Fall 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
I did this type of study in Summer 2016 and Summer
2015. This is the first time I did this
type of study during the Fall.
Methodology
Timing –
I began on Wednesday, September 7, and went through Tuesday,
January 3 (After Labor Day weekend to after New Year). 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. This study was for 17
weeks. The Summer 2016 report was for 15
weeks.
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 17 weeks, I traveled, 7,854 miles miles within
Michigan (Summer 2016 was 7,023 miles).
I logged 794 out of state license plates (Summer 2016 was 1,031 license
plates). So, the Fall 2016 study was for
2 weeks longer, I traveled 800+ more miles, and I saw 237 fewer license plates.
The top 5 were:
Fall 2016 Summer
2016
Illinois – 118 Illinois
-195
Ohio – 96 Ohio
- 123
Indiana – 67 Indiana
- 115
Florida – 66 Florida
- 88
Texas – 42 Texas
- 38
These 5 states made up just a little over 50% of my
sightings.
The states that I saw the fewest of:
Utah – 1
New Hampshire - 1
Delaware – 1
Rhode Island – 1
North Dakota – 1
Hawaii – 1
West Virginia - 0
As compared to -
Summer 2016 bottom 5:
Maine -1
Rhode Island -1
South Dakota - 1
Hawaii - 1
Delaware - 0
Other interesting
information:
License Plate count by week –
|
Week Number
|
Mileage
|
Observations that week
|
Week Start Date
|
|
Week 1
|
531
|
39
|
Wednesday, September 07, 2016
|
|
Week 2
|
343
|
44
|
Wednesday, September 14, 2016
|
|
Week 3
|
425
|
34
|
Wednesday, September 21, 2016
|
|
Week 4
|
509
|
63
|
Wednesday, September 28, 2016
|
|
Week 5
|
508
|
55
|
Wednesday, October 05, 2016
|
|
Week 6
|
478
|
45
|
Wednesday, October 12, 2016
|
|
Week 7
|
523
|
46
|
Wednesday, October 19, 2016
|
|
Week 8
|
508
|
31
|
Wednesday, October 26, 2016
|
|
Week 9
|
514
|
59
|
Wednesday, November 02, 2016
|
|
Week 10
|
624
|
90
|
Wednesday, November 09, 2016
|
|
Week 11
|
385
|
42
|
Wednesday, November 16, 2016
|
|
Week 12
|
443
|
84
|
Wednesday, November 23, 2016
|
|
Week 13
|
441
|
36
|
Wednesday, November 30, 2016
|
|
Week 14
|
355
|
26
|
Wednesday, December 07, 2016
|
|
Week 15
|
398
|
9
|
Wednesday, December 14, 2016
|
|
Week 16
|
467
|
39
|
Wednesday, December 21, 2016
|
|
Week 17
|
402
|
52
|
Wednesday, December 28, 2016
|
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: 50%
correlation
Distance: 30% inverse
correlation
Per Capita Income (PCI):
0% correlation
Per Capita Income Adjusted (PCIA): 26% 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: .646
R Squared: .418
Adjusted R Squared: .378
Pop t-stat: 4.55
Distance t-stat: -2.67
PCIA t-stat: 2.09
This looks at 48 states for the 3 variables – Population,
Distance, and PCIA. The Adjusted R
Squared value is above .3, and all three variables are significant.
Population and Distance without Hawaii – 48 states
Multiple R: .600
R Squared: .360
Adjusted R Squared:
.331
Population t-stat:
4.366
Distance t-stat:
-2.78
This looks at 48 states with only two variables –
Population and Distance.
The Adjusted R-squared value is above .3, and the two
variables are significant.
Residuals
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, 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 (42 states)
Multiple R: .846
R Squared: .716
Adjusted R Squared:
.693
Population t-stat:
9.501
Distance t-stat:
-4.237
PCIA – 2.194
Here we see a huge jump in the Multiple R values and the
R Squared values. There is an Adjusted R
Squared value of .693. 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 9.5 indicates that this is the most important factor, with
Distance next, and the PCIA income variable contributing to the prediction.
