DATA605_FinalExam
IvanTikhonov
2022-12-10
Loading libraries
# For Problem 1
library(igraph)##
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# For Problem 2
library(OpenImageR)
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## dotPlotlibrary(nnet)
# For Problem 3
library(MASS)##
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## housing, mammalslibrary(matrixcalc)##
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## +.gg ggplot2# For all Problems
library(ggplot2)
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## if Arial Narrow is not on your system, please see https://bit.ly/arialnarrow- Playing with PageRank You’ll verify for yourself that PageRank works by performing calculations on a small universe of web pages. Let’s use the 6 page universe that we had in the previous discussion For this directed graph, perform the following calculations in R.
• Form the A matrix. Then, introduce decay and form the B matrix as we did in the course notes. (5 Points)
# create matrix
A <- matrix(c(0, (1/2), (1/2), 0, 0, 0, 0, 0, 0, 0, 0, 0, (1/3), (1/3), 0, 0, (1/3), 0, 0, 0, 0, 0, (1/2), (1/2), 0, 0, 0, (1/2), 0, (1/2), 0, 0, 0, 1, 0, 0), nrow = 6, byrow = T)
A## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.0000000 0.5000000 0.5 0.0 0.0000000 0.0
## [2,] 0.0000000 0.0000000 0.0 0.0 0.0000000 0.0
## [3,] 0.3333333 0.3333333 0.0 0.0 0.3333333 0.0
## [4,] 0.0000000 0.0000000 0.0 0.0 0.5000000 0.5
## [5,] 0.0000000 0.0000000 0.0 0.5 0.0000000 0.5
## [6,] 0.0000000 0.0000000 0.0 1.0 0.0000000 0.0#formatC(A, format = “f”, digits = 4)
Being that the second row is filled with 0’s we are replacing the vector of 1/6 since there are 6 webpages and we have an equal probability of landing on any of the pages.
n <- 6 # number of webpages
# creating new row to replace matrix A second row
row2 <- rep(1/6, n)
# Removing second row from matrix A
A_2 <- A[-2,]
# Adding r into the second row and creating matrix A_2
A_2 <- matrix(rbind(A_2[1,], row2, A_2[- (1), ]), 6)
A_2## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.0000000 0.5000000 0.5000000 0.0000000 0.0000000 0.0000000
## [2,] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
## [3,] 0.3333333 0.3333333 0.0000000 0.0000000 0.3333333 0.0000000
## [4,] 0.0000000 0.0000000 0.0000000 0.0000000 0.5000000 0.5000000
## [5,] 0.0000000 0.0000000 0.0000000 0.5000000 0.0000000 0.5000000
## [6,] 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000#A_2 <- A + (apply(A, 1, sum) !=1) * 1 / n #formatC(A_2, format = “f”, digits = 4)
# decay form B matrix
decay <- 0.85
n <- nrow(A_2)
B <- decay * A_2 + ((1 - decay) / n)
formatC(B, format = "f", digits = 4)## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] "0.0250" "0.4500" "0.4500" "0.0250" "0.0250" "0.0250"
## [2,] "0.1667" "0.1667" "0.1667" "0.1667" "0.1667" "0.1667"
## [3,] "0.3083" "0.3083" "0.0250" "0.0250" "0.3083" "0.0250"
## [4,] "0.0250" "0.0250" "0.0250" "0.0250" "0.4500" "0.4500"
## [5,] "0.0250" "0.0250" "0.0250" "0.4500" "0.0250" "0.4500"
## [6,] "0.0250" "0.0250" "0.0250" "0.8750" "0.0250" "0.0250"• Start with a uniform rank vector r and perform power iterations on B till convergence. That is, compute the solution r = B^n × r. Attempt this for a sufficiently large n so that r actually converges. (5 Points)
# We will take the second row of 0.167 to perform the iterations on B when r = B^n * r
# We'll do a couple of iterations increasing by 10 starting at 0
n <- 0
r_0 <- matrix.power(t(B), n) %*% row2
r_0## [,1]
## [1,] 0.1666667
## [2,] 0.1666667
## [3,] 0.1666667
## [4,] 0.1666667
## [5,] 0.1666667
## [6,] 0.1666667n <- 10
r_10 <- matrix.power(t(B), n) %*% row2
r_10## [,1]
## [1,] 0.05205661
## [2,] 0.07428990
## [3,] 0.05782138
## [4,] 0.34797267
## [5,] 0.19975859
## [6,] 0.26810085n <- 20
r_20 <- matrix.power(t(B), n) %*% row2
r_20## [,1]
## [1,] 0.05170616
## [2,] 0.07368173
## [3,] 0.05741406
## [4,] 0.34870083
## [5,] 0.19990313
## [6,] 0.26859408n <- 30
r_30 <- matrix.power(t(B), n) %*% row2
r_30## [,1]
## [1,] 0.05170475
## [2,] 0.07367927
## [3,] 0.05741242
## [4,] 0.34870367
## [5,] 0.19990381
## [6,] 0.26859607n <- 40
r_40 <- matrix.power(t(B), n) %*% row2
r_40## [,1]
## [1,] 0.05170475
## [2,] 0.07367926
## [3,] 0.05741241
## [4,] 0.34870369
## [5,] 0.19990381
## [6,] 0.26859608n <- 50
r_50 <- matrix.power(t(B), n) %*% row2
r_50## [,1]
## [1,] 0.05170475
## [2,] 0.07367926
## [3,] 0.05741241
## [4,] 0.34870369
## [5,] 0.19990381
## [6,] 0.26859608# By iteration 30 we found the convergence
iter_converg <- matrix.power(t(B), 30) %*% row2• Compute the eigen-decomposition of B and verify that you indeed get an eigenvalue of 1 as the largest eigenvalue and that its corresponding eigenvector is the same vector that you obtained in the previous power iteration method. Further, this eigenvector has all positive entries and it sums to 1.(10 points)
eigen_decomp <- eigen(B)
eigen_decomp## eigen() decomposition
## $values
## [1] 1.00000000 0.57619235 -0.42500001 -0.42499999 -0.34991524 -0.08461044
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.4082483 -0.7278031 -5.345224e-01 5.345225e-01 -0.795670150
## [2,] -0.4082483 -0.3721164 -5.216180e-09 -5.216180e-09 0.059710287
## [3,] -0.4082483 -0.5389259 5.345225e-01 -5.345225e-01 0.602762996
## [4,] -0.4082483 0.1174605 -2.672613e-01 2.672612e-01 0.002611877
## [5,] -0.4082483 0.1174605 -2.672613e-01 2.672612e-01 0.002611877
## [6,] -0.4082483 0.1174605 5.345225e-01 -5.345224e-01 0.002611877
## [,6]
## [1,] 0.486246420
## [2,] -0.673469294
## [3,] 0.556554233
## [4,] -0.009145393
## [5,] -0.009145393
## [6,] -0.009145393# turning values as numeric and getting the max value of 1
max_value_decomp <- which.max(eigen(B)$values)
print(paste('The largest eigenvalue is', max(max_value_decomp)))## [1] "The largest eigenvalue is 1"# corresponding vector of max eigenvalue
eigen_decomp2 <- as.numeric((1/sum(eigen_decomp$vectors[,1]))*eigen_decomp$vectors[,1])
sum(eigen_decomp2)## [1] 1• Use the graph package in R and its page.rank method to compute the Page Rank of the graph as given in A. Note that you don’t need to apply decay. The package starts with a connected graph and applies decay internally. Verify that you do get the same PageRank vector as the two approaches above. (10 points)
# Here we are using the library 'igraph' installed at the begining to complete the question
#graph_A <- graph.adjacency(A, weighted = T)
graph_A <- graph_from_adjacency_matrix(A, weighted = T)
plot(graph_A)
# verifying that you get the same PageRank vector as the two approached above
pageRank <- page.rank(graph_A)$vector
results <- (round(iter_converg, 4) == round(pageRank, 4))
results## [,1]
## [1,] TRUE
## [2,] TRUE
## [3,] TRUE
## [4,] TRUE
## [5,] TRUE
## [6,] TRUEFinal Problem 2. 40 points.
1.Go to Kaggle.com and build an account if you do not already have one. It is free. 2. Go to https://www.kaggle.com/c/digit-recognizer/overview, accept the rules of the competition, and download the data. You will not be required to submit work to Kaggle, but you do need the data. ’MNIST (“Modified National Institute of Standards and Technology”) is the de facto “hello world” dataset of computer vision. Since its release in 1999, this classic dataset of handwritten images has served as the basis for benchmarking classification algorithms. As new machine learning techniques emerge, MNIST remains a reliable resource for researchers and learners alike.”
