CSS160030 P2 Embassy Weather

#Embassy Weather Prediction with Regression

https://archive.ics.uci.edu/ml/datasets/Beijing+PM2.5+Data No: row number year: year of data in this row month: month of data in this row day: day of data in this row hour: hour of data in this row pm2.5: PM2.5 concentration (ug/m^3) DEWP: Dew Point (℃) TEMP: Temperature (℃) PRES: Pressure (hPa) cbwd: Combined wind direction Iws: Cumulated wind speed (m/s) Is: Cumulated hours of snow Ir: Cumulated hours of rain

ew <- read.csv("embassy.csv", header=TRUE)

str(ew)

'data.frame':   43824 obs. of  13 variables:
 $ No   : int  1 2 3 4 5 6 7 8 9 10 ...
 $ year : int  2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 ...
 $ month: int  1 1 1 1 1 1 1 1 1 1 ...
 $ day  : int  1 1 1 1 1 1 1 1 1 1 ...
 $ hour : int  0 1 2 3 4 5 6 7 8 9 ...
 $ pm2.5: int  NA NA NA NA NA NA NA NA NA NA ...
 $ DEWP : int  -21 -21 -21 -21 -20 -19 -19 -19 -19 -20 ...
 $ TEMP : num  -11 -12 -11 -14 -12 -10 -9 -9 -9 -8 ...
 $ PRES : num  1021 1020 1019 1019 1018 ...
 $ cbwd : Factor w/ 4 levels "cv","NE","NW",..: 3 3 3 3 3 3 3 3 3 3 ...
 $ Iws  : num  1.79 4.92 6.71 9.84 12.97 ...
 $ Is   : int  0 0 0 0 0 0 0 0 0 0 ...
 $ Ir   : int  0 0 0 0 0 0 0 0 0 0 ...

head(ew)

###Removing Nas

sapply(ew, function(x) sum(is.na(x)))

   No  year month   day  hour pm2.5  DEWP  TEMP  PRES  cbwd   Iws    Is    Ir 
    0     0     0     0     0  2067     0     0     0     0     0     0     0 

ew <- na.exclude(ew)

Let’s remove No, since it’s a useless column

ew <- ew[,-1]

attach(ew)

Let’s take a look at Temperature based on all other predictors

##Plots

plot(ew$TEMP, ew$month, main="Temperature based on Month", xlab="Temperature in Fahrenheight", ylab="Month")

Middle of the year is the hottest.

plot(ew$TEMP, ew$Iws, main="Temperature vs Windspeed", xlab="Temperature in Fahrenheight", ylab="Windspeed m/s")

Higher Wind speeds make cooler temperatures

plot(ew$TEMP, ew$PRES, main="Temperature vs Pressure", xlab="Temperature", ylab="Pressure")

Higher pressures correlate with lower temperatures

plot(ew$TEMP, ew$hour)

Temperature is higher in the afternoons and cooler in the twightlight hours of the morning. ##Train test split

set.seed(1234)
i <- sample(1:nrow(ew), .8*nrow(ew), replace=FALSE)
ewtrain <- ew[i,]
ewtest <- ew[-i,]

##Predicting Temperature based on all other predictors via Linear Regression

ew_lm <- lm(TEMP~., data=ewtrain)
summary(ew_lm)

Call:
lm(formula = TEMP ~ ., data = ewtrain)

Residuals:
     Min       1Q   Median       3Q      Max 
-17.0726  -3.4019  -0.2823   3.1559  22.1552 

