Ridge Regression
Unsa Jamil
7/1/2021
Loading Libraries
library(caret)
library(glmnet)
library(mlbench)
library(psych)
library(markovchain)Reading Data
weatherData <- read.csv("weather_data.csv",header = TRUE)View Data
dim(weatherData)## [1] 4032 15colnames(weatherData)## [1] "country_region_code"
## [2] "country_region"
## [3] "sub_region_1"
## [4] "sub_region_2"
## [5] "metro_area"
## [6] "iso_3166_2_code"
## [7] "census_fips_code"
## [8] "place_id"
## [9] "date"
## [10] "retail_and_recreation_percent_change_from_baseline"
## [11] "grocery_and_pharmacy_percent_change_from_baseline"
## [12] "parks_percent_change_from_baseline"
## [13] "transit_stations_percent_change_from_baseline"
## [14] "workplaces_percent_change_from_baseline"
## [15] "residential_percent_change_from_baseline"Check Null Values
table(is.na(weatherData$residential_percent_change_from_baseline))##
## FALSE TRUE
## 3648 384Replace Null Values With Mean and in categorical data we will replace null values with “Not Available”
weatherData$sub_region_2[is.na(weatherData$sub_region_2)] <- "Not Available"
weatherData$census_fips_code[is.na(weatherData$census_fips_code)] <- "Not Available"
weatherData$retail_and_recreation_percent_change_from_baseline[is.na(weatherData$retail_and_recreation_percent_change_from_baseline)] <- mean(weatherData$retail_and_recreation_percent_change_from_baseline, na.rm = TRUE)
weatherData$grocery_and_pharmacy_percent_change_from_baseline[is.na(weatherData$grocery_and_pharmacy_percent_change_from_baseline)] <- mean(weatherData$grocery_and_pharmacy_percent_change_from_baseline, na.rm = TRUE)
weatherData$transit_stations_percent_change_from_baseline[is.na(weatherData$transit_stations_percent_change_from_baseline)] <- mean(weatherData$transit_stations_percent_change_from_baseline, na.rm = TRUE)
weatherData$residential_percent_change_from_baseline[is.na(weatherData$residential_percent_change_from_baseline)] <- mean(weatherData$residential_percent_change_from_baseline, na.rm = TRUE)Change Column Names
colnames(weatherData) <- c("Region_Code", "Region", "Sub_Region_1","Sub_Region_2","Metro_rea","ISO_Code","Census_Code","Place_Id","Date",
"Retail_And_Recreation_Percent","Grocery_And_Pharmacy_Percent","Parks_Percent","Transit_Stations_Percent","Workplace_Percent","Residential_Percent")
colnames(weatherData)## [1] "Region_Code" "Region"
## [3] "Sub_Region_1" "Sub_Region_2"
## [5] "Metro_rea" "ISO_Code"
## [7] "Census_Code" "Place_Id"
## [9] "Date" "Retail_And_Recreation_Percent"
## [11] "Grocery_And_Pharmacy_Percent" "Parks_Percent"
## [13] "Transit_Stations_Percent" "Workplace_Percent"
## [15] "Residential_Percent"head(weatherData)## Region_Code Region Sub_Region_1 Sub_Region_2 Metro_rea ISO_Code
## 1 PK Pakistan Not Available
## 2 PK Pakistan Not Available
## 3 PK Pakistan Not Available
## 4 PK Pakistan Not Available
## 5 PK Pakistan Not Available
## 6 PK Pakistan Not Available
## Census_Code Place_Id Date
## 1 Not Available ChIJH3X9-NJS2zgRXJIU5veht0Y 2021-01-01
## 2 Not Available ChIJH3X9-NJS2zgRXJIU5veht0Y 2021-01-02
## 3 Not Available ChIJH3X9-NJS2zgRXJIU5veht0Y 2021-01-03
## 4 Not Available ChIJH3X9-NJS2zgRXJIU5veht0Y 2021-01-04
## 5 Not Available ChIJH3X9-NJS2zgRXJIU5veht0Y 2021-01-05
## 6 Not Available ChIJH3X9-NJS2zgRXJIU5veht0Y 2021-01-06
## Retail_And_Recreation_Percent Grocery_And_Pharmacy_Percent Parks_Percent
## 1 1 22 13
## 2 -4 23 7
## 3 1 23 13
## 4 9 34 14
## 5 -6 14 0
## 6 5 29 11
## Transit_Stations_Percent Workplace_Percent Residential_Percent
## 1 17 -12 7
## 2 19 2 6
## 3 22 10 4
## 4 26 -3 5
## 5 11 -7 7
## 6 22 -3 5Pull Out Spring Dates Only
spring <- weatherData[1:2000,]States
- Partly Cloudy
- Cloudy
- Clear
** Add the states to the dataset
spring$rain <- ifelse(spring$Transit_Stations_Percent > 0,1,0)
spring$rain## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [35] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [69] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [103] 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1
## [137] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [171] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [205] 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1
## [239] 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
## [273] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0
## [307] 0 1 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
## [341] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [375] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1
## [409] 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [443] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [477] 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1
## [511] 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [545] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [579] 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [613] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [647] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
## [681] 1 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1
## [715] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [749] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0
## [783] 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1
## [817] 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0
## [851] 1 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
## [885] 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1
## [919] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [953] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [987] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1021] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1055] 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1
## [1089] 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1123] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1157] 0 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1
## [1191] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1225] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 0 0 0
## [1259] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1
## [1293] 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1327] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0
## [1361] 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1395] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1429] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1
## [1463] 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1497] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1531] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1565] 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1599] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1
## [1633] 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0
## [1667] 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1701] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1735] 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1769] 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1803] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0