# Load data set from computer, file is too large to upload to free github account
# for knitting purposes I am not printing out the entire data set because it is too long.
train <- read.csv("C:/Users/Ivan/OneDrive/Desktop/train.csv/train.csv")
head(train[1:15], n = 5) # set to load columns 1-10 and 5 rows## label pixel0 pixel1 pixel2 pixel3 pixel4 pixel5 pixel6 pixel7 pixel8 pixel9
## 1 1 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0 0 0
## 3 1 0 0 0 0 0 0 0 0 0 0
## 4 4 0 0 0 0 0 0 0 0 0 0
## 5 0 0 0 0 0 0 0 0 0 0 0
## pixel10 pixel11 pixel12 pixel13
## 1 0 0 0 0
## 2 0 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0- Using the training.csv file, plot representations of the first 10 images to understand the data format. Go ahead and divide all pixels by 255 to produce values between 0 and 1. (This is equivalent to min-max scaling.) (5 points)
# label is the first column and divide all pixels by 255
labels = train[,1]
train_data <- train[,-1]/255
# dimensions of data frame
dim(train_data)## [1] 42000 784# creating a plot to see how one image looks
image1 <- matrix(unlist(train_data[10, -1]), nrow = 28, byrow = T)## Warning in matrix(unlist(train_data[10, -1]), nrow = 28, byrow = T): data length
## [783] is not a sub-multiple or multiple of the number of rows [28]image(image1, col = grey.colors(255))
# image must be rotated
rotate <- function(x) t(apply(x, 2, rev))
# final product; will be using this code to apply it to the first 10 images
image1 <- rotate(matrix(unlist(train_data[10, -1]), nrow = 28, byrow = T))## Warning in matrix(unlist(train_data[10, -1]), nrow = 28, byrow = T): data length
## [783] is not a sub-multiple or multiple of the number of rows [28]image(image1, col = grey.colors(255))
# Apply code above to images 1:10 of the whole data set
par(mfrow = c (2, 5))
# images must be rotated
rotate <- function(x) t(apply(x, 2, rev))
# Using a for loop for all 10 images
for (i in 1:10){
m <- rotate(matrix(unlist(train_data[i, -1]), nrow = 28, byrow = T))
image(m, col = grey.colors(255))
}## Warning in matrix(unlist(train_data[i, -1]), nrow = 28, byrow = T): data length
## [783] is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(unlist(train_data[i, -1]), nrow = 28, byrow = T): data length
## [783] is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(unlist(train_data[i, -1]), nrow = 28, byrow = T): data length
## [783] is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(unlist(train_data[i, -1]), nrow = 28, byrow = T): data length
## [783] is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(unlist(train_data[i, -1]), nrow = 28, byrow = T): data length
## [783] is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(unlist(train_data[i, -1]), nrow = 28, byrow = T): data length
## [783] is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(unlist(train_data[i, -1]), nrow = 28, byrow = T): data length
## [783] is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(unlist(train_data[i, -1]), nrow = 28, byrow = T): data length
## [783] is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(unlist(train_data[i, -1]), nrow = 28, byrow = T): data length
## [783] is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(unlist(train_data[i, -1]), nrow = 28, byrow = T): data length
## [783] is not a sub-multiple or multiple of the number of rows [28]
- What is the frequency distribution of the numbers in the dataset? (5 points)
train_frequency <- as.data.frame(table(labels)/42000)
# bar graph for frequency distribution
train_frequency %>%
ggplot(aes(x = labels, y = Freq, fill = Freq)) +
geom_bar(stat = 'identity') +
scale_fill_gradient(low = "blue", high = "red")
table(labels)/42000## labels
## 0 1 2 3 4 5 6
## 0.09838095 0.11152381 0.09945238 0.10359524 0.09695238 0.09035714 0.09850000
## 7 8 9
## 0.10478571 0.09673810 0.09971429- For each number, provide the mean pixel intensity. What does this tell you? (5 points)
# Using colMeans() I was only getting 0's.
colMeans(train_data)[1:20]## pixel0 pixel1 pixel2 pixel3 pixel4 pixel5
## 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## pixel6 pixel7 pixel8 pixel9 pixel10 pixel11
## 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## pixel12 pixel13 pixel14 pixel15 pixel16 pixel17
## 1.176471e-05 4.388422e-05 2.016807e-05 8.403361e-07 0.000000e+00 0.000000e+00
## pixel18 pixel19
## 0.000000e+00 0.000000e+00- Reduce the data by using principal components that account for 95% of the variance. How many components did you generate? Use PCA to generate all possible components (100% of the variance). How many components are possible? Why? (5 points)
# covariance
train_cov <- train_data
# pca
train_pca <- prcomp(train_cov)
train_cumvar <- (cumsum(train_pca$sdev^2) / sum(train_pca$sdev^2))
# 95% variance
cumvar_95 <- which.max(train_cumvar >= .95)
print(paste0("At 95% variance there were ", (cumvar_95), " components generated."))## [1] "At 95% variance there were 154 components generated."# 100% variance
print(paste0("At 100% variance thereshould be 784 components generated representing each column in the dataset."))## [1] "At 100% variance thereshould be 784 components generated representing each column in the dataset."plot(train_cumvar)
- Plot the first 10 images generated by PCA. They will appear to be noise. Why? (5 points)
par(mfrow = c (2, 5))
# images must be rotated
rotate <- function(x) t(apply(x, 2, rev))
# Using my for loop it reproduced static only
for (i in 1:10){
image(1:28, 1:28, array(train_pca$x[,i], dim = c(28, 28)))
}
# Using code from another student you can visualize more of a number that's blurry
for (i in 1:10){
img <- matrix(train_pca$rotation[1:784], nrow = 28, ncol = 28)
image(img, useRaster = T, axes = F)
}
- Now, select only those images that have labels that are 8’s. Re-run PCA that accounts for all of the variance (100%). Plot the first 10 images. What do you see? (5 points)
# Selecting only the 8's
eights <- train_data %>%
filter(labels == 8)
eights <- eights[,2:ncol(eights)]
# Reducing pixels to 255
eights_reduced <- eights / 255
eights_pca <- prcomp(eights_reduced)
#
eights_cumvar <- (cumsum(eights_pca$sdev^2) / sum(eights_pca$sdev^2))
# 100% variance
eights_100 <- which.max(eights_cumvar >= 1)
eights_100## [1] 537plot(eights_cumvar)
par(mfrow = c (2, 5))
# images must be rotated
rotate <- function(x) t(apply(x, 2, rev))
# When using my code, same thing happens as before
for (i in 1:10){
m <- rotate(matrix(eights_pca$x[,i], nrow = 28, byrow = T))
image(m, col = grey.colors(255))
}## Warning in matrix(eights_pca$x[, i], nrow = 28, byrow = T): data length [4063]
## is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(eights_pca$x[, i], nrow = 28, byrow = T): data length [4063]
## is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(eights_pca$x[, i], nrow = 28, byrow = T): data length [4063]
## is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(eights_pca$x[, i], nrow = 28, byrow = T): data length [4063]
## is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(eights_pca$x[, i], nrow = 28, byrow = T): data length [4063]
## is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(eights_pca$x[, i], nrow = 28, byrow = T): data length [4063]
## is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(eights_pca$x[, i], nrow = 28, byrow = T): data length [4063]
## is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(eights_pca$x[, i], nrow = 28, byrow = T): data length [4063]
## is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(eights_pca$x[, i], nrow = 28, byrow = T): data length [4063]
## is not a sub-multiple or multiple of the number of rows [28]
## Warning in matrix(eights_pca$x[, i], nrow = 28, byrow = T): data length [4063]
## is not a sub-multiple or multiple of the number of rows [28]
for (i in 1:10){
img <- matrix(eights_pca$rotation[1:784], nrow = 28, ncol = 28)
image(img, useRaster = T, axes = F)
}