Coefficients:
              Estimate Std. Error  t value Pr(>|t|)    
(Intercept) -2.376e+02  3.893e+01   -6.103 1.05e-09 ***
year         3.606e-01  1.920e-02   18.786  < 2e-16 ***
month        5.215e-02  8.377e-03    6.225 4.87e-10 ***
day          1.977e-02  3.093e-03    6.391 1.67e-10 ***
hour         2.219e-01  4.045e-03   54.851  < 2e-16 ***
pm2.5       -2.634e-02  3.133e-04  -84.083  < 2e-16 ***
DEWP         4.630e-01  3.412e-03  135.698  < 2e-16 ***
PRES        -4.699e-01  4.354e-03 -107.924  < 2e-16 ***
cbwdNE       2.117e-01  9.975e-02    2.123   0.0338 *  
cbwdNW       2.831e-02  8.279e-02    0.342   0.7324    
cbwdSE       1.360e+00  7.668e-02   17.730  < 2e-16 ***
Iws          8.000e-03  6.106e-04   13.101  < 2e-16 ***
Is          -6.958e-01  3.521e-02  -19.763  < 2e-16 ***
Ir          -5.014e-01  1.944e-02  -25.791  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.942 on 33391 degrees of freedom
Multiple R-squared:  0.8358,    Adjusted R-squared:  0.8358 
F-statistic: 1.308e+04 on 13 and 33391 DF,  p-value: < 2.2e-16

ew_lm_pred <- predict(ew_lm, newdata=ewtest)
ew_lm_mse <- mean((ew_lm_pred - ewtest$TEMP)^2)
ew_lm_cor <- cor(ew_lm_pred, ewtest$TEMP)
print(paste("Linear Regression accuracy: ", ew_lm_cor))

[1] "Linear Regression accuracy:  0.91238975053004"

##Predicting Temperature based on all other predictors via Decision Tree

library(tree)
ew_tree <- tree(TEMP~., data=ewtrain)
ew_tree

node), split, n, deviance, yval
      * denotes terminal node

 1) root 33405 4967000 12.3900  
   2) DEWP < 2.5 17159 1395000  3.3970  
     4) PRES < 1019.25 5029  421200 10.9100  
       8) pm2.5 < 80.5 2885  201600 14.5100  
        16) month < 10.5 2342  132000 16.5400 *
        17) month > 10.5 543   18200  5.7380 *
       9) pm2.5 > 80.5 2144  131700  6.0620 *
     5) PRES > 1019.25 12130  572600  0.2832  
      10) month < 2.5 4930  115200 -3.5960 *
      11) month > 2.5 7200  332400  2.9390  
        22) month < 11.5 4818  174800  5.7030 *
        23) month > 11.5 2382   46320 -2.6520 *
   3) DEWP > 2.5 16246  718800 21.8900  
     6) PRES < 1010.5 9642  254900 24.9800  
      12) hour < 8.5 3562   57750 21.5900 *
      13) hour > 8.5 6080  132100 26.9700 *
     7) PRES > 1010.5 6604  236400 17.3600  
      14) month < 9.5 4454  130600 19.5200 *
      15) month > 9.5 2150   42330 12.9000 *

summary(ew_tree)

Regression tree:
tree(formula = TEMP ~ ., data = ewtrain)
Variables actually used in tree construction:
[1] "DEWP"  "PRES"  "pm2.5" "month" "hour" 
Number of terminal nodes:  10 
Residual mean deviance:  29.38 = 981100 / 33400 
Distribution of residuals:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-26.54000  -3.51700   0.09628   0.00000   3.41000  25.94000 

plot(ew_tree)
text(ew_tree, cex=.7, pretty=1)

ew_tree_pred <- predict(ew_tree, newdata=ewtest)
ew_tree_mse <- mean((ew_tree_pred - ewtest$TEMP)^2)
ew_tree_cor <- cor(ew_tree_pred, ewtest$TEMP)
print(paste("Decision Tree accuracy: ", ew_tree_cor))

[1] "Decision Tree accuracy:  0.89266297926514"

##Predicting Temperature based on all other predictors via RandomForest

library("randomForest")

randomForest 4.6-14
Type rfNews() to see new features/changes/bug fixes.

set.seed(1234)
ew_rf <- randomForest(TEMP~., data=ewtest)
ew_rf

Call:
 randomForest(formula = TEMP ~ ., data = ewtest) 
               Type of random forest: regression
                     Number of trees: 500
No. of variables tried at each split: 3

