Laky_Homework 5
Laky, Ryann
2023-04-10
You should complete the following problems in R. Be sure to provide the instructor with both your code and output.
- Load the
homesdataset into R. This dataset contains information about houses sold in King County, Washington in 2014.
homes <- read.csv("/Users/ryannlaky/Documents/University of Indianapolis/MSDA 622/Homework/Homework 5/homes.csv")
str(homes)## 'data.frame': 76 obs. of 18 variables:
## $ Price : num 388 450 386 350 156 ...
## $ Floor : num 2.18 2.05 2.11 1.44 1.8 ...
## $ Lot : int 4 5 5 6 1 5 4 4 4 5 ...
## $ Bath : num 3 3 2 1 2 2 1.1 2 2.1 2.1 ...
## $ Bed : int 4 4 4 2 4 3 4 4 4 3 ...
## $ BathBed: num 12 12 8 2 8 6 4.4 8 8.4 6.3 ...
## $ Year : int 1940 1957 1955 1956 1994 1940 1958 1961 1965 1968 ...
## $ Age : num -3 -1.3 -1.5 -1.4 2.4 -3 -1.2 -0.9 -0.5 -0.2 ...
## $ AgeSq : num 9 1.69 2.25 1.96 5.76 9 1.44 0.81 0.25 0.04 ...
## $ Gar : int 0 2 2 1 1 1 1 2 2 2 ...
## $ Status : chr "Sold" "Sold" "Sold" "Active" ...
## $ DAc : int 0 0 0 1 0 0 1 0 1 0 ...
## $ School : chr "Edison" "Edison" "Edison" "Adams" ...
## $ DEd : int 1 1 1 0 0 0 0 0 0 0 ...
## $ DHa : int 0 0 0 0 0 0 0 0 0 0 ...
## $ DAd : int 0 0 0 1 1 1 0 0 0 0 ...
## $ DCr : int 0 0 0 0 0 0 0 0 0 0 ...
## $ DPa : int 0 0 0 0 0 0 1 1 1 1 ...- Use R to remove any non-numeric columns of data, and then normalize the numeric data.
homes <- homes[,-c(3,5,7,10:18)]
str(homes)## 'data.frame': 76 obs. of 6 variables:
## $ Price : num 388 450 386 350 156 ...
## $ Floor : num 2.18 2.05 2.11 1.44 1.8 ...
## $ Bath : num 3 3 2 1 2 2 1.1 2 2.1 2.1 ...
## $ BathBed: num 12 12 8 2 8 6 4.4 8 8.4 6.3 ...
## $ Age : num -3 -1.3 -1.5 -1.4 2.4 -3 -1.2 -0.9 -0.5 -0.2 ...
## $ AgeSq : num 9 1.69 2.25 1.96 5.76 9 1.44 0.81 0.25 0.04 ...maxs <- apply(homes, 2, max) # maximum value of each column
mins <- apply(homes, 2, min) #minimum value of each column
scaled <- as.data.frame(scale(homes, center = mins, scale = maxs - mins))
summary(scaled)## Price Floor Bath BathBed
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.2963 1st Qu.:0.2890 1st Qu.:0.4762 1st Qu.:0.3077
## Median :0.4092 Median :0.3616 Median :0.4762 Median :0.3308
## Mean :0.4424 Mean :0.3643 Mean :0.5752 Mean :0.4363
## 3rd Qu.:0.6154 3rd Qu.:0.4584 3rd Qu.:0.9524 3rd Qu.:0.5385
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## Age AgeSq
## Min. :0.0000 Min. :0.000000
## 1st Qu.:0.5275 1st Qu.:0.005917
## Median :0.6450 Median :0.028876
## Mean :0.6441 Mean :0.128991
## 3rd Qu.:0.7500 3rd Qu.:0.213018
## Max. :1.0000 Max. :1.000000- In the normalized data, randomly select 85% of the rows to create your training set, and use the remaining rows in your testing set.
index <- sample(nrow(homes), nrow(homes)*0.85)
train_homes <- scaled[index,]
test_homes <- scaled[-index,]- Use your training set to develop a neural network model with three hidden layers. The first hidden layer should contain 2 neurons (i.e., nodes), the second hidden layer should contain 3 neurons, and the third hidden layer should contain 2 neurons. Use Price as your target variable, and use all other numeric columns of data as your covariates.
#install.packages("neuralnet")
library(neuralnet)
nn <- neuralnet(train_homes$Price ~ ., data=train_homes, hidden=c(2,3,2), linear.output=T)
nn$act.fct #activation function## function (x)
## {
## 1/(1 + exp(-x))
## }
## <bytecode: 0x1207319f0>
## <environment: 0x12074f208>
## attr(,"type")
## [1] "logistic"- Create a plot of your neural network displaying all hidden layers and all weights.
#install.packages('devtools')
library(devtools)
source_url('https://gist.githubusercontent.com/fawda123/7471137/raw/466c1474d0a505ff044412703516c34f1a4684a5/nnet_plot_update.r')
plot.nnet(nn)
- Use your neural network model to develop predictions for the data in your testing set. Be sure that these predictions are transformed to conform with the original scale of the target variable (i.e., the predictions should neither be standardized nor normalized). Place a comment in your code clearly indicating the line that provides the final, unstandardized predictions. Calculate the mean squared error resulting from your predictions for the data in your testing set.