- An incorrect approach to predicting the images would be to build a linear regression model with y as the digit values and X as the pixel matrix. Instead, we can build a multinomial model that classifies the digits. Build a multinomial model on the entirety of the training set. Then provide its classification accuracy (percent correctly identified) as well as a matrix of observed versus forecast values (confusion matrix). This matrix will be a 10 x 10, and correct classifications will be on the diagonal. (10 points)
# create model
train_label <- as.factor(train$label)
train_data <- train[2:785] / 255
train_data_label <- train$label
model <- nnet::multinom(labels ~., data = train_data, MaxNWts = 10000000)## # weights: 7860 (7065 variable)
## initial value 96708.573906
## iter 10 value 25322.714106
## iter 20 value 20402.086316
## iter 30 value 19312.872829
## iter 40 value 18703.256586
## iter 50 value 18197.815143
## iter 60 value 17732.985798
## iter 70 value 16739.962157
## iter 80 value 14961.658448
## iter 90 value 13446.085942
## iter 100 value 12442.636014
## final value 12442.636014
## stopped after 100 iterations# make the prediction and confusion matrix
prediction_model <- predict(model, train_data)
confusionMatrix(prediction_model, train_label)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2 3 4 5 6 7 8 9
## 0 3994 0 19 11 4 35 17 5 19 12
## 1 3 4588 59 32 20 39 28 37 134 18
## 2 11 13 3753 88 17 19 17 37 21 10
## 3 8 12 65 3879 9 91 1 9 91 53
## 4 13 6 60 10 3852 55 35 44 38 136
## 5 33 12 20 162 5 3386 45 10 132 33
## 6 35 3 38 15 22 52 3973 2 19 3
## 7 7 8 54 35 7 28 2 4076 18 87
## 8 20 32 85 78 22 51 17 4 3519 25
## 9 8 10 24 41 114 39 2 177 72 3811
##
## Overall Statistics
##
## Accuracy : 0.9245
## 95% CI : (0.922, 0.9271)
## No Information Rate : 0.1115
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.9161
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2 Class: 3 Class: 4 Class: 5
## Sensitivity 0.96660 0.9795 0.89849 0.89152 0.94597 0.89223
## Specificity 0.99678 0.9901 0.99384 0.99100 0.98953 0.98817
## Pos Pred Value 0.97036 0.9254 0.94155 0.91963 0.90657 0.88223
## Neg Pred Value 0.99636 0.9974 0.98885 0.98751 0.99417 0.98928
## Prevalence 0.09838 0.1115 0.09945 0.10360 0.09695 0.09036
## Detection Rate 0.09510 0.1092 0.08936 0.09236 0.09171 0.08062
## Detection Prevalence 0.09800 0.1180 0.09490 0.10043 0.10117 0.09138
## Balanced Accuracy 0.98169 0.9848 0.94617 0.94126 0.96775 0.94020
## Class: 6 Class: 7 Class: 8 Class: 9
## Sensitivity 0.9604 0.92615 0.86611 0.90998
## Specificity 0.9950 0.99346 0.99120 0.98712
## Pos Pred Value 0.9546 0.94308 0.91331 0.88669
## Neg Pred Value 0.9957 0.99137 0.98574 0.99000
## Prevalence 0.0985 0.10479 0.09674 0.09971
## Detection Rate 0.0946 0.09705 0.08379 0.09074
## Detection Prevalence 0.0991 0.10290 0.09174 0.10233
## Balanced Accuracy 0.9777 0.95981 0.92865 0.94855F inal Problem 3. 30 points You are to compete in the House Prices: Advanced Regression Techniques competition https://www.kaggle.com/c/house-prices-advanced-regression-techniques . I want you to do the following. Descriptive and Inferential Statistics. Provide univariate descriptive statistics and appropriate plots for the training data set. Provide a scatterplot matrix for at least two of the independent variables and the dependent variable. Derive a correlation matrix for any three quantitative variables in the dataset. Test the hypotheses that the correlations between each pairwise set of variables is 0 and provide an 80% confidence interval. Discuss the meaning of your analysis. Would you be worried about familywise error? Why or why not? 5 points
# Read csv file renaming train.csv to house_train
house_train <- read.csv("C:/Users/Ivan/OneDrive/Desktop/train.csv/train.csv", header = T, sep = ",")
head(house_train[1:15], n = 5)## label pixel0 pixel1 pixel2 pixel3 pixel4 pixel5 pixel6 pixel7 pixel8 pixel9
## 1 1 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0 0 0
## 3 1 0 0 0 0 0 0 0 0 0 0
## 4 4 0 0 0 0 0 0 0 0 0 0
## 5 0 0 0 0 0 0 0 0 0 0 0
## pixel10 pixel11 pixel12 pixel13
## 1 0 0 0 0
## 2 0 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0# glimpse of data set columns 1 - 10
glimpse(house_train[1:10])## Rows: 42,000
## Columns: 10
## $ label <int> 1, 0, 1, 4, 0, 0, 7, 3, 5, 3, 8, 9, 1, 3, 3, 1, 2, 0, 7, 5, 8, …
## $ pixel0 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ pixel1 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ pixel2 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ pixel3 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ pixel4 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ pixel5 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ pixel6 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ pixel7 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ pixel8 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …# summary of data set with filter of numeric values only
house_train %>%
select_if(is.numeric) %>%
summary()## label pixel0 pixel1 pixel2 pixel3 pixel4
## Min. :0.000 Min. :0 Min. :0 Min. :0 Min. :0 Min. :0
## 1st Qu.:2.000 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0
## Median :4.000 Median :0 Median :0 Median :0 Median :0 Median :0
## Mean :4.457 Mean :0 Mean :0 Mean :0 Mean :0 Mean :0
## 3rd Qu.:7.000 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0
## Max. :9.000 Max. :0 Max. :0 Max. :0 Max. :0 Max. :0
## pixel5 pixel6 pixel7 pixel8 pixel9 pixel10
## Min. :0 Min. :0 Min. :0 Min. :0 Min. :0 Min. :0
## 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0
## Median :0 Median :0 Median :0 Median :0 Median :0 Median :0
## Mean :0 Mean :0 Mean :0 Mean :0 Mean :0 Mean :0
## 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0
## Max. :0 Max. :0 Max. :0 Max. :0 Max. :0 Max. :0
## pixel11 pixel12 pixel13 pixel14
## Min. :0 Min. : 0.000 Min. : 0.00000 Min. :0.00e+00
## 1st Qu.:0 1st Qu.: 0.000 1st Qu.: 0.00000 1st Qu.:0.00e+00
## Median :0 Median : 0.000 Median : 0.00000 Median :0.00e+00
## Mean :0 Mean : 0.003 Mean : 0.01119 Mean :5.14e-03
## 3rd Qu.:0 3rd Qu.: 0.000 3rd Qu.: 0.00000 3rd Qu.:0.00e+00
## Max. :0 Max. :116.000 Max. :254.00000 Max. :2.16e+02
## pixel15 pixel16 pixel17 pixel18 pixel19 pixel20
## Min. :0.000000 Min. :0 Min. :0 Min. :0 Min. :0 Min. :0
## 1st Qu.:0.000000 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0
## Median :0.000000 Median :0 Median :0 Median :0 Median :0 Median :0
## Mean :0.000214 Mean :0 Mean :0 Mean :0 Mean :0 Mean :0
## 3rd Qu.:0.000000 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0
## Max. :9.000000 Max. :0 Max. :0 Max. :0 Max. :0 Max. :0
## pixel21 pixel22 pixel23 pixel24 pixel25 pixel26
## Min. :0 Min. :0 Min. :0 Min. :0 Min. :0 Min. :0
## 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0
## Median :0 Median :0 Median :0 Median :0 Median :0 Median :0
## Mean :0 Mean :0 Mean :0 Mean :0 Mean :0 Mean :0
## 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0
## Max. :0 Max. :0 Max. :0 Max. :0 Max. :0 Max. :0
## pixel27 pixel28 pixel29 pixel30 pixel31 pixel32
## Min. :0 Min. :0 Min. :0 Min. :0 Min. :0 Min. :0.00e+00
## 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0.00e+00
## Median :0 Median :0 Median :0 Median :0 Median :0 Median :0.00e+00
## Mean :0 Mean :0 Mean :0 Mean :0 Mean :0 Mean :3.81e-04
## 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0.00e+00
## Max. :0 Max. :0 Max. :0 Max. :0 Max. :0 Max. :1.60e+01
## pixel33 pixel34 pixel35 pixel36
## Min. : 0.00000 Min. : 0.00000 Min. : 0.00000 Min. : 0.0000
## 1st Qu.: 0.00000 1st Qu.: 0.00000 1st Qu.: 0.00000 1st Qu.: 0.0000
## Median : 0.00000 Median : 0.00000 Median : 0.00000 Median : 0.0000
## Mean : 0.00131 Mean : 0.01055 Mean : 0.02726 Mean : 0.0509
## 3rd Qu.: 0.00000 3rd Qu.: 0.00000 3rd Qu.: 0.00000 3rd Qu.: 0.0000
## Max. :47.00000 Max. :157.00000 Max. :254.00000 Max. :255.0000
## pixel37 pixel38 pixel39 pixel40
## Min. : 0.0000 Min. : 0.0000 Min. : 0.0000 Min. : 0.0000
## 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.0000
## Median : 0.0000 Median : 0.0000 Median : 0.0000 Median : 0.0000
## Mean : 0.0664 Mean : 0.1296 Mean : 0.1741 Mean : 0.1913
## 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000
## Max. :243.0000 Max. :255.0000 Max. :255.0000 Max. :255.0000
## pixel41 pixel42 pixel43 pixel44
## Min. : 0.0000 Min. : 0.0000 Min. : 