DOTS Traffic MLR Model
DC20045
2/28/2020
Libraries
This projecti ncludes the following libraries.
library(dplyr)
library(rockchalk)
library(psych)
library(splines)
library(car)Data Cleaning and Set Up
In this step, we load in the CSV containing sensor data joined with weather data. Since weather is measured hourly, we filter sensor data to only include the hourly measurements. In this specific model, we examine the intersection of Regents ad Stadium Drive, which combines readings from four sensors.
#import data
dat <- read.csv("Datasets/dots_data.csv")
summary(dat)
#data recode
dat.r <- dat[dat$minutes==0,] #include only hourly sensor data
#combine four sensors on Regents Stadium intersection
dat.r$location <- combineLevels(dat.r$location, c("Regents_Dr_&_Stadium_Dr_1",
"Regents_Dr_&_Stadium_Dr_2",
"Regents_Dr_&_Stadium_Dr_3",
"Stadium_Dr_East_Of_Regents_Dr"), newLabel = "Regents_Stadium_combo")
dat.regStd <- dat.r[dat.r$location == "Regents_Stadium_combo",]Examine the Data and Trends
Examining a histogram of the car variable, we see that it is strongly right-skewed. This ma be due to the large amount of “zero traffic” which we have discovered to may be linked to sensor failure. Regardless, the scatterplot matrix showcases the numerical variables and their extremely mishapen nature.
#Histogram of Car
hist(dat.regStd$car)
#Scatterplot matrix
pairs(~ cars + hours + Temperature + Wind.Speed + Pressure + Humidity, data = dat.regStd)
Model 1: Draft
The first draft of the multiple linear regression model includes all of the numerical variables in conjunction with a dummy-coded condition (weather description) variable. This initial model posed several issues:
- While most variables were significant within the model at an alpha of 0.05, the Condition variable was not in all of the levels.
- The VIF scores showed that Humidity and Pressure were posing significant multicollinearity issues.
- The R-squared value implies a low substantive significance.
#Model 1: Condition, Temperature, Hour, Wind spd, Pressure, Humidity
regstd.car = lm(dat.regStd$car ~ factor(dat.regStd$Condition) + dat.regStd$Temperature + dat.regStd$hours
+ dat.regStd$Wind.Speed + dat.regStd$Pressure + dat.regStd$Humidity)
#Correlation and model summary
summary(regstd.car)##
## Call:
## lm(formula = dat.regStd$car ~ factor(dat.regStd$Condition) +
## dat.regStd$Temperature + dat.regStd$hours + dat.regStd$Wind.Speed +
## dat.regStd$Pressure + dat.regStd$Humidity)
##
## Residuals:
## Min 1Q Median 3Q Max
## -161.76 -52.97 -18.62 34.75 357.89
##
## Coefficients:
## Estimate Std. Error
## (Intercept) -1259.8299 1385.5628
## factor(dat.regStd$Condition)Fair 8.8182 6.7933
## factor(dat.regStd$Condition)Light Rain -7.7607 13.1519
## factor(dat.regStd$Condition)Mostly Cloudy 0.9787 11.3994
## factor(dat.regStd$Condition)Partly Cloudy 15.3896 9.6972
## factor(dat.regStd$Condition)Partly Cloudy / Windy -14.2115 22.1433
## factor(dat.regStd$Condition)T-Storm -20.3282 19.0305
## dat.regStd$Temperature 1.8712 0.4727
## dat.regStd$hours 7.8177 0.3012
## dat.regStd$Wind.Speed 2.4598 0.7109
## dat.regStd$Pressure 36.6236 45.8149
## dat.regStd$Humidity 46.8541 45.2474
## t value Pr(>|t|)
## (Intercept) -0.909 0.363380
## factor(dat.regStd$Condition)Fair 1.298 0.194486
## factor(dat.regStd$Condition)Light Rain -0.590 0.555235
## factor(dat.regStd$Condition)Mostly Cloudy 0.086 0.931597
## factor(dat.regStd$Condition)Partly Cloudy 1.587 0.112745
## factor(dat.regStd$Condition)Partly Cloudy / Windy -0.642 0.521115
## factor(dat.regStd$Condition)T-Storm -1.068 0.285627
## dat.regStd$Temperature 3.959 7.93e-05 ***
## dat.regStd$hours 25.955 < 2e-16 ***
## dat.regStd$Wind.Speed 3.460 0.000557 ***
## dat.regStd$Pressure 0.799 0.424211
## dat.regStd$Humidity 1.036 0.300618
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 76.05 on 1336 degrees of freedom
## Multiple R-squared: 0.3592, Adjusted R-squared: 0.3539
## F-statistic: 68.08 on 11 and 1336 DF, p-value: < 2.2e-16#VIF Scores
vif(regstd.car)## GVIF Df GVIF^(1/(2*Df))
## factor(dat.regStd$Condition) 76.131936 6 1.434819
## dat.regStd$Temperature 4.154470 1 2.038252
## dat.regStd$hours 1.013649 1 1.006802
## dat.regStd$Wind.Speed 4.874290 1 2.207779
## dat.regStd$Pressure 9.450152 1 3.074110
## dat.regStd$Humidity 8.290033 1 2.879242#Regression Plots
plot(regstd.car, which = c(2,3,4))
Model 2: Refined
We then recreated the model and removed Condition, Humidity, and Pressure, which left a model with four significant dependant variables and an overall significant model at alpha 0.05. However, we still had some major issues:
- The diagnostic plots (esp. scatter-location) indicated a fan pattern. This suggests that there is a pattern in the data that may make the linear model ineffective.
- The R-squared value was still low.
regstd.car2 = lm(dat.regStd$car ~ dat.regStd$Temperature + dat.regStd$hours
+ dat.regStd$Wind.Speed)
#Correlation and model summary
summary(regstd.car2)##
## Call:
## lm(formula = dat.regStd$car ~ dat.regStd$Temperature + dat.regStd$hours +
## dat.regStd$Wind.Speed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -150.03 -53.60 -19.86 36.29 369.55
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -78.3326 12.4446 -6.294 4.17e-10 ***
## dat.regStd$Temperature 1.3214 0.2344 5.638 2.10e-08 ***
## dat.regStd$hours 7.7719 0.3013 25.793 < 2e-16 ***
## dat.regStd$Wind.Speed 0.7577 0.3254 2.329 0.02 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 76.52 on 1344 degrees of freedom
## Multiple R-squared: 0.3474, Adjusted R-squared: 0.3459
## F-statistic: 238.5 on 3 and 1344 DF, p-value: < 2.2e-16#VIF Scores
vif(regstd.car2)## dat.regStd$Temperature dat.regStd$hours dat.regStd$Wind.Speed
## 1.009241 1.002105 1.008585#Regression Plots
plot(regstd.car2, which = c(2,3,4))
