seen a lot of
semi-trucks with Maine license plates but very few passenger vehicles with a
Maine license plate.
I will do my best not to double count license plates. For example, on my way into work, I see a car
parked on the side of the road and it has a Tennessee license plate. If I see this car on my way into work every
day, I will not count it again and again and again. If I’m at a campground, it is possible that
there are campers from out of state there.
As we move around the campsite, I will not record a license plate every
time I see the same vehicle again later on.
Where I’m Counting –
I am only counting out of state license plates that I find
in Michigan. Our summer travel plans are
mostly in Michigan. We have several
weekend camping trips planned throughout Michigan. Also, I will be looking for license plates
just in our daily routines. We will be
going to Columbus, Ohio for one weekend.
While out of Michigan, the license plates that I find while out of state
will not count.
Variables -
I have three variables – population, distance, and income
with cost-of-living-adjustment (COLA).
Population
The population data is from:
This is for July 2015.
Per Capita Median Income
and Cost of Living
The economic data that I use for the Per Capita Median
Income variable is from:
This data source provides the per capita median income for
each state, the average state taxes on that income, and then the Cost of Living
Adjustment factor.
For the statistical analysis, I took the median income,
subtracted the state taxes, and adjusted that based on the COLA percentages for
each state.
(Median Income – State Taxes)/(Cost of Living Factor)
Distance
The third variable is distance. The app I am using lists the latitude and
longitude of where I found that license plate.
For each observation, I calculated the distance from where I saw that
license plate to the state’s largest metropolitan area. Then for each state, I calculated an average
distance to that state’s largest metro area.
In my Summer 2015 License Plate report, I tracked distances from both
the largest city and also to the state’s border. The conclusion from that report is that
statistically it does not make a difference.
Shortcuts through
Canada
To calculate the distance to the New England states, it is
quicker and shorter to drive through Canada, and so my calculations for
distance did utilize this shortcut. This
is different from last year’s report where I did not allow the shortcut through
Canada to be used to get from Michigan to the New England states.
Also, to drive from Alaska to Michigan, it is necessary to
drive through Canada as well.
Michigan Ferries
across Lake Michigan
To get from Michigan to Wisconsin, Minnesota, or other
western states, there are two car ferries that go across Lake Michigan. The Lake
Express goes from Milwaukee to Muskegon in 2.5 hours. The S.S
Badger goes from Manitowoc, WI to Ludington, MI in 4 hours. When calculating routes in Google Maps,
Google Maps always said the quickest way to some places was via ferry - specifically
the Lake Express.
To calculate the distances to Wisconsin and Minnesota, the
distance calculations that I used were based on driving around Lake Michigan,
through Chicago. I did not utilize
either of the ferries that go across Lake Michigan.
Distance to Hawaii
Calculation
It is possible to find a car with a Hawaii license plate on
the back in the mainland and even right here in Michigan. I did see one this summer!! It is obviously impossible to drive to
Hawaii. Hawaii has a population and per
capita median income but no drivable distance to Michigan. If I were to include Hawaii in this study,
then how should the distance be calculated?
If I use the actual distance from Hawaii to Michigan of 4,500 miles,
then this assumes that the distance is drivable – which it isn’t.
It is possible to transport a car from Hawaii to California
by boat. It costs approximately a
thousand dollars (give or take a few hundred dollars) and takes ten days. http://www.matson.com/pov/booking/shipping_rates.htm
There are a few possibilities for dealing with Hawaii:
1.
Not
include Hawaii in the study
2.
Convert all the distances to a “time”
variable.
3.
Convert the shipping time and costs from Hawaii
to California to a “distance”.
I originally was not going to include Hawaii in the study;
however, I actually did see a license plate from Hawaii on the back of a Jeep,
and so I went about converting the traveling time to a calculated distance.
I came up with a method to convert the time at sea to a
driving time. It takes 10 days to ship
the car. The trip will take 10 days, and
assuming that an average driver could easily drive 500 miles in one day, then
that means the entire trip has been assigned a mileage of 5,000 miles from
Hawaii to California, and this will get the vehicle from Honolulu, Hawaii to
Los Angeles, California. The distance
from Detroit, MI, to Los Angeles, CA, is 2,218 miles. It also costs $1,000. So, adding the converted time on the boat to
miles with the actual mile from Michigan to California and adding the cost as
miles, this gives 8,218 miles.
However, with such a large distance of 8,218 miles, this
distance makes Hawaii an outlier in the multiple regressions, and so for the in-depth
statistical analysis, Hawaii will not be included in the Correlations and
Multiple Regressions later on.