## [1837] 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1
## [1871] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1905] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1939] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1973] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1spring$markov_states <- ifelse(spring$rain == 1 & spring$rain < 32, "Cloudy", ifelse(spring$rain == 0 & spring$rain < 32 , "Clear","Partly Cloudy"))
spring$markov_states## [1] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [8] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [15] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [22] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [29] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [36] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [43] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [50] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [57] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [64] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [71] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [78] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [85] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [92] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [99] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear"
## [106] "Clear" "Clear" "Clear" "Clear" "Cloudy" "Cloudy" "Cloudy"
## [113] "Clear" "Clear" "Clear" "Cloudy" "Cloudy" "Clear" "Clear"
## [120] "Clear" "Clear" "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [127] "Cloudy" "Clear" "Clear" "Clear" "Clear" "Clear" "Cloudy"
## [134] "Clear" "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [141] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [148] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [155] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [162] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [169] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [176] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [183] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [190] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [197] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [204] "Cloudy" "Cloudy" "Cloudy" "Clear" "Cloudy" "Cloudy" "Cloudy"
## [211] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [218] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [225] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [232] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Cloudy"
## [239] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Cloudy"
## [246] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [253] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [260] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [267] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Cloudy"
## [274] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [281] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [288] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [295] "Cloudy" "Clear" "Clear" "Clear" "Clear" "Clear" "Cloudy"
## [302] "Cloudy" "Cloudy" "Clear" "Clear" "Clear" "Clear" "Cloudy"
## [309] "Cloudy" "Clear" "Cloudy" "Clear" "Clear" "Clear" "Cloudy"
## [316] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear" "Clear"
## [323] "Clear" "Clear" "Clear" "Clear" "Clear" "Cloudy" "Cloudy"
## [330] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [337] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [344] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [351] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [358] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [365] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [372] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [379] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [386] "Cloudy" "Cloudy" "Cloudy" "Clear" "Cloudy" "Cloudy" "Cloudy"
## [393] "Cloudy" "Clear" "Cloudy" "Cloudy" "Clear" "Cloudy" "Clear"
## [400] "Clear" "Clear" "Clear" "Clear" "Clear" "Cloudy" "Clear"
## [407] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [414] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear"
## [421] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [428] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [435] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [442] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [449] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [456] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [463] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [470] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [477] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [484] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear" "Clear"
## [491] "Clear" "Clear" "Cloudy" "Clear" "Cloudy" "Cloudy" "Clear"
## [498] "Clear" "Clear" "Cloudy" "Clear" "Clear" "Clear" "Clear"
## [505] "Clear" "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [512] "Clear" "Clear" "Clear" "Clear" "Clear" "Clear" "Clear"
## [519] "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [526] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [533] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [540] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [547] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [554] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [561] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [568] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [575] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear"
## [582] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [589] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [596] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [603] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [610] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [617] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [624] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [631] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [638] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [645] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [652] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [659] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [666] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [673] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [680] "Clear" "Cloudy" "Clear" "Clear" "Clear" "Cloudy" "Cloudy"
## [687] "Cloudy" "Clear" "Cloudy" "Clear" "Clear" "Cloudy" "Cloudy"
## [694] "Cloudy" "Clear" "Clear" "Clear" "Clear" "Cloudy" "Cloudy"
## [701] "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear" "Clear" "Clear"
## [708] "Clear" "Clear" "Cloudy" "Clear" "Cloudy" "Cloudy" "Cloudy"
## [715] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [722] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [729] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [736] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [743] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [750] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [757] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [764] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [771] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [778] "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear" "Clear" "Clear"
