Exploring Regressions on Smith Rock

Smith Rock Regression

I want to look at the difference between weather bins and temperature means in a given month to SmithRock. I am praticularly interested in what your thoughts are of the results in regression 4.

Below are the descriptions of the independent variables.

Most of the variables are of the assumed the correct sign (except for precent change in growth of the county population in Deschutes County, Oregon)

The lag I chose is one month. It is assumed that last months uploads are increasing visitation by providing advertisment. This changes the individuals choice set by exposing users to new areas. This would show a significate increase in the number of visitations in the given month by looking at the participation in a prior month.

(1) Weather Means

The first regression does not contain weather bins.

Independent Variable	Description
tmax.mean	Is the average monthly max temperature in a given month.
tmin.mean	Is the average monthly min temperature in a given month.
tdmean.mean	Is the average monthly dew point of a given month.
AQI.mean	Is the average monthly Air Quality Index for the County in Deschutes County.
RGDI	is a quaterly Real Gross Domestic Income, precent change from quater from the start of January 2002. A linear approximation was used to get monthly values.
Gas_Prices	Is an average of the West Coast (excluding California) prices in a given month.
Pre.Change.Des	Precent change in Deschutes county to account for the growth in the area.

(2) Weather Means with Number of Photos Upload with #SmithRockStatePark

Number of post are lagged one month per Kassahun’s recommendation. There may be some endogenity going on with the number of post uploaded. ## Same Variables with these two new variables

Social Media Interactions	Description
dum2012	A dummy variable to account for the time before Instagram to Interact with the variables colected from Instagram. Instagram variables have NA values prior to the first person who used the hashtag smithrockstatepark. Prior to 2012 = 0 and after 2012 = 1.
iNum.Posts.sum-1	Is a lagged variable by one month of the number of photos uploaded to Instagram with the hashtag #SmithRockStatePark.
iLikes>=1000.sum-1	Is a lagged variable by one month of the number of photos with 1000 likes or more with the hashtag #SmithRockStatePark.

Each one of the previous Social Media measurements are interacted with the dummy variable for 2012.

Interpretation of Social Media Variable

iNum.Post.sum-1 : Visitation increases with every uploaded photo given the hashtag #smithrockstatepark. From this first model it suggest that each individual photo uploaded the previous month increases visitation the next month by roughly 32 vistors.

When there is a Viral photo (a photo with 1,000 likes or more) it increase visitation the next month by 1,395.

(3) Weather Bins: Omitted Temperature Bin 70F-80F (t_70), Omitted Preception Bin days over .3 inches (pptheavy)

Independent Variable	Description
t_100	Days with temperatures equal to or greater than 100F
t_90	Days with temperatures equal to or greater than 90F below 100F
t_80	Days with temperatures equal to or greater than 80F below 90F
t_70	Days with temperatures equal to or greater than 70F below 80F
t_60	Days with temperatures equal to or greater than 60F below 70F
t_50	Days with temperatures equal to or greater than 50F below 60F
t_40	Days with temperatures equal to or greater than 40F below 50F
t_30	Days with temperatures equal to or greater than 30F below 40F
t_20	Days with temperatures equal to or greater than 20F below 30F
t_20Less	Days with temperatures below 20F
pptheavy	Days with rainful over .3 inches aggr. up monthly (excluded from the model).
pptmoderate	Days with rainful equal or over .1 and under .3 inches aggr. up monthly.
pptlight	Days with rainful over 0 and under and under .1 aggr. up monthly.
pptnorain	Days with no rainful aggr. up monthly.
AQI.mean	Is the average monthly Air Quality Index for the County in Deschutes County.
RGDI	is a quaterly Real Gross Domestic Income, precent change from quater from the start of January 2002. A linear approximation was used to get monthly values.
Gas_Prices	Is an average of the West Coast (excluding California) prices in a given month.
Pre.Change.Des	Precent change in Deschutes county to account for the growth in the area.