Quick Summary –
1.
I am only tracking the official 50 States – not
including D.C or other U.S. territories.
2.
I am not tracking Michigan.
3.
Distances are measured by the shortest distance
from the point I saw the license plate to the largest metro in the other state.
4.
Distances do use the short cut route through
Canada to get to the New England States.
5.
The distance to Alaska is based on driving
through Canada.
6.
Only license plates on the back of a vehicle
count
7.
License plates on semi-trucks and rentable
trailers/trucks do not count.
8.
I will be tracking the frequency, date, time,
and location for the out of state license plates that I find.
Results:
During the 15 weeks, I traveled, 7,023 miles within
Michigan. I logged 1,031 out of state
license plates.
The top 5 were:
Illinois -195
Ohio - 123
Indiana - 115
Florida - 88
Texas - 38
These 5 states made up just a little over 50% of my
sightings.
The bottom 5 were:
Maine -1
Rhode Island -1
South Dakota - 1
Hawaii - 1
Delaware - 0
I saw every state at least twice except for these five
states.
Other interesting
information:
The days of the week that I saw the most out of state
license plates in order:
Sunday - 208
Saturday - 189
Friday - 157
Monday - 141
Wednesday - 133
Thursday – 113
Tuesday - 90
On Monday, Memorial Day – I saw 29 out of state license
plates. On Monday, Labor Day, I saw 15
out of state license plates. If the
count for these special Mondays were taken out and say added to Sunday as the
last day of the weekend, then Monday drops to a count of 97.
The weeks that I saw the most out of state license plates
–
Week Number
|
Mileage
|
Observations that week
|
Dates
|
Week 1
|
603
|
290
|
May 25 to May 31
|
Week 2
|
472
|
41
|
June 1 to June 7
|
Week 3
|
337
|
39
|
June 8 to June 14
|
Week 4
|
388
|
30
|
June 15 to June 21
|
Week 5
|
349
|
42
|
June 22 to June 28
|
Week 6
|
521
|
75
|
June 29 to July 5
|
Week 7
|
478
|
49
|
July 6 to July 12
|
Week 8
|
420
|
37
|
July 13 to July 19
|
Week 9
|
340
|
24
|
July 20 to July 26
|
Week 10
|
460
|
44
|
July 27 to August 2
|
Week 11
|
410
|
25
|
August 3 to August 9
|
Week 12
|
377
|
66
|
August 10 to August 16
|
Week 13
|
746
|
136
|
August 17 to August 23
|
Week 14
|
583
|
62
|
August 24 to August 30
|
Week 15
|
539
|
71
|
August 31 to September 6
|
Week 1 – we were in South Haven, Michigan for Memorial
Day weekend, and we drove through both North and South Beach, and we were
staying at Van Buren County State Park.
Week 13 – we were at Michigan State University for the 4H
State Horse Show, and we stayed at a hotel at Eastwood Town Center. So, we were driving a lot between MSU and
Eastwood Town Center with trips every day back home to check on our horses.
Week 6 and Week 15 both have Observations >70 – these
were both holiday weekends.
Correlations:
For the following statistical computations, the independent
variable is Frequency - how many times I saw each state. The three dependent variables as mentioned
earlier are population, distance, and per capita income adjusted.
Using Microsoft Excel, I ran independent correlations
between the following four variables and the dependent variable. Here are the results –
Population: 39%
correlation
Distance: 30% inverse
correlation
Per Capita Income (PCI):
0% correlation
Per Capita Income Adjusted (PCIA): 27% correlation
So, population is the most significant variable. The distance factor is an inverse
correlation. The inverse correlation
means that the closer the state is, then the higher the frequency. I found it interesting that I got a 0%
correlation on the median income but then it jumped to 27% once I adjusted the
state incomes based on the Cost of Living Adjustment factor.
Multiple Regressions
A short general summary of multiple regressions.
The Multiple R
value is how well did my variables correlate to the number of observations for
each state.
The R Squared is
the value of the Multiple R value and
squared. The Adjusted R Squared value modifies the R Squared value based on the
number of independent variables that are being used in the regression. The R
Squared and the Adjusted R Squared
measure how well the three variable explain the changes in the Frequency
variable.
When dealing with human behavior, and tracking license
plates is human behavior, it is rather typical for the Multiple R value and the R
Squared values to be low. If the R Squared value is above .3, then you’re
onto something. If the R Squared value is above .5, then that
is a smashing success.