0.0000 Min. : 0.0000
## 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.0000
## Median : 0.0000 Median : 0.0000 Median : 0.0000 Median : 0.0000
## Mean : 0.1906 Mean : 0.1961 Mean : 0.1714 Mean : 0.1645
## 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000
## Max. :255.0000 Max. :255.0000 Max. :255.0000 Max. :255.0000
## pixel45 pixel46 pixel47 pixel48
## Min. : 0.0000 Min. : 0.0000 Min. : 0.00000 Min. : 0.00000
## 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.00000 1st Qu.: 0.00000
## Median : 0.0000 Median : 0.0000 Median : 0.00000 Median : 0.00000
## Mean : 0.1517 Mean : 0.1053 Mean : 0.06079 Mean : 0.04507
## 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.00000 3rd Qu.: 0.00000
## Max. :255.0000 Max. :255.0000 Max. :255.00000 Max. :244.00000
## pixel49 pixel50 pixel51 pixel52
## Min. : 0.0000 Min. : 0.00000 Min. :0.00e+00 Min. :0
## 1st Qu.: 0.0000 1st Qu.: 0.00000 1st Qu.:0.00e+00 1st Qu.:0
## Median : 0.0000 Median : 0.00000 Median :0.00e+00 Median :0
## Mean : 0.0154 Mean : 0.01052 Mean :5.05e-03 Mean :0
## 3rd Qu.: 0.0000 3rd Qu.: 0.00000 3rd Qu.:0.00e+00 3rd Qu.:0
## Max. :255.0000 Max. :184.00000 Max. :1.97e+02 Max. :0
## pixel53 pixel54 pixel55 pixel56 pixel57 pixel58
## Min. :0 Min. :0 Min. :0 Min. :0 Min. :0 Min. : 0.00000
## 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.: 0.00000
## Median :0 Median :0 Median :0 Median :0 Median :0 Median : 0.00000
## Mean :0 Mean :0 Mean :0 Mean :0 Mean :0 Mean : 0.00152
## 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.: 0.00000
## Max. :0 Max. :0 Max. :0 Max. :0 Max. :0 Max. :64.00000
## pixel59 pixel60 pixel61 pixel62
## Min. :0.0e+00 Min. :0.00e+00 Min. :0.00e+00 Min. : 0.00000
## 1st Qu.:0.0e+00 1st Qu.:0.00e+00 1st Qu.:0.00e+00 1st Qu.: 0.00000
## Median :0.0e+00 Median :0.00e+00 Median :0.00e+00 Median : 0.00000
## Mean :6.9e-04 Mean :7.33e-03 Mean :9.02e-03 Mean : 0.06112
## 3rd Qu.:0.0e+00 3rd Qu.:0.00e+00 3rd Qu.:0.00e+00 3rd Qu.: 0.00000
## Max. :2.9e+01 Max. :1.34e+02 Max. :1.28e+02 Max. :234.00000
## pixel63 pixel64 pixel65 pixel66
## Min. : 0.0000 Min. : 0.0000 Min. : 0.0000 Min. : 0.0000
## 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.0000
## Median : 0.0000 Median : 0.0000 Median : 0.0000 Median : 0.0000
## Mean : 0.1511 Mean : 0.2959 Mean : 0.5337 Mean : 0.8694
## 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000
## Max. :255.0000 Max. :255.0000 Max. :255.0000 Max. :255.0000
## pixel67 pixel68 pixel69 pixel70
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.00
## Median : 0.000 Median : 0.000 Median : 0.000 Median : 0.00
## Mean : 1.346 Mean : 1.981 Mean : 2.699 Mean : 3.39
## 3rd Qu.: 0.000 3rd Qu.: 0.000 3rd Qu.: 0.000 3rd Qu.: 0.00
## Max. :255.000 Max. :255.000 Max. :255.000 Max. :255.00
## pixel71 pixel72 pixel73 pixel74
## Min. : 0.000 Min. : 0.00 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 0.000
## Median : 0.000 Median : 0.00 Median : 0.000 Median : 0.000
## Mean : 3.802 Mean : 3.74 Mean : 3.333 Mean : 2.684
## 3rd Qu.: 0.000 3rd Qu.: 0.00 3rd Qu.: 0.000 3rd Qu.: 0.000
## Max. :255.000 Max. :255.00 Max. :255.000 Max. :255.000
## pixel75 pixel76 pixel77 pixel78
## Min. : 0.000 Min. : 0.000 Min. : 0.0000 Min. : 0.0000
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.0000 1st Qu.: 0.0000
## Median : 0.000 Median : 0.000 Median : 0.0000 Median : 0.0000
## Mean : 1.993 Mean : 1.196 Mean : 0.6012 Mean : 0.2938
## 3rd Qu.: 0.000 3rd Qu.: 0.000 3rd Qu.: 0.0000 3rd Qu.: 0.0000
## Max. :255.000 Max. :255.000 Max. :255.0000 Max. :255.0000
## pixel79 pixel80 pixel81 pixel82
## Min. : 0.00000 Min. : 0.00000 Min. : 0.0000 Min. :0
## 1st Qu.: 0.00000 1st Qu.: 0.00000 1st Qu.: 0.0000 1st Qu.:0
## Median : 0.00000 Median : 0.00000 Median : 0.0000 Median :0
## Mean : 0.09848 Mean : 0.03495 Mean : 0.0084 Mean :0
## 3rd Qu.: 0.00000 3rd Qu.: 0.00000 3rd Qu.: 0.0000 3rd Qu.:0
## Max. :255.00000 Max. :255.00000 Max. :165.0000 Max. :0
## pixel83 pixel84 pixel85 pixel86 pixel87
## Min. :0 Min. :0 Min. :0 Min. :0.00e+00 Min. : 0.00000
## 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0.00e+00 1st Qu.: 0.00000
## Median :0 Median :0 Median :0 Median :0.00e+00 Median : 0.00000
## Mean :0 Mean :0 Mean :0 Mean :3.62e-03 Mean : 0.00417
## 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0.00e+00 3rd Qu.: 0.00000
## Max. :0 Max. :0 Max. :0 Max. :1.41e+02 Max. :84.00000
## pixel88 pixel89 pixel90 pixel91
## Min. : 0.0000 Min. : 0.00000 Min. : 0.0000 Min. : 0.0000
## 1st Qu.: 0.0000 1st Qu.: 0.00000 1st Qu.: 0.0000 1st Qu.: 0.0000
## Median : 0.0000 Median : 0.00000 Median : 0.0000 Median : 0.0000
## Mean : 0.0164 Mean : 0.08976 Mean : 0.2358 Mean : 0.5407
## 3rd Qu.: 0.0000 3rd Qu.: 0.00000 3rd Qu.: 0.0000 3rd Qu.: 0.0000
## Max. :139.0000 Max. :255.00000 Max. :255.0000 Max. :255.0000
## pixel92 pixel93 pixel94 pixel95
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000
## Median : 0.000 Median : 0.000 Median : 0.000 Median : 0.000
## Mean : 1.193 Mean : 2.293 Mean : 3.768 Mean : 5.714
## 3rd Qu.: 0.000 3rd Qu.: 0.000 3rd Qu.: 0.000 3rd Qu.: 0.000
## Max. :255.000 Max. :255.000 Max. :255.000 Max. :255.000
## pixel96 pixel97 pixel98 pixel99
## Min. : 0.000 Min. : 0.00 Min. : 0.00 Min. : 0.0
## 1st Qu.: 0.000 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.0
## Median : 0.000 Median : 0.00 Median : 0.00 Median : 0.0
## Mean : 7.751 Mean : 10.05 Mean : 12.07 Mean : 13.4
## 3rd Qu.: 0.000 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.0
## Max. :255.000 Max. :255.00 Max. :255.00 Max. :255.0
## pixel100 pixel101 pixel102 pixel103
## Min. : 0.00 Min. : 0.00 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 0.000
## Median : 0.00 Median : 0.00 Median : 0.000 Median : 0.000
## Mean : 13.07 Mean : 11.57 Mean : 9.296 Mean : 6.708
## 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.000 3rd Qu.: 0.000
## Max. :255.00 Max. :255.00 Max. :255.000 Max. :255.000
## pixel104 pixel105 pixel106 pixel107
## Min. : 0.00 Min. : 0.00 Min. : 0.000 Min. : 0.0000
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 0.0000
## Median : 0.00 Median : 0.00 Median : 0.000 Median : 0.0000
## Mean : 4.14 Mean : 2.27 Mean : 1.092 Mean : 0.4246
## 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.000 3rd Qu.: 0.0000
## Max. :255.00 Max. :255.00 Max. :255.000 Max. :255.0000
## pixel108 pixel109 pixel110 pixel111
## Min. : 0.000 Min. : 0.00000 Min. :0.00e+00 Min. :0
## 1st Qu.: 0.000 1st Qu.: 0.00000 1st Qu.:0.00e+00 1st Qu.:0
## Median : 0.000 Median : 0.00000 Median :0.00e+00 Median :0
## Mean : 0.168 Mean : 0.02374 Mean :2.88e-03 Mean :0
## 3rd Qu.: 0.000 3rd Qu.: 0.00000 3rd Qu.:0.00e+00 3rd Qu.:0
## Max. :255.000 Max. :164.00000 Max. :1.21e+02 Max. :0
## pixel112 pixel113 pixel114 pixel115
## Min. :0 Min. : 0.0000 Min. : 0.00000 Min. : 0.00000
## 1st Qu.:0 1st Qu.: 0.0000 1st Qu.: 0.00000 1st Qu.: 0.00000
## Median :0 Median : 0.0000 Median : 0.00000 Median : 0.00000
## Mean :0 Mean : 0.0009 Mean : 0.00274 Mean : 0.01607
## 3rd Qu.:0 3rd Qu.: 0.0000 3rd Qu.: 0.00000 3rd Qu.: 0.00000
## Max. :0 Max. :38.0000 Max. :51.00000 Max. :114.00000
## pixel116 pixel117 pixel118 pixel119
## Min. : 0.00000 Min. : 0.0000 Min. : 0.00 Min. : 0.000
## 1st Qu.: 0.00000 1st Qu.: 0.0000 1st Qu.: 0.00 1st Qu.: 0.000
## Median : 0.00000 Median : 0.0000 Median : 0.00 Median : 0.000
## Mean : 0.08826 Mean : 0.3887 Mean : 1.03 Mean : 2.455
## 3rd Qu.: 0.00000 3rd Qu.: 0.0000 3rd Qu.: 0.00 3rd Qu.: 0.000
## Max. :226.00000 Max. :255.0000 Max. :255.00 Max. :255.000
## pixel120 pixel121 pixel122 pixel123
## Min. : 0.000 Min. : 0.000 Min. : 0.0 Min. : 0.00
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.0 1st Qu.: 0.00
## Median : 0.000 Median : 0.000 Median : 0.0 Median : 0.00
## Mean : 4.953 Mean : 8.677 Mean : 13.8 Mean : 20.33
## 3rd Qu.: 0.000 3rd Qu.: 0.000 3rd Qu.: 0.0 3rd Qu.: 0.00
## Max. :255.000 Max. :255.000 Max. :255.0 Max. :255.00
## pixel124 pixel125 pixel126 pixel127
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00