(4) Weather Bins with #SmithRockStatePark.

Last regression is weather bins with the social media indicator lagged one month.

Social Media Interactions	Description
dum2012	A dummy variable to account for the time before Instagram to Interact with the variables colected from Instagram. Instagram variables have NA values prior to the first person who used the hashtag smithrockstatepark. Prior to 2012 = 0 and after 2012 = 1.
iNum.Posts.sum-1	Is a lagged variable by one month of the number of photos uploaded to Instagram with the hashtag #SmithRockStatePark.
iLikes>=1000.sum-1	Is a lagged variable by one month of the number of photos with 1000 likes or more with the hashtag #SmithRockStatePark.

Each one of the previous Social Media measurements are interacted with the dummy variable for 2012.

Interpretation of Social Media Variable

iNum.Post.sum-1 : Visitation increases with every uploaded photo given the hashtag #smithrockstatepark. From this first model it suggest that each individual photo uploaded the previous month increases visitation the next month by roughly 31 vistors the following month.

When there is a Viral photo (a photo with 1,000 likes or more) it increase visitation the next month by 1,533 the following month.

load("SmithRockmonthly.RData")

library(stargazer, quietly = TRUE)
regmodel <-lm(Visits~tmax.mean+tmin.mean+tdmean.mean+ppt.mean+AQI.mean+Gas_Prices+`Personal Income`+`Unemploy.Oregon`, data=SmithRockmonthly)

regmodel2 <-lm(Visits~tmax.mean+tmin.mean+tdmean.mean+ppt.mean+AQI.mean+Gas_Prices+`Personal Income` +Unemploy.Oregon+dum2012+`iNum.Posts.sum`+`iLikes>=1000.sum-1`, data=SmithRockmonthly)


regmodel3 <-lm(Visits~t_100+t_90+t_80+t_60+t_50+t_40+t_30+t_20+t_less20++pptmoderate+pptlight+pptnorain+Moderate+SensitiveAbove+Gas_Prices+`Personal Income`+`Unemploy.Oregon`, data=SmithRockmonthly)

regmodel4 <-lm(Visits~t_100+t_90+t_80+t_60+t_50+t_40+t_30+t_20+t_less20++pptmoderate+pptlight+pptnorain+Moderate+SensitiveAbove+Gas_Prices+`Personal Income`+`Unemploy.Oregon`+dum2012+`iNum.Posts.sum`+`iLikes>=1000.sum-1`, data=SmithRockmonthly)

regmodel5 <- lm(Visits~t_100+t_90+t_80+t_60+t_50+t_40+t_30+t_20+t_less20+pptmoderate+pptlight+pptnorain+Moderate+SensitiveAbove+Gas_Prices+`Personal Income`+`Unemploy.Oregon`+dum2012+`iNum.Posts.sum-1`+`iLikes>=1000.sum-1`, data=SmithRockmonthly)


stargazer(regmodel, regmodel2, regmodel3, regmodel4, type = 'html')