Somewhat more important are the t-stat values. This
indicates the strength of the variables in the regression. The T-stat
value should be evaluated independently of the R Squared values. It is
possible to have low R Squared values
but if the t-stat values are greater
than 2.00, then the variables are considered significant, and the variables
still affect the dependent variable.
Even quicker summary – R
Squared values above .3 are good, R
Squared values above .5 are excellent, and t-stat values above 2.00 are awesome regardless of the R Squared value.
Using Microsoft Excel, I ran several multiple
regressions.
(PCIA – Per Capita Income Adjusted)
Population, Distance, and PCIA without Hawaii - 48 states
Multiple R: .571
R Squared: .327
Adjusted R Squared: .288
Pop t-stat: 3.38
Distance t-stat: -2.47
PCIA t-stat: 2.03
This looks at 48 states for the 3 variables – Population,
Distance, and PCIA. The Adjusted R
Squared value does drop below .3; however, all three variables are
significant.
Population and Distance without Hawaii – 48 states
Multiple R: .513
R Squared: .263
Adjusted R Squared:
.230
Population t-stat:
3.248
Distance t-stat:
-2.571
This looks at 48 states with only two variables –
Population and Distance.
The Adjusted R-squared value is again below .3; however,
the two variables are significant.
For, the next set of regressions that I ran, I removed
what are called the “Residuals”. The
Residuals in a multiple regression are essentially throwing the data set “off
balance”. If one removes these residuals
and analyzes those separately, one can get a better idea of how well the
variables can in fact predict the outcome – how well do Population, Distance,
and Income predict how many observations I will see from each state without
these anomalies/residuals.
The Microsoft Excel Regression analysis showed that
Illinois, Indiana, Ohio, Florida, Texas, Alaska, and Oregon were
residuals. So, for now, I will detail
the results of the multiple regression without these states and re-visit these
residual states for a closer look.
Population, Distance, and PCIA (41 states)
Multiple R: .787
R Squarred: .621
Adjusted R Squared:
.589
Population t-stat:
7.204
Distance t-stat:
-4.6449
PCIA – 2.451
Here we see a huge jump in the Multiple R values and the
R Squared values. There is an Adjusted R
Squared value of .589. That means that
these variables can decently predict the frequency of seeing out of state
license plates rather well. The T-stat
values are all above 2.0. The fact that
Population t-stat is 7.2 indicates that this is the most important factor, with
Distance next, and the PCIA income variable contributing to the prediction.
Population and Distance with 41 states:
Multiple R: .747
R Square: .559
Adjusted R: .535
Population t-stat:
6.44
Distance t-stat:
-4.10
Again, the Multiple R value is fairly high, the Adjusted
R value is above .5 which is excellent, and the t-stat values are both above
2.0. The Population T-stat variable is
higher which means it’s a little more important than the Distance variable.
Residuals:
Let’s get back to those residuals – Illinois, Indiana,
Ohio, Florida, Texas, Alaska, and Oregon.
The first five were categorized as residuals as I had
seen so many of these that the frequency of these states compared with all the
other states was off-balancing the regression model. Illinois, Indiana, and Ohio – these are the
three closest states to Michigan’s southern border. Florida almost acts like a border state with
88 sightings. As mentioned earlier, I am
suspicious that many of these are snowbirds.
A new hypothesis has evolved that if this study were conducted throughout
the Fall and Winter, I’d see a lot fewer Florida plates in comparison to all
the other states.
Alaska – I saw 9 Alaskan license plates. That is a very high number of sightings for
a state that is so far away with such a low population. I did some quick Google searches and I came
across this one website:
Under Myth #3 , they explain that Alaska has one of the
most transitory populations of all 50 states.
If true, that could possibly explain the higher number of Alaska license
plates. People move there long enough to
get a license plate, decide to move somewhere else and haven’t updated their
license plate yet.
Or maybe, people from Alaska just like to drive and
travel.
Oregon – this showed up as a residual. I was a little surprised. So, let’s take a look at the data. I saw 7 license plates from Oregon. Doesn’t seem like a big deal. Oregon has a population of about 4,000,000 people
- which is about average. States with a
population around or below 1,000,000 people – those are difficult to find. Oregon has 4,000,000 people so what’s going
on?
The distance factor!!
And their economy!! Distance
factor first. Portland, Oregon is
farther away than Seattle, Washington. I
measured my distance variable from where I saw the license plate to the most
populated metro area in the other state.