## [785] "Clear" "Cloudy" "Cloudy" "Clear" "Clear" "Clear" "Cloudy"
## [792] "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear" "Clear" "Cloudy"
## [799] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear"
## [806] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear"
## [813] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [820] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear"
## [827] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [834] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [841] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [848] "Clear" "Cloudy" "Clear" "Cloudy" "Clear" "Cloudy" "Clear"
## [855] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear"
## [862] "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear"
## [869] "Clear" "Cloudy" "Cloudy" "Clear" "Clear" "Clear" "Clear"
## [876] "Clear" "Clear" "Clear" "Clear" "Clear" "Clear" "Clear"
## [883] "Clear" "Clear" "Clear" "Clear" "Clear" "Clear" "Clear"
## [890] "Clear" "Clear" "Cloudy" "Clear" "Cloudy" "Cloudy" "Clear"
## [897] "Clear" "Clear" "Clear" "Clear" "Clear" "Clear" "Clear"
## [904] "Clear" "Clear" "Cloudy" "Clear" "Clear" "Clear" "Clear"
## [911] "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear"
## [918] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [925] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [932] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [939] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [946] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [953] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [960] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [967] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [974] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [981] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [988] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [995] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1002] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1009] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1016] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1023] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1030] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1037] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1044] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1051] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1058] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear"
## [1065] "Clear" "Clear" "Clear" "Clear" "Clear" "Clear" "Clear"
## [1072] "Clear" "Clear" "Clear" "Clear" "Clear" "Clear" "Clear"
## [1079] "Clear" "Clear" "Clear" "Clear" "Cloudy" "Clear" "Cloudy"
## [1086] "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear" "Clear" "Cloudy"
## [1093] "Cloudy" "Clear" "Clear" "Clear" "Cloudy" "Cloudy" "Cloudy"
## [1100] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1107] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1114] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1121] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1128] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1135] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1142] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1149] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1156] "Cloudy" "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1163] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear" "Clear"
## [1170] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1177] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1184] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Cloudy" "Cloudy"
## [1191] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1198] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1205] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1212] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1219] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1226] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1233] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1240] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear"
## [1247] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear"
## [1254] "Cloudy" "Cloudy" "Clear" "Clear" "Clear" "Clear" "Clear"
## [1261] "Clear" "Clear" "Clear" "Clear" "Clear" "Clear" "Clear"
## [1268] "Clear" "Clear" "Clear" "Clear" "Clear" "Clear" "Clear"
## [1275] "Cloudy" "Clear" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear"
## [1282] "Clear" "Clear" "Clear" "Clear" "Clear" "Clear" "Clear"
## [1289] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Cloudy"
## [1296] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1303] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1310] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1317] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1324] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1331] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1338] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1345] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1352] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear"
## [1359] "Clear" "Clear" "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1366] "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1373] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1380] "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1387] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1394] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1401] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1408] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1415] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1422] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1429] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1436] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1443] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear"
## [1450] "Clear" "Clear" "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1457] "Clear" "Clear" "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1464] "Clear" "Clear" "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1471] "Cloudy" "Clear" "Clear" "Clear" "Clear" "Clear" "Cloudy"
## [1478] "Clear" "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1485] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1492] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1499] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1506] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1513] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1520] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1527] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1534] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1541] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1548] "Cloudy" "Cloudy" "Cloudy" "Clear" "Cloudy" "Cloudy" "Cloudy"