	Dependent variable:
	Visits
	(1)	(2)	(3)	(4)
tmax.mean	1,891.717***	1,802.857***
	(362.082)	(230.537)
tmin.mean	-3,327.150***	-3,150.138***
	(760.180)	(484.196)
tdmean.mean	1,995.135***	1,788.719***
	(584.339)	(372.056)
ppt.mean	24,534.930	15,296.480
	(63,187.940)	(40,504.680)
AQI.mean	24.235	-76.915*
	(66.511)	(42.525)
t_100			-4,209.563	-1,365.812
			(3,649.181)	(2,272.084)
t_90			9.571	-309.126
			(463.844)	(288.320)
t_80			-419.317	-31.087
			(452.121)	(282.981)
t_60			-100.353	64.397
			(478.252)	(298.497)
t_50			-103.860	-23.027
			(329.104)	(205.729)
t_40			-1,087.046***	-855.127***
			(344.414)	(216.605)
t_30			-1,502.231***	-948.045***
			(451.383)	(281.901)
t_20			-1,233.822	-2,082.868***
			(872.421)	(548.806)
t_less20			-476.397	-704.195
			(1,880.157)	(1,168.054)
pptmoderate			2,405.658**	1,095.101
			(1,201.918)	(749.073)
pptlight			1,152.511	1,041.565*
			(983.129)	(611.211)
pptnorain			1,642.107*	1,180.034**
			(958.734)	(597.309)
Moderate			-345.604	-317.858*
			(293.470)	(183.421)
SensitiveAbove			1,338.926***	-100.712
			(511.757)	(329.908)
Gas_Prices	1,703.260	-683.834	1,891.936	-371.266
	(1,442.716)	(1,042.799)	(1,387.761)	(988.695)
Personal Income	1,119.118	1,034.063	920.609	851.330
	(1,224.725)	(775.877)	(1,157.083)	(719.791)
Unemploy.Oregon	-591.814	528.061	-929.472*	235.899
	(504.086)	(332.947)	(479.945)	(315.228)
dum2012		11,401.430***		10,105.570***
		(1,891.859)		(1,805.546)
iNum.Posts.sum		30.503***		31.301***
		(6.403)		(5.977)
iLikes> =1000.sum-1		911.910		1,030.616*
		(629.634)		(597.691)
Constant	-24,024.490***	-15,661.080***	4,382.537	13,170.990
	(7,992.279)	(5,075.670)	(28,806.070)	(17,962.450)
Observations	193	193	193	193
R2	0.425	0.775	0.517	0.818
Adjusted R2	0.400	0.761	0.470	0.797
Residual Std. Error	13,913.030 (df = 184)	8,780.493 (df = 181)	13,077.900 (df = 175)	8,102.615 (df = 172)
F Statistic	17.003*** (df = 8; 184)	56.592*** (df = 11; 181)	11.012*** (df = 17; 175)	38.579*** (df = 20; 172)
Note:	p<0.1; p<0.05; p<0.01

Smith Summary and Plots Results

Plots not that great because I haven’t figured out how to plot in R yet.

load("SmithRockmonthly.RData")
library(stargazer, quietly = TRUE)
stargazer(SmithRockmonthly, type="text")