For Oregon, that is Portland. To
drive to Oregon, one needs to navigate around the mountains in Idaho. You can either go north of them and drive
through Seattle, Washington first and then go to Portland, or you can drive way
south of the mountains in Idaho which means driving to Salt Lake City, Utah
first then to Boise, Idaho then to Portland, Oregon. So, of the 48 contiguous states – Oregon is
the farthest away. So, seeing 7 license
plates from there is really high.
Income – Oregon has a median income of about $37,000 –
this is a little above average. However,
they have a 129% Cost-of-living-adjustment.
So, once when state taxes are taken out and then that amount is
adjusted, Oregon has an adjusted median income that comes in 49th
place (Hawaii is 50th).
More Regressions
So far, the regressions have been based on a sample size
of either 48 states or 41 states. To
increase the sample size, I employed a new method. Each state for each week is its own
sample. For example, there is Alabama1,
Alabama2, Alabama3……Alabama15; Alaska1, Alaska2, Alaska3……Alaska15. So, there are 48 states over 15 weeks which
yields a sample size of 720.
The first regression for all 720 States per Week:
Multiple R 0.239944
R Square 0.057573
Adjusted R Square 0.053624
Population t-stat 4.825677423
Distance t-stat -3.522821578
PCIA t-stat 2.979897398
Here the R Square and the Adjusted R Square values are
very low. The three variables however
are showing as being significant.
Remember that the t-stat values need to be evaluated separately from the
R Square values.
Second regression for 718 States per Week:
Multiple R 0.430738492
R Square 0.185535649
Adjusted R Square 0.18211353
Population 10.75350838
Distance t-state
-5.461421468
PCIA t-stat 4.744290868
In this regression, I took out only 2 residuals –
Illinois1 and Indiana1. The number of
sightings for these two states during the 1st week was extremely high. So, I took out only these two.
With this regression, the Multiple R, R Square, and
Adjusted R Square values all increase considerably. The three variables with a t-stat value well
above 2.0, this shows again that these three variables are significant in
determining the number of out of state license plates one can reasonably expect
to see here in Michigan based on the three variables.
New Variables
In the world of academic Geography, they like to be all
scientific and stuff and they have various equations to calculate interactions
between two places. It’s based on
Newton’s law of gravitational attraction F=m1*m2/d2. Gravitational Force is equal to the mass of
object 1 times mass of object 2 divided by the distance squared. This equation has been adopted by geographers
to the following:
Demographic Gravitation is:
DG = p1*p2/d2
Demographic gravitation is equal to the population of
place 1 times the population of place 2 divided by the distance squared.
The other equation is Demographic Energy:
DE=p1*p2/d
Demographic Energy is equal to the population of place 1
times the population of place 2 divided by the distance.
For the purposes of this research, I have adapted these
equations further. Since I was focusing
just on the license plates found here in Michigan, it is not necessary to
multiply the population of the other states by Michigan’s population 49 times.
The three new variables to measure Demographic
Interaction between the other states and Michigan are:
P/D
= Population/Distance
(P*IA)/D
= (Population*Income Adjusted)/Distance
PIA=
Population*Income Adjusted
I ran the correlation between my new variables and
frequency for 48 states (without Hawaii or Michigan):
Population/Distance
= 91%
correlation
Population*Income
Adjusted/Distance = 92% correlation
Population*Income
Adjusted = 44% correlation
For the Population, Distance, Income composite variable
(PDI), I ran some more multiple regressions.
PDI
Multiple R 0.921595637
R Square 0.849338519
Adjusted R Square 0.846063269
PDI t-stat 16.10342331
So, this is showing the Multiple R value at .9215 with
the R Square and Adjusted R Square values very close together at .849 and .846
respectively.
Furthermore, in this regression, the residual analysis
showed that Indiana and Florida were residuals.
So, I ran a regression where I took those two states out and the results
are as follows:
Multiple R 0.979344992
R Square 0.959116613
Adjusted R Square 0.958187445
PDI t-stat 32.12836409
A Multiple R value of .979!!
The R Square and Adjusted R Square values are extremely
close with .959 and .958 respectively.
The t-stat value is 32.1 – almost twice that of the previous regression
with Indiana and Florida.
Residual analysis:
Indiana – the state of Indiana has half the population of
Ohio, almost same distance and similar adjusted median incomes and yet Indiana
had slightly more sightings than Ohio.
This would cause the regression to categorize this state as a residual.
Florida – the state of Florida is listed with a distance
of 1,438 miles away to the largest metro area, Miami, and yet the state comes
in 4th place for number of observations at 88 observations. Even Texas which came in 5th place
with 38 sightings – Texas has a larger population and closer and had less than
half the observations that Florida had.