Population and Distance with 42 states:
Multiple R: .824
R Square: .680
Adjusted R: .663
Population t-stat:
8.93
Distance t-stat:
-3.88
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 Review:
Let’s get back to those residuals – Illinois, Indiana,
Ohio, Florida, 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
66 sightings – Florida was almost tied with Indiana at 67!
In my Summer 2016 report, I thought that the large
sightings of Florida license plates was due to the fact that they were
snowbirds. They might be snowbirds but
they haven’t all left. The number of
Florida plates seen could be just a factor of their population. As with these studies the most frequently
seen license plates are either very close to Michigan or one of the more
populated states – California, New York, Texas, and Florida.
Alaska – I saw 3 Alaskan license plates. Last summer I saw 9. Three license plates from Alaska though was
enough to through the regression off-balance still and have it registered as a
residual.
Oregon – this showed up as a residual - again. So, let’s take a look at the data. I saw 6 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 42 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……Alabama17; Alaska1, Alaska2, Alaska3……Alaska17. So, there are 48 states over 17 weeks which
yields a sample size of 816.
The first regression for all 816 States per Week:
Multiple R 0.446
R Square 0.199
Adjusted R Square 0.196
Population t-stat 11.479
Distance t-stat -6.784
PCIA t-stat 5.462
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 814 States per Week:
Multiple R 0.521
R Square 0.271
Adjusted R Square 0.269
Population 14.994
Distance t-stat -7.374
PCIA t-stat 5.759
In this regression, I took out only 4 residuals –
Illinois10, Ohio10, Illinois12, and Indiana 12.
The number of sightings for these states was higher than normal.
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
= 94%
correlation
Population*Income
Adjusted/Distance = 93% correlation
Population*Income
Adjusted = 55% correlation
For the Population, Distance, Income composite variable
(PDI), I ran some more multiple regressions.
PDI
Multiple R 0.940
R Square 0.894
Adjusted R Square 0.881
PDI t-stat 18.76
So, this is showing the Multiple R value at .94 with the
R Square and Adjusted R Square values very close together at .8941 and .881
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 0.982
R Square 0.964
Adjusted R Square 0.963
PDI t-stat 34.57
A Multiple R value of .982!!
The R Square and Adjusted R Square values are extremely
close with .964 and .963 respectively.
The t-stat value is 34.57 – 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
The findings from this study are extremely similar to the