##
## ===========================================================================================================
## Statistic              N      Mean       St. Dev.        Min        Pctl(25)      Pctl(75)         Max
## -----------------------------------------------------------------------------------------------------------
## iupload.sr-1          205    371.605      765.999       0.000         0.000        235.000      3,642.000
## ilike1000sr-1         205     3.702        8.843        0.000         0.000         0.000        63.000
## upload.sr             92    1,065.000     922.927       1.000        225.750      1,782.500     3,642.000
## likes1000sr           92     10.902       11.747        0.000         0.000        17.250        63.000
## like.sr               92   113,253.100  114,061.300    112.000      6,494.250    193,240.000   437,496.000
## commentsr             92    3,721.739    3,567.177      9.000        445.750      6,038.000    13,786.000
## 7wonder.sr            92      6.978        8.261        0.000         0.000        11.000        31.000
## TraOre.sr             92     49.076       42.137        0.000         2.000        78.250        156.000
## upload.srsp           82     262.427      272.999       1.000        21.000        424.000      1,162.000
## sumlikes1000srsp      82      2.354        2.664        0.000         0.000         3.750        12.000
## sumlike.srsp          82   27,281.710   28,808.210     10.000        819.000     41,106.250    112,075.000
## sumlikes500srsp       82      5.122        5.855        0.000         0.000         8.000        22.000
## 7wonder.srsp          82      2.098        2.827        0.000         0.000         3.750        12.000
## TraOre.srsp           82     17.012       16.353        0.000         0.000        28.000        62.000
## Personal Income       199     1.126        0.967       -2.500         0.733         1.600         4.200
## Value                 204     7.032        2.137        3.800         5.300         8.500        11.900
## Net.Unempl.Oregon     204    -0.018        0.171       -0.300        -0.100         0.000         0.900
## Unemploy.Oregon       204    -0.294        2.281       -4.300        -1.600         0.000        10.500
## Moderate              199     2.995        3.624        0.000         0.000         5.000        16.000
## Very.Hazardous        199     0.080        0.646        0.000         0.000         0.000         7.000
## Sens.Unhealthy        199     0.276        1.410        0.000         0.000         0.000        12.000
## ModerateBelow         199    29.121        4.434        5.000        30.000        31.000        31.000
## SensitiveAbove        199     0.357        1.943        0.000         0.000         0.000        17.000
## AQIGood               199    26.126        5.674        2.000        25.000        30.000        31.000
## AQIModerate           199     2.995        3.624        0.000         0.000         5.000        16.000
## AQIUnhealthySen.Group 199     0.111        0.548        0.000         0.000         0.000         6.000
## AQIUnhealthy          199     0.166        1.086        0.000         0.000         0.000        11.000
## AQIVeryUnhealthy      199     0.030        0.244        0.000         0.000         0.000         3.000
## AQIHazardous          199     0.050        0.423        0.000         0.000         0.000         4.000
## iLikes> =1000.sum-6   200     0.810        1.874        0.000         0.000         0.000        12.000
## iLikes> =1000.sum-5   201     0.826        1.883        0.000         0.000         0.000        12.000
## iLikes> =1000.sum-4   202     0.847        1.901        0.000         0.000         0.000        12.000
## iLikes> =1000.sum-3   203     0.852        1.898        0.000         0.000         0.000        12.000
## iLikes> =1000.sum-2   204     0.892        1.977        0.000         0.000         0.000        12.000
## iLikes> =1000.sum-1   205     0.888        1.973        0.000         0.000         0.000        12.000
## iLikes> =500.sum-1    205     1.937        4.347        0.000         0.000         1.000        22.000
## iLikes> =500.sum-5    201     1.736        4.007        0.000         0.000         0.000        22.000
## iLikes> =500.sum-6    200     1.660        3.868        0.000         0.000         0.000        22.000
## iLikes.sum-6          200   8,958.210   19,499.970      0.000         0.000       1,550.000    99,949.000
## iLikes.sum-5          201   9,253.741   19,897.300      0.000         0.000       1,844.000    99,949.000
## iLikes.sum-4          202   9,762.757   21,125.120      0.000         0.000       2,146.250    112,075.000
## iLikes.sum-3          203  10,143.040   21,758.190      0.000         0.000       2,264.000    112,075.000
## iLikes.sum-2          204  10,489.340   22,260.970      0.000         0.000       2,303.500    112,075.000
## iLikes.sum-1          205  10,438.180   22,218.420      0.000         0.000       2,281.000    112,075.000
## Deschutes Annual pop. 193  155,462.100  17,596.520   122,794.000   143,316.000   166,400.000   188,980.000
## OregonAnnualPop       193 3,831,811.000 187,407.700 3,500,000.000 3,690,000.000 3,960,000.000 4,195,300.000
## Per.Change.Des        193     2.720        1.475        0.332         1.489         3.521         5.698
## Per.Change.Oregon     193     1.125        0.347        0.262         0.945         1.405         1.750