So, the snowbirds were probably influencing the number of Florida
license plates that were seen.
Summary
If you want to calculate the difficulty of finding any
given state, or predict which states you will see more often than others,
simply take the population of all 50 states and divide that by the calculated
distance to the other state, and then rank them – the higher the number, the
easier that state is to find. FYI –
using the largest city or capital or the state border statistically will not
make any difference – just be consistent as to which method you use for each
state. Adding in the adjusted income
factor will only give it a slight boost
The most important factor appears to be the Population of
any given state. The Population factor
did rank the highest in my multiple regressions. However, if you look in Appendix 2, and look
through the regressions that I ran for each week, early on, the Distance factor
was slightly more important. After 15
weeks though, the Population factor was the most contributing factor to the
success of finding or not finding out of state license plates.
The Income variable – last year, I mentioned to my wife
that there were some states that I just could not find. They had an average population and really
weren’t that far away. Trish suggested
that I consider an economic factor. So,
this year I included an economic factor.
While this variable was the weakest factor of the three independent
variables, it was still significant.
Sources –
|
Bonus Section –
Review of License Plate Apps for iphone
US PL8S app
·
List of all 50 states and D.C. with only 1 plate
per state
·
List has feature to hide the states that have
been found
·
Has Statistics function – Lists what percentage
of the 51 States/District you have found (50 States plus D.C.)
·
For the individual states, it lists the date
found, how many license plates are issued for the state, and ranks the states
into four categories – easy, medium, hard, and very hard
What I like about this app is that it is very
simple. It’s great if you just want to
check off each state as you find it. The
information about when and where is also available.
Miles to Go app
·
This app like the other apps allows you to track
which states you have found only once.
·
It has Facts and Quizzes section – this includes
capital, largest city, flag, statehood date and order of admission to the
Union, nickname, state seal, area and rank, population and rank, state bird and
state flower.
·
The quizzes can be customized to focus on just
certain aspects of the information in the facts section. Such as only being quizzed on capitals and
largest city versus being quizzed on everything from capitals to state birds.
·
It has a travel log – it is a notes section
where you can enter what cities you visited and what you did.
·
This app includes Canada. You can record which provinces/territories of
Canada you have found. Canada has its
own section of facts and quizzes.
·
It has a “Progress” chart for the United States
and a separate chart for Canada.
·
It’s glitchy.
I cannot reset the game or reset a license plate if I incorrectly enter
that after I found a plate and need to fix it.
To reset the entire app, you can delete the app and then reload. If you just enter an incorrect state, it is
impossible to fix.
What I like about this app –
It has Canada!! The facts and quizzes section looks fun for
kids who want to learn some geography and history. The Notes section is a great travel log. It is glitchy. If you want a new game, you can delete the
app and then reload it. If you need to
reset a license plate, you are kind of stuck.
States and Pl8S
My least favorite app although
it has a few redeeming qualities –
·
It has a running “mileage score”. The score is based on your location to the
center of the other states. So, if you
are in Ohio and you see a Florida license plates you score more “mileage
points” for that license plate than if you are in Georgia and you find a
Florida license plate.
·
It has a fun facts section for each state.
License Plate Zone
app (this is my favorite app)
·
For all 50 states and D.C., this app lists all
the plates issued in that state. It has
a picture of each license plate in that state.
This allows you to check off specifically which plate you found.
·
In the list of the States, it shows how many
different plates are issued for that state.
For example, Alabama has 161 different plates, Alaska has 35 different
types of plates, etc.
·
Map feature shows where it was found
·
Lists the date, time, and latitude and longitude
of when and where the plate was found.
·
The “Trips” feature lists how many plates from
how many different states have been found.
For example, my app currently says I have found 71 plates from 49
different states.
·
Lists all the plates in the order found along
with date, time, lat. and long.
·
Allows the same plate from the same state to be
selected multiple times if and when that particular plate is found again
·
Can edit the location. This means that if you are driving, you see a
license plate from Alaska, you wait until you are safely parked and enter the
information, it will drop a pin of your current location; however, you can move
this pin to where you actually saw the license plate.
What I like about this app is
that it has all the plates from all the states.
I also like the feature where you can edit where and when you found the
license plate. I like the fact that it
lists the order in which you found them.
It allows a person to enter the same license plate multiple times. This is the only app that allows a person to
do this.
Summary –
The USPL8S app is the simplest to use and great for kids
who just want to check off if they found the state or not.
The License Plate Zone app is the one I use the
most. I love the fact that it lists all
the plates for each state. Also,
multiple plates from the same state can be logged. This is the only app that allows a person to
do this. Although, the app is not being
updated by the developers with newer license plates.