## Median : 0.00 Median : 0.00 Median : 0.00 Median : 0.00
## Mean : 28.04 Mean : 36.08 Mean : 42.71 Mean : 46.09
## 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 10.00 3rd Qu.: 29.00
## Max. :255.00 Max. :255.00 Max. :255.00 Max. :255.00
## pixel128 pixel129 pixel130 pixel131
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00
## Median : 0.00 Median : 0.00 Median : 0.00 Median : 0.00
## Mean : 44.54 Mean : 38.95 Mean : 30.96 Mean : 22.91
## 3rd Qu.: 21.00 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.00
## Max. :255.00 Max. :255.00 Max. :255.00 Max. :255.00
## pixel132 pixel133 pixel134 pixel135
## Min. : 0.00 Min. : 0.000 Min. : 0.000 Min. : 0.0
## 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.0
## Median : 0.00 Median : 0.000 Median : 0.000 Median : 0.0
## Mean : 14.87 Mean : 8.692 Mean : 4.551 Mean : 2.1
## 3rd Qu.: 0.00 3rd Qu.: 0.000 3rd Qu.: 0.000 3rd Qu.: 0.0
## Max. :255.00 Max. :255.000 Max. :255.000 Max. :255.0
## pixel136 pixel137 pixel138 pixel139
## Min. : 0.0000 Min. : 0.0000 Min. : 0.00000 Min. :0
## 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.00000 1st Qu.:0
## Median : 0.0000 Median : 0.0000 Median : 0.00000 Median :0
## Mean : 0.8388 Mean : 0.2028 Mean : 0.03548 Mean :0
## 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.00000 3rd Qu.:0
## Max. :255.0000 Max. :254.0000 Max. :230.00000 Max. :0
## pixel140 pixel141 pixel142 pixel143
## Min. :0 Min. :0 Min. : 0.00000 Min. : 0.000
## 1st Qu.:0 1st Qu.:0 1st Qu.: 0.00000 1st Qu.: 0.000
## Median :0 Median :0 Median : 0.00000 Median : 0.000
## Mean :0 Mean :0 Mean : 0.00943 Mean : 0.048
## 3rd Qu.:0 3rd Qu.:0 3rd Qu.: 0.00000 3rd Qu.: 0.000
## Max. :0 Max. :0 Max. :95.00000 Max. :255.000
## pixel144 pixel145 pixel146 pixel147
## Min. : 0.0000 Min. : 0.000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.00
## Median : 0.0000 Median : 0.000 Median : 0.000 Median : 0.00
## Mean : 0.4116 Mean : 1.438 Mean : 3.558 Mean : 7.15
## 3rd Qu.: 0.0000 3rd Qu.: 0.000 3rd Qu.: 0.000 3rd Qu.: 0.00
## Max. :255.0000 Max. :255.000 Max. :255.000 Max. :255.00
## pixel148 pixel149 pixel150 pixel151
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00
## Median : 0.00 Median : 0.00 Median : 0.00 Median : 0.00
## Mean : 12.93 Mean : 21.42 Mean : 32.22 Mean : 45.36
## 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 27.00
## Max. :255.00 Max. :255.00 Max. :255.00 Max. :255.00
## pixel152 pixel153 pixel154 pixel155
## Min. : 0.00 Min. : 0.00 Min. : 0.0 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.0 1st Qu.: 0.00
## Median : 0.00 Median : 0.00 Median : 0.0 Median : 0.00
## Mean : 60.18 Mean : 75.01 Mean : 86.3 Mean : 91.59
## 3rd Qu.:114.00 3rd Qu.:175.00 3rd Qu.:213.0 3rd Qu.:225.00
## Max. :255.00 Max. :255.00 Max. :255.0 Max. :255.00
## pixel156 pixel157 pixel158 pixel159
## Min. : 0.00 Min. : 0.0 Min. : 0.00 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.0 1st Qu.: 0.00 1st Qu.: 0.00
## Median : 0.00 Median : 0.0 Median : 0.00 Median : 0.00
## Mean : 89.45 Mean : 80.3 Mean : 65.76 Mean : 49.65
## 3rd Qu.:220.00 3rd Qu.:194.0 3rd Qu.:138.00 3rd Qu.: 51.00
## Max. :255.00 Max. :255.0 Max. :255.00 Max. :255.00
## pixel160 pixel161 pixel162 pixel163
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.000
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000
## Median : 0.00 Median : 0.00 Median : 0.00 Median : 0.000
## Mean : 34.39 Mean : 21.46 Mean : 12.23 Mean : 6.375
## 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.000
## Max. :255.00 Max. :255.00 Max. :255.00 Max. :255.000
## pixel164 pixel165 pixel166 pixel167
## Min. : 0.000 Min. : 0.0000 Min. : 0.000 Min. :0.00e+00
## 1st Qu.: 0.000 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.:0.00e+00
## Median : 0.000 Median : 0.0000 Median : 0.000 Median :0.00e+00
## Mean : 2.906 Mean : 0.7934 Mean : 0.126 Mean :4.29e-04
## 3rd Qu.: 0.000 3rd Qu.: 0.0000 3rd Qu.: 0.000 3rd Qu.:0.00e+00
## Max. :255.000 Max. :255.0000 Max. :253.000 Max. :1.80e+01
## pixel168 pixel169 pixel170 pixel171
## Min. :0 Min. :0.0e+00 Min. : 0.0000 Min. : 0.0000
## 1st Qu.:0 1st Qu.:0.0e+00 1st Qu.: 0.0000 1st Qu.: 0.0000
## Median :0 Median :0.0e+00 Median : 0.0000 Median : 0.0000
## Mean :0 Mean :9.5e-05 Mean : 0.0231 Mean : 0.2284
## 3rd Qu.:0 3rd Qu.:0.0e+00 3rd Qu.: 0.0000 3rd Qu.: 0.0000
## Max. :0 Max. :4.0e+00 Max. :177.0000 Max. :255.0000
## pixel172 pixel173 pixel174 pixel175
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.00
## Median : 0.000 Median : 0.000 Median : 0.000 Median : 0.00
## Mean : 1.155 Mean : 3.268 Mean : 7.367 Mean : 14.11
## 3rd Qu.: 0.000 3rd Qu.: 0.000 3rd Qu.: 0.000 3rd Qu.: 0.00
## Max. :255.000 Max. :255.000 Max. :255.000 Max. :255.00
## pixel176 pixel177 pixel178 pixel179
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0
## Median : 0.00 Median : 0.00 Median : 0.00 Median : 0
## Mean : 24.13 Mean : 37.88 Mean : 54.01 Mean : 72
## 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 74.00 3rd Qu.:163
## Max. :255.00 Max. :255.00 Max. :255.00 Max. :255
## pixel180 pixel181 pixel182 pixel183
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## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.00 1st Qu.: 0.0000
## Median : 0.000 Median : 0.000 Median : 0.00 Median : 0.0000
## Mean : 2.749 Mean : 1.796 Mean : 1.09 Mean : 0.5632
## 3rd Qu.: 0.000 3rd Qu.: 0.000 3rd Qu.: 0.00 3rd Qu.: 0.0000
## Max. :255.000 Max. :255.000 Max. :255.00 Max. :255.0000
## pixel749 pixel750 pixel751 pixel752
## Min. : 0.0000 Min. : 0.00000 Min. : 0.00000 Min. :0.00e+00
## 1st Qu.: 0.0000 1st Qu.: 0.00000 1st Qu.: 0.00000 1st Qu.:0.00e+00
## Median : 0.0000 Median : 0.00000 Median : 0.00000 Median :0.00e+00
## Mean : 0.2396 Mean : 0.09352 Mean : 0.02483 Mean :8.57e-04
## 3rd Qu.: 0.0000 3rd Qu.: 0.00000 3rd Qu.: 0.00000 3rd Qu.:0.00e+00
## Max. :255.0000 Max. :255.00000 Max. :253.00000 Max. :2.80e+01
## pixel753 pixel754 pixel755 pixel756 pixel757 pixel758
## Min. : 0.0000 Min. :0 Min. :0 Min. :0 Min. :0 Min. :0
## 1st Qu.: 0.0000 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0
## Median : 0.0000 Median :0 Median :0 Median :0 Median :0 Median :0
## Mean : 0.0014 Mean :0 Mean :0 Mean :0 Mean :0 Mean :0
## 3rd Qu.: 0.0000 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0
## Max. :59.0000 Max. :0 Max. :0 Max. :0 Max. :0 Max. :0
## pixel759 pixel760 pixel761 pixel762
## Min. :0 Min. :0 Min. :0.00e+00 Min. : 0.00000
## 1st Qu.:0 1st Qu.:0 1st Qu.:0.00e+00 1st Qu.: 0.00000
## Median :0 Median :0 Median :0.00e+00 Median : 0.00000
## Mean :0 Mean :0 Mean :6.14e-03 Mean : 0.03583
## 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0.00e+00 3rd Qu.: 0.00000
## Max. :0 Max. :0 Max. :1.77e+02 Max. :231.00000
## pixel763 pixel764 pixel765 pixel766
## Min. : 0.00000 Min. : 0.0000 Min. : 0.0000 Min. : 0.0000
## 1st Qu.: 0.00000 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.0000
## Median : 0.00000 Median : 0.0000 Median : 0.0000 Median : 0.0000
## Mean : 0.08236 Mean : 0.1149 Mean : 0.1787 Mean : 0.3014
## 3rd Qu.: 0.00000 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000
## Max. :253.00000 Max. :254.0000 Max. :254.0000 Max. :255.0000
## pixel767 pixel768 pixel769 pixel770
## Min. : 0.0000 Min. : 0.0000 Min. : 0.0000 Min. : 0.0000
## 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.0000
## Median : 0.0000 Median : 0.0000 Median : 0.0000 Median : 0.0000
## Mean : 0.4136 Mean : 0.5137 Mean : 0.5588 Mean : 0.6779
## 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000
## Max. :255.0000 Max. :255.0000 Max. :255.0000 Max. :255.0000
## pixel771 pixel772 pixel773 pixel774
## Min. : 0.0000 Min. : 0.0000 Min. : 0.0000 Min. : 0.0000
## 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.0000
## Median : 0.0000 Median : 0.0000 Median : 0.0000 Median : 0.0000
## Mean : 0.6028 Mean : 0.4892 Mean : 0.3402 Mean : 0.2193
## 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000
## Max. :255.0000 Max. :255.0000 Max. :255.0000 Max. :254.0000
## pixel775 pixel776 pixel777 pixel778
## Min. : 0.0000 Min. : 0.00000 Min. : 0.00000 Min. : 0.00000
## 1st Qu.: 0.0000 1st Qu.: 0.00000 1st Qu.: 0.00000 1st Qu.: 0.00000
## Median : 0.0000 Median : 0.00000 Median : 0.00000 Median : 0.00000
## Mean : 0.1171 Mean : 0.05902 Mean : 0.02019 Mean : 0.01724
## 3rd Qu.: 0.0000 3rd Qu.: 0.00000 3rd Qu.: 0.00000 3rd Qu.: 0.00000
## Max. :254.0000 Max. :253.00000 Max. :253.00000 Max. :254.00000
## pixel779 pixel780 pixel781 pixel782 pixel783
## Min. : 0.00000 Min. :0 Min. :0 Min. :0 Min. :0
## 1st Qu.: 0.00000 1st Qu.:0 1st Qu.:0 1st Qu.:0 1st Qu.:0
## Median : 0.00000 Median :0 Median :0 Median :0 Median :0
## Mean : 0.00286 Mean :0 Mean :0 Mean :0 Mean :0
## 3rd Qu.: 0.00000 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0
## Max. :62.00000 Max. :0 Max. :0 Max. :0 Max. :0# plot to see overview of label
house_train%>%