pr_nn <- compute(nn, test_homes[,2:6]) #function used for predictions on a neural network
pr_nn_org <- pr_nn$net.result*(max(homes$Price) - min(homes$Price)) + min(homes$Price)
pr_nn_org #provides the final, unstandardized predictions## [,1]
## 14 303.7929
## 18 225.3665
## 20 218.5979
## 22 200.0108
## 23 260.3561
## 32 230.2863
## 36 274.5236
## 40 319.1962
## 46 271.3713
## 58 319.8534
## 70 270.7519
## 75 237.7602test_r <- (test_homes$Price)*(max(homes$Price) - min(homes$Price)) + min(homes$Price) #convert back to scaleMSPE_nn <- sum((test_r - pr_nn_org)^2)/nrow(test_homes)
MSPE_nn## [1] 1695.506
- Load the datasets called
trainandtestinto R. Use thetraindataset as your training set, and use thetestdataset as your testing set.
train <- read.csv("/Users/ryannlaky/Documents/University of Indianapolis/MSDA 622/Homework/Homework 5/train.csv")
str(train)## 'data.frame': 480 obs. of 14 variables:
## $ crim : num 4.2224 6.2881 11.8123 0.5578 0.0616 ...
## $ zn : num 0 0 0 0 0 0 0 0 0 40 ...
## $ indus : num 18.1 18.1 18.1 21.89 4.39 ...
## $ chas : int 1 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.77 0.74 0.718 0.624 0.442 0.437 0.631 0.499 0.437 0.429 ...
## $ rm : num 5.8 6.34 6.82 6.33 5.9 ...
## $ age : num 89 96.4 76.5 98.2 52.3 18.4 100 68.2 45.8 34.5 ...
## $ dis : num 1.9 2.07 1.79 2.11 8.01 ...
## $ rad : int 24 24 24 4 3 4 24 5 5 1 ...
## $ tax : int 666 666 666 437 352 289 666 279 398 335 ...
## $ ptratio: num 20.2 20.2 20.2 21.2 18.8 16 20.2 19.2 18.7 19.7 ...
## $ black : num 353 318 48.5 394.7 364.6 ...
## $ lstat : num 14.6 17.8 22.7 17 12.7 ...
## $ medv : num 16.8 14.9 8.4 18.1 17.2 23.9 50 18.9 20.8 26.6 ...test <- read.csv("/Users/ryannlaky/Documents/University of Indianapolis/MSDA 622/Homework/Homework 5/test.csv")
str(test)## 'data.frame': 26 obs. of 14 variables:
## $ crim : num 0.0324 0.7503 0.0519 0.169 0.59 ...
## $ zn : num 0 0 0 0 0 0 0 0 0 0 ...
## $ indus : num 2.18 8.14 4.49 25.65 21.89 ...
## $ chas : int 0 0 0 0 0 0 1 0 0 0 ...
## $ nox : num 0.458 0.538 0.449 0.581 0.624 0.624 0.871 0.605 0.605 0.51 ...
## $ rm : num 7 5.92 6.01 5.99 6.37 ...
## $ age : num 45.8 94.1 45.1 88.4 97.9 93.5 88 97.4 100 84.1 ...
## $ dis : num 6.06 4.4 4.43 1.99 2.33 ...
## $ rad : int 3 4 3 2 4 4 5 5 5 5 ...
## $ tax : int 222 307 247 188 437 437 403 403 403 296 ...
## $ ptratio: num 18.7 21 18.5 19.1 21.2 21.2 14.7 14.7 14.7 16.6 ...
## $ black : num 395 394 396 385 386 ...
## $ lstat : num 2.94 16.3 12.86 14.81 11.12 ...
## $ medv : num 33.4 15.6 22.5 21.4 23 17.4 15.3 41.3 24.3 23.6 ...- Using all columns in your training set, develop a LASSO regression model to predict medv.
#install.packages("glmnet")
library(glmnet)
lreg <- glmnet(x = as.matrix(train[, -14]), y = train[, 14], alpha = 1)
lambda_info <- cv.glmnet(x = as.matrix(train[, -14]), y = train[, 14], alpha = 1)
min_lambda <- lambda_info$lambda.min
min_lambda## [1] 0.03043668- Use your LASSO regression to make predictions for the data in your testing set, and calculate the corresponding mean squared error. When making these predictions, be sure to use the optimal lambda selected through 10-fold cross validation.
y_predicted <- predict(lreg, s = min_lambda, newx = as.matrix(test[,-14]))
print(paste0("MSE: ", mean((test[,14] - y_predicted)^2)))## [1] "MSE: 24.0933577028936"- Which covariates turned out to be insignificant?
coef(lreg, s = min_lambda)## 14 x 1 sparse Matrix of class "dgCMatrix"
## s1
## (Intercept) 34.184228273
## crim -0.098203107
## zn 0.042147254
## indus .
## chas 2.859623514
## nox -15.386141974
## rm 3.776202467
## age .
## dis -1.377510667
## rad 0.246784455
## tax -0.009494388
## ptratio -0.904718617
## black 0.008943527
## lstat -0.547515273* According to the above, the variables `indus` and `age` were considered insignificant in this LASSO regression.