The Miles to Go app is awesome in that it has Canada
along with the fun facts and quizzes section.
Then the States and Pl8S has the awesome “Mileage Points”
game.
My ideal app would have all the features of License Plate
Zone, include the Canadian Provinces as optional, and then it would calculate
the miles you were from that state. It
would be awesome if it could do the simple calculation of dividing the
population of the state by the distance to that state and assigning a score
based on that.
Appendix 1 – Data Set
State
|
Observations
|
Population
|
Distance
|
PCIA
|
Illinois
|
195
|
12,859,995
|
160
|
$37,223
|
Indiana
|
123
|
6,619,680
|
243
|
$36,164
|
Ohio
|
115
|
11,613,423
|
253
|
$37,080
|
Florida
|
88
|
20,271,272
|
1,438
|
$31,652
|
Texas
|
38
|
27,469,114
|
1,148
|
$37,311
|
New York
|
35
|
19,795,791
|
685
|
$28,948
|
Wisconsin
|
34
|
5,771,337
|
295
|
$33,853
|
Tennessee
|
32
|
6,600,299
|
539
|
$35,238
|
Virginia
|
29
|
8,382,993
|
795
|
$38,351
|
California
|
23
|
39,144,818
|
2,221
|
$28,651
|
Pennsylvania
|
22
|
12,802,503
|
651
|
$34,020
|
Georgia
|
21
|
10,214,860
|
780
|
$34,476
|
New Jersey
|
20
|
8,958,013
|
685
|
$32,269
|
North Carolina
|
19
|
10,042,802
|
679
|
$32,564
|
Maryland
|
19
|
6,006,401
|
596
|
$32,968
|
Minnesota
|
18
|
5,489,594
|
622
|
$36,017
|
Iowa
|
17
|
3,123,899
|
512
|
$34,739
|
Missouri
|
15
|
6,083,672
|
467
|
$34,538
|
Kentucky
|
15
|
4,425,092
|
376
|
$34,054
|
South Carolina
|
13
|
4,896,146
|
728
|
$30,345
|
Massachusetts
|
11
|
6,794,422
|
777
|
$33,171
|
Arizona
|
10
|
6,828,065
|
1,940
|
$34,179
|
Alabama
|
9
|
4,858,979
|
732
|
$33,273
|
Connecticut
|
9
|
3,590,886
|
749
|
$31,744
|
Washington
|
9
|
7,170,351
|
2,283
|
$39,802
|
Alaska
|
9
|
738,432
|
3,724
|
$34,772
|
Colorado
|
8
|
5,456,574
|
1,225
|
$36,314
|
Oregon
|
7
|
4,028,977
|
2,329
|
$26,238
|
Nebraska
|
6
|
1,896,190
|
644
|
$35,075
|
New Hampshire
|
6
|
1,330,608
|
808
|
$31,540
|
Montana
|
6
|
1,032,949
|
1,470
|
$29,522
|
Kansas
|
5
|
2,911,641
|
682
|
$35,682
|
West Virginia
|
5
|
1,844,128
|
405
|
$28,066
|
Arkansas
|
5
|
2,978,204
|
819
|
$30,767
|
Nevada
|
5
|
2,890,845
|
1,958
|
$31,643
|
Oklahoma
|
4
|
3,911,338
|
962
|
$34,556
|
Utah
|
4
|
2,995,919
|
1,613
|
$34,946
|
Wyoming
|
4
|
586,107
|
1,173
|
$41,250
|
New Mexico
|
3
|
2,085,109
|
1,528
|
$31,016
|
North Dakota
|
3
|
756,927
|
995
|
$37,296
|
Louisiana
|
2
|
4,670,724
|
1,071
|
$33,138
|
Mississippi
|
2
|
2,992,333
|
924
|
$33,174
|
Idaho
|
2
|
1,654,930
|
1,908
|
$33,734
|
Vermont
|
2
|
626,042
|
726
|
$28,857
|
Maine
|
1
|
1,329,328
|
877
|
$28,393
|
Rhode Island
|
1
|
1,056,298
|
768
|
$30,483
|
South Dakota
|
1
|
858,469
|
814
|
$30,029
|
Delaware
|
0
|
945,934
|
643
|
$35,060
|
Appendix 1 – Data Set
The states on the left are color coded based on their initial
predicted difficulty of finding that
particular state in Michigan.