findings from the Summer report. The
population variable in this study is showing as being more significant than it
was in the Summer report. The income
variable continues to remain significant as well.
|
Sources –
|
|
|
Appendix 1 – Data Set
|
State
|
Observations
|
Population
|
Distance
|
PCIA
|
|
Illinois
|
118
|
12,859,995
|
201
|
$37,223
|
|
Ohio
|
96
|
11,613,423
|
234
|
$37,080
|
|
Indiana
|
67
|
6,619,680
|
251
|
$36,164
|
|
Florida
|
66
|
20,271,272
|
1,432
|
$31,652
|
|
Texas
|
42
|
27,469,114
|
1,135
|
$37,311
|
|
New York
|
33
|
19,795,791
|
677
|
$28,948
|
|
Wisconsin
|
28
|
5,771,337
|
315
|
$33,853
|
|
Georgia
|
26
|
10,214,860
|
768
|
$34,476
|
|
California
|
23
|
39,144,818
|
2,230
|
$28,651
|
|
Tennessee
|
22
|
6,600,299
|
543
|
$35,238
|
|
Kentucky
|
21
|
4,425,092
|
367
|
$34,054
|
|
Pennsylvania
|
20
|
12,802,503
|
657
|
$34,020
|
|
North Carolina
|
17
|
10,042,802
|
679
|
$32,564
|
|
Virginia
|
17
|
8,382,993
|
792
|
$38,351
|
|
Minnesota
|
17
|
5,489,594
|
631
|
$36,017
|
|
Massachusetts
|
12
|
6,794,422
|
786
|
$33,171
|
|
Colorado
|
12
|
5,456,574
|
1,190
|
$36,314
|
|
Arizona
|
12
|
6,828,065
|
1,939
|
$34,179
|
|
New Jersey
|
11
|
8,958,013
|
669
|
$32,269
|
|
Maryland
|
11
|
6,006,401
|
582
|
$32,968
|
|
Missouri
|
9
|
6,083,672
|
482
|
$34,538
|
|
Alabama
|
9
|
4,858,979
|
754
|
$33,273
|
|
Connecticut
|
9
|
3,590,886
|
717
|
$31,744
|
|
Arkansas
|
9
|
2,978,204
|
836
|
$30,767
|
|
Iowa
|
8
|
3,123,899
|
537
|
$34,739
|
|
Louisiana
|
8
|
4,670,724
|
1,065
|
$33,138
|
|
South Carolina
|
7
|
4,896,146
|
715
|
$30,345
|
|
Oklahoma
|
6
|
3,911,338
|
972
|
$34,556
|
|
Washington
|
6
|
7,170,351
|
2,269
|
$39,802
|
|
Nebraska
|
6
|
1,896,190
|
678
|
$35,075
|
|
Oregon
|
6
|
4,028,977
|
2,328
|
$26,238
|
|
Maine
|
5
|
1,329,328
|
919
|
$28,393
|
|
Mississippi
|
4
|
2,992,333
|
927
|
$33,174
|
|
Kansas
|
3
|
2,911,641
|
671
|
$35,682
|
|
Nevada
|
3
|
2,890,845
|
1,885
|
$31,643
|
|
New Mexico
|
3
|
2,085,109
|
1,490
|
$31,016
|
|
South Dakota
|
3
|
858,469
|
797
|
$30,029
|
|
Montana
|
3
|
1,032,949
|
1,681
|
$29,522
|
|
Alaska
|
3
|
738,432
|
3,792
|
$34,772
|
|
Idaho
|
2
|
1,654,930
|
1,911
|
$33,734
|
|
Vermont
|
2
|
626,042
|
721
|
$28,857
|
|
Wyoming
|
2
|
586,107
|
1,168
|
$41,250
|
|
Utah
|
1
|
2,995,919
|
1,608
|
$34,946
|
|
New Hampshire
|
1
|
1,330,608
|
812
|
$31,540
|
|
Delaware
|
1
|
945,934
|
644
|
$35,060
|
|
Rhode Island
|
1
|
1,056,298
|
774
|
$30,483
|
|
North Dakota
|
1
|
756,927
|
865
|
$37,296
|
|
West Virginia
|
0
|
1,844,128
|
387
|
$28,066
|
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
|
0.68999
|
0.47609
|
0.44037
|
5.67576
|
-2.27366
|
1.95812
|
|
Week 1 to 2
|
0.67033
|
0.44935