          Mean of squared residuals: 6.113181
                    % Var explained: 95.83

ew_rf_pred <- predict(ew_rf, newdata=ewtest)
ew_rf_mse <- mean((ew_rf_pred - ewtest$TEMP)^2)
ew_rf_cor <- cor(ew_rf_pred, ewtest$TEMP)
print(paste("RandomForest accuracy: ", ew_rf_cor))

[1] "RandomForest accuracy:  0.995525009204737"

##Predicting Temperature based on all other predictors via K Nearest Neighbors

ew$cbwd <- as.integer(ew$cbwd)
ewknndata <- data.frame(scale(ew[,1:12]))
ewknntrain <- ewknndata[i,]
ewknntest <- ewknndata[-i,]

ew_knn <- knnreg(ewknntrain[,c("year", "month", "day", "hour", "pm2.5", "DEWP", "PRES", "cbwd", "Iws", "Is", "Ir")], ewknntrain[,"TEMP"], k=3)
ew_knn_pred <- predict(ew_knn, ewknntest[, c("year", "month", "day", "hour", "pm2.5", "DEWP", "PRES", "cbwd", "Iws", "Is", "Ir")])
ew_knn_cor <- cor(ew_knn_pred, ewknntest$TEMP)
ew_knn_mse <- mean((ew_knn_pred - ewknntest$TEMP)^2)
print(paste("KNN with k=3 accuracy: ", ew_knn_cor))

[1] "KNN with k=3 accuracy:  0.981239623058666"

ew_knn2 <- knnreg(ewknntrain[,c("year", "month", "day", "hour", "pm2.5", "DEWP", "PRES", "cbwd", "Iws", "Is", "Ir")], ewknntrain[,"TEMP"], k=2)
ew_knn_pred2 <- predict(ew_knn2, ewknntest[, c("year", "month", "day", "hour", "pm2.5", "DEWP", "PRES", "cbwd", "Iws", "Is", "Ir")])
ew_knn_cor2 <- cor(ew_knn_pred2, ewknntest$TEMP)
ew_knn_mse2 <- mean((ew_knn_pred2 - ewknntest$TEMP)^2)
print(paste("KNN with k=2 accuracy: ", ew_knn_cor2))

[1] "KNN with k=2 accuracy:  0.982482967925183"

##Embassy Weather Machine Learning Results ###Accuracy of Models

print(paste("Linear Regression accuracy: ", ew_lm_cor))

[1] "Linear Regression accuracy:  0.91238975053004"

print(paste("Decision Tree accuracy: ", ew_tree_cor))

[1] "Decision Tree accuracy:  0.89266297926514"

print(paste("RandomForest accuracy: ", ew_rf_cor))

[1] "RandomForest accuracy:  0.995525009204737"

print(paste("KNN with k=2 accuracy: ", ew_knn_cor2))

[1] "KNN with k=2 accuracy:  0.982482967925183"

The decision tree was the least accurate. Probably because it assumed othogonal binary separations that did not exist in the data and could not change those separations after the fact after it learned more about the data Linear regression was more accurate than decision trees, probably because it had less bias about the shape of the data. It assumed a linear relationship. Random Forest was more accurate than everything else, probably because it took the deficiency of decision trees, and averaged 500 of them. Any individual deficiency was overcome by the collective. KNN was second most accurate, because a time’s temperature can be assumed to be like similar times’ temperatures. However this assumption is not perfect, and that’s why it did worse than random forest. Also though 2 neighbors was the highest accuracy, in a perfect world every observation would have a twin we could predict from instead of having to average 2.

###What we learned. We can predict with a 99.5% accuracy what temperature the US embassy in Beijing’s temperature will be based on air pressure, date, dew point, and precipitation with the random forest model. Looking at the decision tree, depending on the dew point, pressure, and date, we can predit with a 90% what temperature it will be. Also, this does not require an opaque algorithm. We also learned the relationships between pressure, windspeed, and temperature.