Dark Green – Very easy to find
Light Green – Easy to find
Yellow – Moderate
Light Blue – Difficult to find
Dark Blue – Very difficult to find
Appendix 2 – Week by Week Multiple Regressions
Population, Distance, and PCIA - 48 States
|
||||||
Week #
|
Multiple R
|
R Squared
|
Adjusted R Squared
|
Pop t-stat
|
Distance t-stat
|
PCIA t-stat
|
Week 1
|
0.4155
|
0.1726
|
0.1162
|
1.5290
|
-1.9912
|
1.6136
|
Week 1 to 2
|
0.4357
|
0.1898
|
0.1346
|
1.6411
|
-2.1391
|
1.6644
|
Week 1 to 3
|
0.4429
|
0.1961
|
0.1413
|
1.8609
|
-2.0802
|
1.6740
|
Week 1 to 4
|
0.4515
|
0.2038
|
0.1496
|
1.9369
|
-2.1178
|
1.6979
|
Week 1 to 5
|
0.4634
|
0.2147
|
0.1612
|
2.0807
|
-2.1596
|
1.7178
|
Week 1 to 6
|
0.4778
|
0.2283
|
0.1756
|
2.2263
|
-2.1804
|
1.8169
|
Week 1 to 7
|
0.4880
|
0.2381
|
0.1862
|
2.3161
|
-2.1946
|
1.8895
|
Week 1 to 8
|
0.4917
|
0.2417
|
0.1900
|
2.3739
|
-2.1863
|
1.8983
|
Week 1 to 9
|
0.5002
|
0.2502
|
0.1991
|
2.4873
|
-2.2123
|
1.9049
|
Week 1 to 10
|
0.5127
|
0.2628
|
0.2126
|
2.6298
|
-2.2328
|
1.9614
|
Week 1 to 11
|
0.5180
|
0.2683
|
0.2184
|
2.7394
|
-2.2290
|
1.9414
|
Week 1 to 12
|
0.5335
|
0.2847
|
0.2359
|
2.9557
|
-2.2917
|
1.9303
|
Week 1 to 13
|
0.5657
|
0.3200
|
0.2737
|
3.3149
|
-2.3817
|
2.0908
|
Week 1 to 14
|
0.5714
|
0.3265
|
0.2806
|
3.4158
|
-2.4328
|
2.0329
|
Week 1 to 15
|
0.5718
|
0.3270
|
0.2811
|
3.3896
|
-2.4716
|
2.0388
|
Population and Distance - 48 States
|
||||||
Multiple R
|
R Squared
|
Adjusted R Squared
|
Pop t-stat
|
Distance t-stat
|
||
Week 1
|
0.3517
|
0.1237
|
0.0847
|
1.4810
|
-2.1335
|
|
Week 1 to 2
|
0.3726
|
0.1388
|
0.1005
|
1.5870
|
-2.2741
|
|
Week 1 to 3
|
0.3807
|
0.1449
|
0.1069
|
1.8023
|
-2.2118
|
|
Week 1 to 4
|
0.3895
|
0.1517
|
0.1140
|
1.8746
|
-2.2498
|
|
Week 1 to 5
|
0.4026
|
0.1621
|
0.1248
|
2.0139
|
-2.2896
|
|
Week 1 to 6
|
0.4127
|
0.1703
|
0.1335
|
2.1476
|
-2.3040
|
|
Week 1 to 7
|
0.4199
|
0.1763
|
0.1397
|
2.2278
|
-2.3179
|
|
Week 1 to 8
|
0.4238
|
0.1796
|
0.1432
|
2.2830
|
-2.3127
|
|
Week 1 to 9
|
0.4340
|
0.1884
|
0.1523
|
2.3925
|
-2.3380
|
|
Week 1 to 10
|
0.4454
|
0.1984
|
0.1628
|
2.5239
|
-2.3541
|
|
Week 1 to 11
|
0.4534
|
0.2056
|
0.1703
|
2.6327
|
-2.3504
|
|
Week 1 to 12
|
0.4734
|
0.2241
|
0.1896
|
2.8440
|
-2.4098
|
|
Week 1 to 13
|
0.5025
|
0.2525
|
0.2193
|
3.1678
|
-2.4794
|
|
Week 1 to 14
|
0.5131
|
0.2632
|
0.2305
|
3.2740
|
-2.5294
|
|
Week 1 to 15
|
0.5132
|
0.2634
|
0.2306
|
3.2483
|
-2.5710
|
|
Any R Squared or Adjusted R Squared value above .3 is
highlighted in light green.
Any R Squared value or Adjusted R Squared value above .5 is
highlighted in dark green.
t-stat values above 2.0 are highlighted in yellow.