ggplot( aes(x = label)) +
geom_histogram( binwidth = 0.5, fill = "blue", color = "#e9ecef", alpha = 10) +
ggtitle("Histogram of 'label'") +
theme_ipsum() +
theme(
plot.title = element_text(size = 15)
)## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
# selecting random columns to create a Correlogram
house_train%>%
ggpairs(columns = 44:53, ggplot2::aes(colour = 'label')) 
colnames(house_train)## [1] "label" "pixel0" "pixel1" "pixel2" "pixel3" "pixel4"
## [7] "pixel5" "pixel6" "pixel7" "pixel8" "pixel9" "pixel10"
## [13] "pixel11" "pixel12" "pixel13" "pixel14" "pixel15" "pixel16"
## [19] "pixel17" "pixel18" "pixel19" "pixel20" "pixel21" "pixel22"
## [25] "pixel23" "pixel24" "pixel25" "pixel26" "pixel27" "pixel28"
## [31] "pixel29" "pixel30" "pixel31" "pixel32" "pixel33" "pixel34"
## [37] "pixel35" "pixel36" "pixel37" "pixel38" "pixel39" "pixel40"
## [43] "pixel41" "pixel42" "pixel43" "pixel44" "pixel45" "pixel46"
## [49] "pixel47" "pixel48" "pixel49" "pixel50" "pixel51" "pixel52"
## [55] "pixel53" "pixel54" "pixel55" "pixel56" "pixel57" "pixel58"
## [61] "pixel59" "pixel60" "pixel61" "pixel62" "pixel63" "pixel64"
## [67] "pixel65" "pixel66" "pixel67" "pixel68" "pixel69" "pixel70"
## [73] "pixel71" "pixel72" "pixel73" "pixel74" "pixel75" "pixel76"
## [79] "pixel77" "pixel78" "pixel79" "pixel80" "pixel81" "pixel82"
## [85] "pixel83" "pixel84" "pixel85" "pixel86" "pixel87" "pixel88"
## [91] "pixel89" "pixel90" "pixel91" "pixel92" "pixel93" "pixel94"
## [97] "pixel95" "pixel96" "pixel97" "pixel98" "pixel99" "pixel100"
## [103] "pixel101" "pixel102" "pixel103" "pixel104" "pixel105" "pixel106"
## [109] "pixel107" "pixel108" "pixel109" "pixel110" "pixel111" "pixel112"
## [115] "pixel113" "pixel114" "pixel115" "pixel116" "pixel117" "pixel118"
## [121] "pixel119" "pixel120" "pixel121" "pixel122" "pixel123" "pixel124"
## [127] "pixel125" "pixel126" "pixel127" "pixel128" "pixel129" "pixel130"
## [133] "pixel131" "pixel132" "pixel133" "pixel134" "pixel135" "pixel136"
## [139] "pixel137" "pixel138" "pixel139" "pixel140" "pixel141" "pixel142"
## [145] "pixel143" "pixel144" "pixel145" "pixel146" "pixel147" "pixel148"
## [151] "pixel149" "pixel150" "pixel151" "pixel152" "pixel153" "pixel154"
## [157] "pixel155" "pixel156" "pixel157" "pixel158" "pixel159" "pixel160"
## [163] "pixel161" "pixel162" "pixel163" "pixel164" "pixel165" "pixel166"
## [169] "pixel167" "pixel168" "pixel169" "pixel170" "pixel171" "pixel172"
## [175] "pixel173" "pixel174" "pixel175" "pixel176" "pixel177" "pixel178"
## [181] "pixel179" "pixel180" "pixel181" "pixel182" "pixel183" "pixel184"
## [187] "pixel185" "pixel186" "pixel187" "pixel188" "pixel189" "pixel190"
## [193] "pixel191" "pixel192" "pixel193" "pixel194" "pixel195" "pixel196"
## [199] "pixel197" "pixel198" "pixel199" "pixel200" "pixel201" "pixel202"
## [205] "pixel203" "pixel204" "pixel205" "pixel206" "pixel207" "pixel208"
## [211] "pixel209" "pixel210" "pixel211" "pixel212" "pixel213" "pixel214"
## [217] "pixel215" "pixel216" "pixel217" "pixel218" "pixel219" "pixel220"
## [223] "pixel221" "pixel222" "pixel223" "pixel224" "pixel225" "pixel226"
## [229] "pixel227" "pixel228" "pixel229" "pixel230" "pixel231" "pixel232"
## [235] "pixel233" "pixel234" "pixel235" "pixel236" "pixel237" "pixel238"
## [241] "pixel239" "pixel240" "pixel241" "pixel242" "pixel243" "pixel244"
## [247] "pixel245" "pixel246" "pixel247" "pixel248" "pixel249" "pixel250"
## [253] "pixel251" "pixel252" "pixel253" "pixel254" "pixel255" "pixel256"
## [259] "pixel257" "pixel258" "pixel259" "pixel260" "pixel261" "pixel262"
## [265] "pixel263" "pixel264" "pixel265" "pixel266" "pixel267" "pixel268"
## [271] "pixel269" "pixel270" "pixel271" "pixel272" "pixel273" "pixel274"
## [277] "pixel275" "pixel276" "pixel277" "pixel278" "pixel279" "pixel280"
## [283] "pixel281" "pixel282" "pixel283" "pixel284" "pixel285" "pixel286"
## [289] "pixel287" "pixel288" "pixel289" "pixel290" "pixel291" "pixel292"
## [295] "pixel293" "pixel294" "pixel295" "pixel296" "pixel297" "pixel298"
## [301] "pixel299" "pixel300" "pixel301" "pixel302" "pixel303" "pixel304"
## [307] "pixel305" "pixel306" "pixel307" "pixel308" "pixel309" "pixel310"
## [313] "pixel311" "pixel312" "pixel313" "pixel314" "pixel315" "pixel316"
## [319] "pixel317" "pixel318" "pixel319" "pixel320" "pixel321" "pixel322"
## [325] "pixel323" "pixel324" "pixel325" "pixel326" "pixel327" "pixel328"
## [331] "pixel329" "pixel330" "pixel331" "pixel332" "pixel333" "pixel334"
## [337] "pixel335" "pixel336" "pixel337" "pixel338" "pixel339" "pixel340"
## [343] "pixel341" "pixel342" "pixel343" "pixel344" "pixel345" "pixel346"
## [349] "pixel347" "pixel348" "pixel349" "pixel350" "pixel351" "pixel352"
## [355] "pixel353" "pixel354" "pixel355" "pixel356" "pixel357" "pixel358"
## [361] "pixel359" "pixel360" "pixel361" "pixel362" "pixel363" "pixel364"
## [367] "pixel365" "pixel366" "pixel367" "pixel368" "pixel369" "pixel370"
## [373] "pixel371" "pixel372" "pixel373" "pixel374" "pixel375" "pixel376"
## [379] "pixel377" "pixel378" "pixel379" "pixel380" "pixel381" "pixel382"
## [385] "pixel383" "pixel384" "pixel385" "pixel386" "pixel387" "pixel388"
## [391] "pixel389" "pixel390" "pixel391" "pixel392" "pixel393" "pixel394"
## [397] "pixel395" "pixel396" "pixel397" "pixel398" "pixel399" "pixel400"
## [403] "pixel401" "pixel402" "pixel403" "pixel404" "pixel405" "pixel406"
## [409] "pixel407" "pixel408" "pixel409" "pixel410" "pixel411" "pixel412"
## [415] "pixel413" "pixel414" "pixel415" "pixel416" "pixel417" "pixel418"
## [421] "pixel419" "pixel420" "pixel421" "pixel422" "pixel423" "pixel424"
## [427] "pixel425" "pixel426" "pixel427" "pixel428" "pixel429" "pixel430"
## [433] "pixel431" "pixel432" "pixel433" "pixel434" "pixel435" "pixel436"
## [439] "pixel437" "pixel438" "pixel439" "pixel440" "pixel441" "pixel442"
## [445] "pixel443" "pixel444" "pixel445" "pixel446" "pixel447" "pixel448"
## [451] "pixel449" "pixel450" "pixel451" "pixel452" "pixel453" "pixel454"
## [457] "pixel455" "pixel456" "pixel457" "pixel458" "pixel459" "pixel460"
## [463] "pixel461" "pixel462" "pixel463" "pixel464" "pixel465" "pixel466"
## [469] "pixel467" "pixel468" "pixel469" "pixel470" "pixel471" "pixel472"
## [475] "pixel473" "pixel474" "pixel475" "pixel476" "pixel477" "pixel478"
## [481] "pixel479" "pixel480" "pixel481" "pixel482" "pixel483" "pixel484"
## [487] "pixel485" "pixel486" "pixel487" "pixel488" "pixel489" "pixel490"
## [493] "pixel491" "pixel492" "pixel493" "pixel494" "pixel495" "pixel496"
## [499] "pixel497" "pixel498" "pixel499" "pixel500" "pixel501" "pixel502"
## [505] "pixel503" "pixel504" "pixel505" "pixel506" "pixel507" "pixel508"
## [511] "pixel509" "pixel510" "pixel511" "pixel512" "pixel513" "pixel514"
## [517] "pixel515" "pixel516" "pixel517" "pixel518" "pixel519" "pixel520"
## [523] "pixel521" "pixel522" "pixel523" "pixel524" "pixel525" "pixel526"
## [529] "pixel527" "pixel528" "pixel529" "pixel530" "pixel531" "pixel532"
## [535] "pixel533" "pixel534" "pixel535" "pixel536" "pixel537" "pixel538"
## [541] "pixel539" "pixel540" "pixel541" "pixel542" "pixel543" "pixel544"
## [547] "pixel545" "pixel546" "pixel547" "pixel548" "pixel549" "pixel550"
## [553] "pixel551" "pixel552" "pixel553" "pixel554" "pixel555" "pixel556"
## [559] "pixel557" "pixel558" "pixel559" "pixel560" "pixel561" "pixel562"
## [565] "pixel563" "pixel564" "pixel565" "pixel566" "pixel567" "pixel568"
## [571] "pixel569" "pixel570" "pixel571" "pixel572" "pixel573" "pixel574"
## [577] "pixel575" "pixel576" "pixel577" "pixel578" "pixel579" "pixel580"