## [1555] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1562] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1569] "Cloudy" "Cloudy" "Cloudy" "Clear" "Cloudy" "Clear" "Cloudy"
## [1576] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1583] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1590] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1597] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1604] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1611] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1618] "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1625] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear" "Cloudy"
## [1632] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear" "Cloudy"
## [1639] "Cloudy" "Clear" "Clear" "Clear" "Clear" "Clear" "Clear"
## [1646] "Clear" "Clear" "Clear" "Clear" "Clear" "Clear" "Clear"
## [1653] "Clear" "Clear" "Clear" "Clear" "Clear" "Clear" "Cloudy"
## [1660] "Clear" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear" "Clear"
## [1667] "Clear" "Clear" "Clear" "Clear" "Clear" "Clear" "Cloudy"
## [1674] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1681] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1688] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1695] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1702] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1709] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1716] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1723] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1730] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1737] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1744] "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear"
## [1751] "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1758] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1765] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1772] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear"
## [1779] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1786] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1793] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1800] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1807] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1814] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1821] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1828] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Clear" "Cloudy" "Clear"
## [1835] "Clear" "Clear" "Cloudy" "Cloudy" "Cloudy" "Clear" "Clear"
## [1842] "Clear" "Cloudy" "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1849] "Cloudy" "Cloudy" "Clear" "Clear" "Cloudy" "Cloudy" "Cloudy"
## [1856] "Cloudy" "Cloudy" "Clear" "Clear" "Cloudy" "Clear" "Clear"
## [1863] "Clear" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1870] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1877] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1884] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1891] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1898] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1905] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1912] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1919] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1926] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1933] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1940] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1947] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1954] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1961] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1968] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1975] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1982] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1989] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [1996] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"Observations
Park mobility observations are taken from the Google Mobility data. The data compares mobility for the report date to the baseline day. Calculated for the report date (unless there are gaps) and reported as a positive or negative percentage. The baseline day is the median value from the 5‑week period Jan 3 – Feb 6, 2020.
Bin the mobility data to create 3 types of observations:
Low Mobility (less than 4)
Moderate Mobility (4 to 19)
High Mobility (> 19)
plot(spring$Parks_Percent)
abline(h=-10,col="red")
abline(h=35,col="red")
Bin mobilty data as low, moderate, high mobility
spring$park_obs <- ifelse(spring$Parks_Percent < -10, "L", ifelse(spring$Parks_Percent >= -4 & spring$Parks_Percent < 35, "M","H"))
spring$park_obs[1:250]## [1] "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M"
## [18] "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M"
## [35] "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M"
## [52] "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M"
## [69] "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M"
## [86] "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M"
## [103] "M" "H" "H" "L" "L" "H" "M" "M" "M" "M" "H" "L" "H" "M" "M" "M" "M"
## [120] "H" "L" "H" "M" "M" "M" "M" "M" "H" "L" "M" "M" "M" "M" "M" "M" "M"
## [137] "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M"
## [154] "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "H" "M" "M" "M" "M" "M"
## [171] "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "H" "M"
## [188] "M" "M" "M" "M" "M" "H" "H" "H" "H" "M" "M" "H" "H" "M" "H" "M" "M"
## [205] "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M"
## [222] "M" "M" "M" "M" "M" "M" "M" "H" "H" "M" "M" "M" "M" "M" "M" "M" "M"
## [239] "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "M" "H"Transition Probabbility Matrix
The transition matrix is the probability of changing from one state to another state. It is represented as a M×M matrix where the rows sum to 1. aij is simply the probability of state ii changing to state j at t+1.
aij=p(s(t+a)=j|s(t)=i
A simple example of a transition matrix with two states time step to 10
spring$markov_states[1:10]## [1] "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy" "Cloudy"
## [8] "Cloudy" "Cloudy" "Cloudy"Compare to output using markovchainFit function.
simple_A <- markovchainFit(spring$markov_states[1:2000])
simple_A$estimate## MLE Fit
## A 2 - dimensional discrete Markov Chain defined by the following states:
## Clear, Cloudy
## The transition matrix (by rows) is defined as follows:
## Clear Cloudy
## Clear 0.70779221 0.2922078
## Cloudy 0.05322295 0.9467771Repeat the same process on all 90 states for the estimated transition matrix.
transition <- markovchainFit(data = spring$markov_states)
transition$estimate## MLE Fit
## A 2 - dimensional discrete Markov Chain defined by the following states:
## Clear, Cloudy
## The transition matrix (by rows) is defined as follows:
## Clear Cloudy
## Clear 0.70779221 0.2922078
## Cloudy 0.05322295 0.9467771```