## t_100                 204     0.044        0.268        0.000         0.000         0.000         2.000
## t_90                  204     1.662        3.477        0.000         0.000         1.000        15.000
## t_80                  204     4.132        6.035        0.000         0.000         7.250        27.000
## t_70                  204     4.245        4.751        0.000         0.000         7.000        18.000
## t_60                  204     4.745        4.603        0.000         1.000         8.000        19.000
## t_50                  204     6.343        5.276        0.000         1.000        11.000        21.000
## t_40                  204     6.196        6.638        0.000         0.000        12.000        26.000
## t_30                  204     2.358        3.956        0.000         0.000         3.000        17.000
## t_20                  204     0.578        1.498        0.000         0.000         0.000         8.000
## t_less20              204     0.132        0.610        0.000         0.000         0.000         5.000
## pptheavy              204     0.578        0.870        0.000         0.000         1.000         4.000
## pptmoderate           204     2.074        1.935        0.000         1.000         3.000         9.000
## pptlight              204     5.588        3.809        0.000         3.000         8.000        18.000
## pptnorain             204    22.196        5.299        7.000        19.000        26.000        31.000
## Likes.sum             82   27,281.710   28,808.210     10.000        819.000     41,106.250    112,075.000
## Comments.sum          82     907.915      995.696       1.000        67.000       1,373.500     4,081.000
## Likes> =1000.sum      82      2.354        2.664        0.000         0.000         3.750        12.000
## Likes> =500.sum       82      5.122        5.855        0.000         0.000         8.000        22.000
## Num.Posts.sum         82     262.427      272.999       1.000        21.000        424.000      1,162.000
## Visits                202  45,058.670   18,221.770   12,196.000    30,605.000    52,830.000    92,320.000
## Month                 202     6.455        3.447        1.000         3.250         9.000        12.000
## AQI.mean              199    29.625       17.127       11.065        18.887        36.524        157.267
## PM2.5.sum             199    23.608       10.684        0.000        21.000        31.000        31.000
## CO.sum                199     0.980        4.000        0.000         0.000         0.000        26.000
## OZONE.sum             199     4.653       10.155        0.000         0.000         0.000        31.000
## PM10.sum              199     0.236        0.611        0.000         0.000         0.000         4.000
## ppt.mean              204     0.027        0.022        0.000         0.011         0.040         0.115
## tmin.mean             204    35.609        9.402       15.952        27.917        43.860        53.616
## tmean.mean            204    48.446       12.375       24.410        37.417        59.224        70.942
## tmax.mean             204    61.283       15.500       32.868        46.892        74.547        89.129
## tdmean.mean           204    31.669        6.531       16.429        26.905        37.046        44.894
## Gas_Prices            205     2.792        0.736        1.186         2.312         3.332         4.234
## dum2012               205     0.405        0.492        0.000         0.000         1.000         1.000
## RGDI                  199     1.969        1.931       -4.300         1.067         3.467         4.900
## iNum.Posts.sum        205    100.590      212.401       0.000         0.000        58.000       1,162.000
## iLikes.sum            205  10,438.180   22,218.420      0.000         0.000       2,281.000    112,075.000
## iLikes> =500.sum      205     1.937        4.347        0.000         0.000         1.000        22.000
## iLikes> =1000.sum     205     0.888        1.973        0.000         0.000         0.000        12.000
## iNum.Posts.sum-1      205    100.590      212.401       0.000         0.000        58.000       1,162.000
## Prior7wonders         205     0.215        0.412        0.000         0.000         0.000         1.000
## i7wonder.srsp         205     0.839        2.058        0.000         0.000         0.000        12.000
## iupload.sr            206    369.801      764.567         0             0           225.8         3,642
## dum201104             206     0.345        0.476          0             0             1             1
## ilike1000sr           206     3.684        8.825          0             0             0            63
## iwondersr             206     2.913        6.496          0             0             0            31
## iTraOresr             206    18.743       36.536          0             0             0            156
## ilikes1000sr-1        206     3.684        8.825          0             0             0            63
## unYear                202   2,009.965      4.902      2,002.000     2,006.000     2,014.000     2,018.000
## -----------------------------------------------------------------------------------------------------------

plot(SmithRockmonthly$Year, SmithRockmonthly$Num.Posts.sum)

plot(SmithRockmonthly$Year, SmithRockmonthly$`Likes>=500.sum`)

plot(SmithRockmonthly$Year, SmithRockmonthly$`Deschutes Annual pop.`)

plot(SmithRockmonthly$Month, SmithRockmonthly$Visits)