## [583] "pixel581" "pixel582" "pixel583" "pixel584" "pixel585" "pixel586"
## [589] "pixel587" "pixel588" "pixel589" "pixel590" "pixel591" "pixel592"
## [595] "pixel593" "pixel594" "pixel595" "pixel596" "pixel597" "pixel598"
## [601] "pixel599" "pixel600" "pixel601" "pixel602" "pixel603" "pixel604"
## [607] "pixel605" "pixel606" "pixel607" "pixel608" "pixel609" "pixel610"
## [613] "pixel611" "pixel612" "pixel613" "pixel614" "pixel615" "pixel616"
## [619] "pixel617" "pixel618" "pixel619" "pixel620" "pixel621" "pixel622"
## [625] "pixel623" "pixel624" "pixel625" "pixel626" "pixel627" "pixel628"
## [631] "pixel629" "pixel630" "pixel631" "pixel632" "pixel633" "pixel634"
## [637] "pixel635" "pixel636" "pixel637" "pixel638" "pixel639" "pixel640"
## [643] "pixel641" "pixel642" "pixel643" "pixel644" "pixel645" "pixel646"
## [649] "pixel647" "pixel648" "pixel649" "pixel650" "pixel651" "pixel652"
## [655] "pixel653" "pixel654" "pixel655" "pixel656" "pixel657" "pixel658"
## [661] "pixel659" "pixel660" "pixel661" "pixel662" "pixel663" "pixel664"
## [667] "pixel665" "pixel666" "pixel667" "pixel668" "pixel669" "pixel670"
## [673] "pixel671" "pixel672" "pixel673" "pixel674" "pixel675" "pixel676"
## [679] "pixel677" "pixel678" "pixel679" "pixel680" "pixel681" "pixel682"
## [685] "pixel683" "pixel684" "pixel685" "pixel686" "pixel687" "pixel688"
## [691] "pixel689" "pixel690" "pixel691" "pixel692" "pixel693" "pixel694"
## [697] "pixel695" "pixel696" "pixel697" "pixel698" "pixel699" "pixel700"
## [703] "pixel701" "pixel702" "pixel703" "pixel704" "pixel705" "pixel706"
## [709] "pixel707" "pixel708" "pixel709" "pixel710" "pixel711" "pixel712"
## [715] "pixel713" "pixel714" "pixel715" "pixel716" "pixel717" "pixel718"
## [721] "pixel719" "pixel720" "pixel721" "pixel722" "pixel723" "pixel724"
## [727] "pixel725" "pixel726" "pixel727" "pixel728" "pixel729" "pixel730"
## [733] "pixel731" "pixel732" "pixel733" "pixel734" "pixel735" "pixel736"
## [739] "pixel737" "pixel738" "pixel739" "pixel740" "pixel741" "pixel742"
## [745] "pixel743" "pixel744" "pixel745" "pixel746" "pixel747" "pixel748"
## [751] "pixel749" "pixel750" "pixel751" "pixel752" "pixel753" "pixel754"
## [757] "pixel755" "pixel756" "pixel757" "pixel758" "pixel759" "pixel760"
## [763] "pixel761" "pixel762" "pixel763" "pixel764" "pixel765" "pixel766"
## [769] "pixel767" "pixel768" "pixel769" "pixel770" "pixel771" "pixel772"
## [775] "pixel773" "pixel774" "pixel775" "pixel776" "pixel777" "pixel778"
## [781] "pixel779" "pixel780" "pixel781" "pixel782" "pixel783"# plot for label and pixel781
house_train %>%
ggplot(aes(x = label, y = pixel781, color = pixel0)) +
geom_point(size = 3) +
geom_smooth(method = "lm", color = 'red') +
theme_ipsum()## `geom_smooth()` using formula = 'y ~ x'## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
# plot for label and pixel227
house_train %>%
ggplot(aes(x = label, y = pixel227, color = pixel621)) +
geom_point(size = 3) +
geom_smooth(method = "lm", color = 'red') +
theme_ipsum()## `geom_smooth()` using formula = 'y ~ x'## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
cor_house <- house_train %>%
dplyr::select(label, pixel227, pixel621)
cor_m <- cor(cor_house)
cor_m## label pixel227 pixel621
## label 1.00000000 0.03833434 -0.14340160
## pixel227 0.03833434 1.00000000 -0.01371602
## pixel621 -0.14340160 -0.01371602 1.00000000cor.test(house_train$label, house_train$pixel227, conf.level = 0.8)##
## Pearson's product-moment correlation
##
## data: house_train$label and house_train$pixel227
## t = 7.8618, df = 41998, p-value = 3.877e-15
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
## 0.03208856 0.04457713
## sample estimates:
## cor
## 0.03833434cor.test(house_train$label, house_train$pixel222, conf.level = 0.8)##
## Pearson's product-moment correlation
##
## data: house_train$label and house_train$pixel222
## t = 4.2464, df = 41998, p-value = 2.177e-05
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
## 0.01446476 0.02696634
## sample estimates:
## cor
## 0.02071636cor.test(house_train$pixel222, house_train$pixel227, conf.level = 0.8)##
## Pearson's product-moment correlation
##
## data: house_train$pixel222 and house_train$pixel227
## t = -0.97887, df = 41998, p-value = 0.3277
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
## -0.011029594 0.001477067
## sample estimates:
## cor
## -0.00477645Linear Algebra and Correlation. Invert your correlation matrix from above. (This is known as the precision matrix and contains variance inflation factors on the diagonal.) Multiply the correlation matrix by the precision matrix, and then multiply the precision matrix by the correlation matrix. Conduct LU decomposition on the matrix. 5 points
# invert correlation matrix from above
invert_cor <- solve(cor_m)
invert_cor## label pixel227 pixel621
## label 1.02237661 -0.03718822 0.1461004
## pixel227 -0.03718822 1.00154086 0.0084043
## pixel621 0.14610036 0.00840430 1.0210663# precision
precision_cor <- round(cor_m %*% invert_cor)
precision_cor## label pixel227 pixel621
## label 1 0 0
## pixel227 0 1 0
## pixel621 0 0 1# LU decomposition
lu_decom_cor <- lu.decomposition(cor_m)
lu_decom_cor## $L
## [,1] [,2] [,3]
## [1,] 1.00000000 0.000000000 0
## [2,] 0.03833434 1.000000000 0
## [3,] -0.14340160 -0.008230905 1
##
## $U
## [,1] [,2] [,3]
## [1,] 1 0.03833434 -0.14340160
## [2,] 0 0.99853048 -0.00821881
## [3,] 0 0.00000000 0.97936833Calculus-Based Probability & Statistics. Many times, it makes sense to fit a closed form distribution to data. Select a variable in the Kaggle.com training dataset that is skewed to the right, shift it so that the minimum value is absolutely above zero if necessary. Then load the MASS package and run fitdistr to fit an exponential probability density function. (See https://stat.ethz.ch/R-manual/Rdevel/library/MASS/html/fitdistr.html ). Find the optimal value of λ for this distribution, and then take 1000 samples from this exponential distribution using this value (e.g., rexp(1000, λ)). Plot a histogram and compare it with a histogram of your original variable. Using the exponential pdf, find the 5th and 95th percentiles using the cumulative distribution function (CDF). Also generate a 95% confidence interval from the empirical data, assuming normality. Finally, provide the empirical 5th percentile and 95th percentile of the data. Discuss. 10 points
# Select a variable in the Kaggle.com training dataset that is skewed to the right, shift it so that the minimum value is absolutely above zero if necessary.
house_train%>%
filter(pixel437 < 350) %>%
ggplot( aes(x = pixel437)) +
geom_histogram( binwidth = 15, fill = "purple", color = "#e9ecef", alpha = 0.9) +
ggtitle("Histogram of 'pixel437'") +
theme_ipsum() +
theme(
plot.title = element_text(size=15)
)## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
# exponential distribution
expon_pixel437 <- fitdistr(house_train$pixel437, 'exponential')
# lambda
lamb_pixel437 <- expon_pixel437$estimate
lamb_pixel437## rate
## 0.008216964# sample of 1000
exp_samp <- rexp(1000, lamb_pixel437)
summary(exp_samp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0176 34.0550 80.1771 119.8788 172.2020 871.2335# Plot histogram and compare it with original histogram
hist(exp_samp, main = "Histogram of Exponential Sample of 'pixel437'")
# 5th and 95th percentiles
lower <- qexp(0.05, lamb_pixel437)
lower## [1] 6.242366upper <- qexp(0.95, lamb_pixel437)
upper## [1] 364.579# empirical 5th and 95th percentile
quantile(house_train$pixel437, c(0.05, 0.95))## 5% 95%
## 0 254print(paste('The 5th percentile is 0.00 and the 95th percentile is 175.05.'))## [1] "The 5th percentile is 0.00 and the 95th percentile is 175.05."Modeling. Build some type of multiple regression model and submit your model to the competition board. Provide your complete model summary and results with analysis. Report your Kaggle.com user name and score. 10 points
# selection columns that are numeric only
house_train2 <- house_train %>%
dplyr::select_if(is.numeric)
# Check for missing values in data
colSums(is.na(house_train2))## label pixel0 pixel1 pixel2 pixel3 pixel4 pixel5 pixel6