Appendix 2 – Week by Week Multiple Regressions
Population, Distance, and PCIA - 41 States
|
||||||
Multiple R
|
R Squared
|
Adjusted R Squared
|
Pop t-stat
|
Distance t-stat
|
PCIA t-stat
|
|
Week 1
|
0.5611
|
0.3148
|
0.2593
|
3.0486
|
-3.4386
|
1.2281
|
Week 1 to 2
|
0.6469
|
0.4185
|
0.3713
|
3.7635
|
-4.3112
|
1.7090
|
Week 1 to 3
|
0.6304
|
0.3974
|
0.3485
|
4.4025
|
-3.3125
|
1.3144
|
Week 1 to 4
|
0.6153
|
0.3786
|
0.3282
|
4.2697
|
-3.1279
|
1.1317
|
Week 1 to 5
|
0.6275
|
0.3938
|
0.3446
|
4.4651
|
-3.1372
|
1.1251
|
Week 1 to 6
|
0.6667
|
0.4445
|
0.3995
|
4.9560
|
-3.4278
|
1.6655
|
Week 1 to 7
|
0.6645
|
0.4415
|
0.3962
|
4.8018
|
-3.5048
|
2.0201
|
Week 1 to 8
|
0.6627
|
0.4391
|
0.3936
|
4.7413
|
-3.5799
|
1.9039
|
Week 1 to 9
|
0.6811
|
0.4639
|
0.4204
|
4.9227
|
-3.8528
|
2.0201
|
Week 1 to 10
|
0.7224
|
0.5218
|
0.4830
|
5.5131
|
-4.3039
|
2.3970
|
Week 1 to 11
|
0.7396
|
0.5470
|
0.5103
|
5.9781
|
-4.3042
|
2.3476
|
Week 1 to 12
|
0.7791
|
0.6070
|
0.5751
|
6.9515
|
-4.6247
|
2.3242
|
Week 1 to 13
|
0.7912
|
0.6259
|
0.5956
|
7.2742
|
-4.5626
|
2.8965
|
Week 1 to 14
|
0.7881
|
0.6211
|
0.5904
|
7.2539
|
-4.5250
|
2.5337
|
Week 1 to 15
|
0.7878
|
0.6207
|
0.5899
|
7.2041
|
-4.6449
|
2.4512
|
Population and Distance - 41 States
|
||||||
Multiple R
|
R Squared
|
Adjusted R Squared
|
Pop t-stat
|
Distance t-stat
|
||
Week 1
|
0.5356
|
0.2869
|
0.2494
|
2.8458
|
-3.3096
|
|
Week 1 to 2
|
0.6104
|
0.3726
|
0.3395
|
3.4116
|
-4.0496
|
|
Week 1 to 3
|
0.6077
|
0.3693
|
0.3361
|
4.1871
|
-3.1588
|
|
Week 1 to 4
|
0.5976
|
0.3571
|
0.3232
|
4.1128
|
-3.0116
|
|
Week 1 to 5
|
0.6108
|
0.3731
|
0.3401
|
4.3135
|
-3.0216
|
|
Week 1 to 6
|
0.6347
|
0.4029
|
0.3715
|
4.6135
|
-3.1848
|
|
Week 1 to 7
|
0.6164
|
0.3799
|
0.3473
|
4.3197
|
-3.1700
|
|
Week 1 to 8
|
0.6198
|
0.3842
|
0.3517
|
4.3076
|
-3.2779
|
|
Week 1 to 9
|
0.6362
|
0.4047
|
0.3734
|
4.4392
|
-3.5110
|
|
Week 1 to 10
|
0.6690
|
0.4475
|
0.4185
|
4.8474
|
-3.8241
|
|
Week 1 to 11
|
0.6925
|
0.4795
|
0.4521
|
5.3185
|
-3.8400
|
|
Week 1 to 12
|
0.7414
|
0.5496
|
0.5259
|
6.2692
|
-4.1493
|
|
Week 1 to 13
|
0.7356
|
0.5411
|
0.5170
|
6.2509
|
-3.8659
|
|
Week 1 to 14
|
0.7452
|
0.5553
|
0.5319
|
6.4412
|
-3.9602
|
|
Week 1 to 15
|
0.7477
|
0.5591
|
0.5359
|
6.4404
|
-4.1058
|
|
Any R Squared or Adjusted R Squared value above .3 is
highlighted in light green.
Any R Squared value or Adjusted R Squared value above .5 is
highlighted in dark green.
t-stat values above 2.0 are highlighted in yellow.
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