|
0.41180
|
5.46024
|
-1.92134
|
1.84606
|
|
Week 1 to 3
|
0.67939
|
0.46157
|
0.42486
|
5.37286
|
-2.52214
|
1.91417
|
|
Week 1 to 4
|
0.66125
|
0.43725
|
0.39888
|
5.16111
|
-2.26594
|
1.85274
|
|
Week 1 to 5
|
0.65906
|
0.43435
|
0.39579
|
4.93319
|
-2.48533
|
2.06433
|
|
Week 1 to 6
|
0.64544
|
0.41659
|
0.37681
|
4.75895
|
-2.41012
|
1.97090
|
|
Week 1 to 7
|
0.63701
|
0.40578
|
0.36527
|
4.65614
|
-2.36140
|
1.92011
|
|
Week 1 to 8
|
0.64487
|
0.41585
|
0.37602
|
4.78044
|
-2.42528
|
1.84001
|
|
Week 1 to 9
|
0.64995
|
0.42243
|
0.38305
|
4.84050
|
-2.53545
|
1.78507
|
|
Week 1 to 10
|
0.63939
|
0.40882
|
0.36852
|
4.59768
|
-2.57547
|
1.84526
|
|
Week 1 to 11
|
0.64953
|
0.42189
|
0.38247
|
4.71575
|
-2.66636
|
1.88675
|
|
Week 1 to 12
|
0.62235
|
0.38731
|
0.34554
|
4.23044
|
-2.57122
|
1.96579
|
|
Week 1 to 13
|
0.62797
|
0.39434
|
0.35305
|
4.29445
|
-2.58309
|
2.02354
|
|
Week 1 to 14
|
0.62702
|
0.39316
|
0.35178
|
4.28894
|
-2.56872
|
2.02010
|
|
Week 1 to 15
|
0.63238
|
0.39990
|
0.35898
|
4.36887
|
-2.57404
|
2.04862
|
|
Week 1 to 16
|
0.63466
|
0.40279
|
0.36207
|
4.39208
|
-2.56959
|
2.08604
|
|
Week 1 to 17
|
0.64664
|
0.41814
|
0.37847
|
4.55733
|
-2.66650
|
2.09562
|
|
Population and Distance -
48 States
|
||||||
|
Multiple R
|
R Squared
|
Adjusted R Squared
|
Pop t-stat
|
Distance t-stat
|
||
|
Week 1
|
0.65607
|
0.43043
|
0.40512
|
5.47722
|
-2.36921
|
|
|
Week 1 to 2
|
0.63773
|
0.40670
|
0.38033
|
5.29341
|
-2.02957
|
|
|
Week 1 to 3
|
0.64555
|
0.41674
|
0.39081
|
5.19346
|
-2.61804
|
|
|
Week 1 to 4
|
0.62718
|
0.39335
|
0.36639
|
5.00058
|
-2.36828
|
|
|
Week 1 to 5
|
0.61609
|
0.37957
|
0.35200
|
4.73427
|
-2.57466
|
|
|
Week 1 to 6
|
0.60422
|
0.36508
|
0.33686
|
4.58534
|
-2.50474
|
|
|
Week 1 to 7
|
0.59665
|
0.35599
|
0.32737
|
4.49553
|
-2.45599
|
|
|
Week 1 to 8
|
0.60902
|
0.37090
|
0.34294
|
4.63216
|
-2.53486
|
|
|
Week 1 to 9
|
0.61693
|
0.38061
|
0.35308
|
4.70141
|
-2.64288
|
|
|
Week 1 to 10
|
0.60256
|
0.36308
|
0.33477
|
4.45308
|
-2.68279
|
|
|
Week 1 to 11
|
0.61247
|
0.37512
|
0.34735
|
4.56006
|
-2.77042
|
|
|
Week 1 to 12
|
0.57750
|
0.33350
|
0.30388
|
4.07548
|
-2.69390
|
|
|
Week 1 to 13
|
0.58136
|
0.33798
|
0.30855
|
4.12681
|
-2.70414
|
|
|
Week 1 to 14
|
0.58041
|
0.33687
|
0.30740
|
4.12190
|
-2.68754
|
|
|
Week 1 to 15
|
0.58537
|
0.34266
|
0.31344
|
4.19374
|
-2.69176
|
|
|
Week 1 to 16
|
0.58628
|
0.34373
|
0.31456
|
4.20911
|
-2.68970
|
|
|
Week 1 to 17
|
0.60006
|
0.36007
|
0.33162
|
4.36644
|
-2.78088
|
|
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 - 42 States
|
||||||
|
Multiple R
|
R Squared
|
Adjusted R Squared
|
Pop t-stat
|
Distance t-stat
|
PCIA t-stat
|
|
|
Week 1
|
0.68718
|
0.47222
|
0.43055
|
5.79623
|
-1.73763
|
1.07487
|
|
Week 1 to 2
|
0.73197
|
0.53578
|
0.49913
|
6.56111
|
-1.67403
|
1.43147
|
|
Week 1 to 3
|
0.72894
|
0.53136
|
0.49436
|
6.43210
|
-2.58248
|
1.47521
|
|
Week 1 to 4
|
0.77621
|
0.60250
|
0.57112
|
7.50473
|
-2.72679
|
1.42596
|
|
Week 1 to 5
|
0.78942
|
0.62318
|
0.59343
|
7.80785
|
-2.95929
|
1.66834
|
|
Week 1 to 6
|
0.81361
|
0.66197
|
0.63528
|
8.47994
|
-3.43116
|
1.69654
|
|
Week 1 to 7
|
0.79663
|
0.63462
|
0.60578
|
7.95959
|
-3.30987
|
1.71070
|
|
Week 1 to 8
|
0.82210
|
0.67585
|
0.65026
|
8.78506
|
-3.41517
|
1.35390
|
|
Week 1 to 9
|
0.83261
|
0.69324
|
0.66902
|
9.12391
|
-3.75422
|
1.20163
|
|
Week 1 to 10
|
0.85143
|
0.72493
|
0.70321
|
9.84039
|
-4.10730
|
1.32752
|
|
Week 1 to 11
|
0.84286
|
0.71041
|
0.68755
|
9.44856
|
-4.13941
|
1.45965
|
|
Week 1 to 12
|
0.83715
|
0.70082
|
0.67721
|
9.26433
|
-3.85128
|
1.60339
|
|
Week 1 to 13
|
0.84240
|
0.70963
|
0.68671
|
9.43714
|
-3.98507
|
1.79387
|
|
Week 1 to 14
|
0.84546
|
0.71480
|
0.69228
|
9.52883
|
-4.11162
|
1.93786
|
|
Week 1 to 15
|
0.85498
|
0.73099
|
0.70975
|
9.92849
|
-4.20511
|
2.08147
|
|
Week 1 to 16
|
0.85164
|
0.72530
|
0.70361
|
9.75148
|
-4.16976
|
2.27066
|
|
Week 1 to 17
|
0.84617
|
0.71601
|
0.69359
|
9.50113
|
-4.23776
|
2.19424
|
|
Population and Distance -
42 States
|
||||||
|
Multiple R
|
R Square
|
Adjusted R Squared
|
Pop t-stat
|
Distance t-stat
|
||
|
Week 1
|
0.67540
|
0.45617
|
0.42828
|
5.71555
|
-1.62652
|
|
|
Week 1 to 2
|
0.71466
|
0.51074
|
0.48565
|
6.38034
|
-1.50978
|
|
|
Week 1 to 3
|
0.71029
|
0.50452
|
0.47911
|
6.23903
|
-2.40276
|
|
|
Week 1 to 4
|
0.76239
|
0.58123
|
0.55976
|
7.31647
|
-2.55536
|
|
|
Week 1 to 5
|
0.77174
|
0.59558
|
0.57484
|
7.52600
|
-2.73155
|
|
|
Week 1 to 6
|
0.79772
|
0.63636
|
0.61772
|
8.17377
|
-3.18926
|
|
|
Week 1 to 7
|
0.77877
|
0.60649
|
0.58630
|
7.65796
|
-3.06567
|
|
|
Week 1 to 8
|
0.81254
|
0.66022
|
0.64279
|
8.61424
|
-3.26624
|
|
|
Week 1 to 9
|
0.82558
|
0.68158
|
0.66525
|
9.00649
|
-3.63555
|
|
|
Week 1 to 10
|
0.84390
|
0.71217
|
0.69741
|
9.67253
|
-3.96155
|
|
|
Week 1 to 11
|
0.83317
|
0.69417
|
0.67849
|
9.23036
|
-3.96253
|
|
|
Week 1 to 12
|
0.82498
|
0.68058
|
0.66420
|
8.99015
|
-3.65925
|
|
|
Week 1 to 13
|
0.82767
|
0.68504
|
0.66889
|
9.07379
|
-3.74530
|
|
|
Week 1 to 14
|
0.82862
|
0.68661
|
0.67054
|
9.09295
|
-3.82913
|
|
|
Week 1 to 15
|
0.83685
|
0.70032
|
0.68495
|
9.40487
|
-3.88083
|
|
|
Week 1 to 16
|
0.82947
|
0.68803
|
0.67203
|
9.13271
|
-3.79754
|
|
|
Week 1 to 17
|
0.82464
|
0.68003
|
0.66362
|
8.93431
|
-3.88058
|
|
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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