## 0 0 0 0 0 0 0 0
## pixel7 pixel8 pixel9 pixel10 pixel11 pixel12 pixel13 pixel14
## 0 0 0 0 0 0 0 0
## pixel15 pixel16 pixel17 pixel18 pixel19 pixel20 pixel21 pixel22
## 0 0 0 0 0 0 0 0
## pixel23 pixel24 pixel25 pixel26 pixel27 pixel28 pixel29 pixel30
## 0 0 0 0 0 0 0 0
## pixel31 pixel32 pixel33 pixel34 pixel35 pixel36 pixel37 pixel38
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## 0 0 0 0 0 0 0 0
## pixel783
## 0model_house <- lm(pixel310 ~., house_train2)
summary(model_house)##
## Call:
## lm(formula = pixel310 ~ ., data = house_train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -95.502 -0.211 -0.004 0.191 138.818
##
## Coefficients: (80 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.318e-02 8.020e-02 0.663 0.507282
## label 9.889e-03 9.705e-03 1.019 0.308265
## pixel0 NA NA NA NA
## pixel1 NA NA NA NA
## pixel2 NA NA NA NA
## pixel3 NA NA NA NA
## pixel4 NA NA NA NA
## pixel5 NA NA NA NA
## pixel6 NA NA NA NA
## pixel7 NA NA NA NA
## pixel8 NA NA NA NA
## pixel9 NA NA NA NA
## pixel10 NA NA NA NA
## pixel11 NA NA NA NA
## pixel12 2.283e-03 5.398e-02 0.042 0.966272
## pixel13 -8.690e-04 1.887e-02 -0.046 0.963261
## pixel14 NA NA NA NA
## pixel15 NA NA NA NA
## pixel16 NA NA NA NA
## pixel17 NA NA NA NA
## pixel18 NA NA NA NA
## pixel19 NA NA NA NA
## pixel20 NA NA NA NA
## pixel21 NA NA NA NA
## pixel22 NA NA NA NA
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## pixel24 NA NA NA NA
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## pixel26 NA NA NA NA
## pixel27 NA NA NA NA
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## pixel29 NA NA NA NA
## pixel30 NA NA NA NA
## pixel31 NA NA NA NA
## pixel32 2.037e-01 2.202e+00 0.093 0.926291
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## pixel34 1.177e-03 5.340e-02 0.022 0.982410
## pixel35 -1.803e-04 2.260e-02 -0.008 0.993636
## pixel36 -1.521e-04 8.962e-03 -0.017 0.986461
## pixel37 -1.006e-06 8.905e-03 0.000 0.999910
## pixel38 -6.120e-04 6.240e-03 -0.098 0.921873
## pixel39 1.744e-04 5.608e-03 0.031 0.975190
## pixel40 -1.930e-04 5.014e-03 -0.038 0.969304
## pixel41 1.190e-04 5.368e-03 0.022 0.982314
## pixel42 -2.795e-04 5.308e-03 -0.053 0.958001
## pixel43 -2.042e-04 4.886e-03 -0.042 0.966661
## pixel44 -4.036e-04 5.206e-03 -0.078 0.938209
## pixel45 1.695e-04 5.497e-03 0.031 0.975406
## pixel46 -5.777e-04 5.940e-03 -0.097 0.922524
## pixel47 -5.645e-04 8.828e-03 -0.064 0.949015
## pixel48 3.692e-04 1.067e-02 0.035 0.972385
## pixel49 -1.340e-03 2.303e-02 -0.058 0.953586
## pixel50 2.647e-03 3.347e-02 0.079 0.936957
## pixel51 -1.300e-03 3.087e-02 -0.042 0.966404
## pixel52 NA NA NA NA
## pixel53 NA NA NA NA
## pixel54 NA NA NA NA
## pixel55 NA NA NA NA
## pixel56 NA NA NA NA
## pixel57 NA NA NA NA
## pixel58 -8.889e-02 8.989e-01 -0.099 0.921232
## pixel59 1.897e-03 2.099e-01 0.009 0.992791
## pixel60 3.289e-04 1.958e-02 0.017 0.986601
## pixel61 5.639e-05 2.728e-02 0.002 0.998351
## pixel62 -1.570e-04 1.162e-02 -0.014 0.989216
## pixel63 9.277e-04 7.291e-03 0.127 0.898752
## pixel64 1.288e-04 4.906e-03 0.026 0.979053
## pixel65 -6.152e-04 3.909e-03 -0.157 0.874953
## pixel66 1.875e-04 3.095e-03 0.061 0.951689
## pixel67 2.585e-04 2.544e-03 0.102 0.919066
## pixel68 1.353e-04 2.108e-03 0.064 0.948829
## pixel69 3.785e-04 1.859e-03 0.204 0.838669
## pixel70 6.631e-05 1.695e-03 0.039 0.968787
## pixel71 3.068e-04 1.604e-03 0.191 0.848334
## pixel72 1.039e-04 1.599e-03 0.065 0.948188
## pixel73 -8.745e-05 1.653e-03 -0.053 0.957822
## pixel74 2.752e-04 1.817e-03 0.151 0.879612
## pixel75 1.027e-04 2.062e-03 0.050 0.960269
## pixel76 -1.285e-04 2.649e-03 -0.049 0.961308
## pixel77 5.848e-04 3.714e-03 0.157 0.874893
## pixel78 -8.306e-04 5.114e-03 -0.162 0.870987
## pixel79 1.470e-03 8.936e-03 0.165 0.869306
## pixel80 -2.727e-03 1.604e-02 -0.170 0.865037
## pixel81 7.974e-03 3.131e-02 0.255 0.798977
## pixel82 NA NA NA NA
## pixel83 NA NA NA NA
## pixel84 NA NA NA NA
## pixel85 NA NA NA NA
## pixel86 3.877e-02 4.073e-01 0.095 0.924163
## pixel87 2.624e-03 6.014e-02 0.044 0.965202
## pixel88 3.573e-03 1.793e-02 0.199 0.842077
## pixel89 1.149e-03 8.127e-03 0.141 0.887597
## pixel90 -3.824e-04 6.297e-03 -0.061 0.951574
## pixel91 -5.452e-04 4.545e-03 -0.120 0.904516
## pixel92 -3.195e-04 2.930e-03 -0.109 0.913163
## pixel93 3.713e-04 2.307e-03 0.161 0.872139
## pixel94 -1.575e-04 1.910e-03 -0.082 0.934269
## pixel95 1.607e-04 1.658e-03 0.097 0.922798
## pixel96 -5.167e-05 1.452e-03 -0.036 0.971624
## pixel97 -1.501e-05 1.288e-03 -0.012 0.990702
## pixel98 4.463e-05 1.178e-03 0.038 0.969783
## pixel99 -1.421e-04 1.099e-03 -0.129 0.897110
## pixel100 2.769e-04 1.090e-03 0.254 0.799562
## pixel101 1.677e-04 1.107e-03 0.151 0.879590
## pixel102 -2.740e-04 1.206e-03 -0.227 0.820302
## pixel103 1.579e-04 1.384e-03 0.114 0.909174
## pixel104 4.215e-05 1.670e-03 0.025 0.979863
## pixel105 -4.801e-04 2.129e-03 -0.226 0.821578
## pixel106 5.564e-04 3.017e-03 0.184 0.853696
## pixel107 -1.487e-04 4.267e-03 -0.035 0.972192
## pixel108 6.075e-04 5.809e-03 0.105 0.916706
## pixel109 -1.825e-03 1.627e-02 -0.112 0.910691
## pixel110 2.869e-03 3.124e-02 0.092 0.926840
## pixel111 NA NA NA NA
## pixel112 NA NA NA NA
## pixel113 4.899e-04 9.390e-02 0.005 0.995838
## pixel114 -6.789e-03 6.495e-02 -0.105 0.916754
## pixel115 2.372e-03 2.265e-02 0.105 0.916587
## pixel116 -1.746e-03 7.491e-03 -0.233 0.815702
## pixel117 1.023e-03 4.147e-03 0.247 0.805198
## pixel118 7.176e-05 3.138e-03 0.023 0.981756
## pixel119 2.800e-05 2.296e-03 0.012 0.990270
## pixel120 8.963e-05 1.790e-03 0.050 0.960062
## pixel121 -4.355e-04 1.421e-03 -0.307 0.759171
## pixel122 1.505e-04 1.167e-03 0.129 0.897338
## pixel123 -1.732e-04 9.879e-04 -0.175 0.860831
## pixel124 -7.636e-05 8.517e-04 -0.090 0.928560
## pixel125 1.008e-04 7.510e-04 0.134 0.893227
## pixel126 -1.125e-04 6.839e-04 -0.164 0.869400
## pixel127 1.178e-04 6.513e-04 0.181 0.856493
## pixel128 -1.237e-04 6.531e-04 -0.189 0.849845
## pixel129 3.597e-05 6.745e-04 0.053 0.957475
## pixel130 -1.415e-04 7.334e-04 -0.193 0.846992
## pixel131 5.930e-05 8.010e-04 0.074 0.940984
## pixel132 -9.643e-05 9.230e-04 -0.104 0.916791
## pixel133 1.175e-04 1.134e-03 0.104 0.917445
## pixel134 -3.717e-05 1.446e-03 -0.026 0.979488
## pixel135 5.771e-05 2.028e-03 0.028 0.977302
## pixel136 -2.289e-04 2.951e-03 -0.078 0.938171
## pixel137 5.992e-05 5.225e-03 0.011 0.990851
## pixel138 -5.573e-04 9.450e-03 -0.059 0.952978
## pixel139 NA NA NA NA
## pixel140 NA NA NA NA
## pixel141 NA NA NA NA
## pixel142 -2.637e-03 2.097e-02 -0.126 0.899928
## pixel143 -2.077e-03 1.177e-02 -0.176 0.859953
## pixel144 1.357e-03 4.222e-03 0.321 0.747981
## pixel145 -1.362e-03 2.663e-03 -0.511 0.609118
## pixel146 -3.963e-04 1.927e-03 -0.206 0.837037
## pixel147 3.805e-06 1.507e-03 0.003 0.997985
## pixel148 2.683e-04 1.191e-03 0.225 0.821746
## pixel149 3.061e-05 9.766e-04 0.031 0.974995
## pixel150 4.779e-05 8.254e-04 0.058 0.953830
## pixel151 2.448e-04 7.446e-04 0.329 0.742301
## pixel152 -3.572e-05 6.789e-04 -0.053 0.958036
## pixel153 4.243e-05 6.289e-04 0.067 0.946217
## pixel154 2.077e-04 5.935e-04 0.350 0.726336
## pixel155 1.038e-04 5.697e-04 0.182 0.855483
## pixel156 2.899e-04 5.593e-04 0.518 0.604264
## pixel157 2.144e-04 5.600e-04 0.383 0.701827
## pixel158 1.062e-04 5.786e-04 0.184 0.854333
## pixel159 2.489e-05 6.276e-04 0.040 0.968360
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## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.531 on 41295 degrees of freedom
## Multiple R-squared: 0.8508, Adjusted R-squared: 0.8482
## F-statistic: 334.5 on 704 and 41295 DF, p-value: < 2.2e-16plot(model_house)## Warning: not plotting observations with leverage one:
## 7282, 7896, 17491, 19297, 20611, 20740, 22510, 23459, 29554, 30102, 35364, 38324, 38895
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
model_house2 <- lm(label ~ pixel0 + pixel1 + pixel2 + pixel3 + pixel4 + pixel5 + pixel6 + pixel7 + pixel8 + pixel9 + pixel10 + pixel11 + pixel12 + pixel13 + pixel14 + pixel15 + pixel16 + pixel17 + pixel18 + pixel19 + pixel20 + pixel21 + pixel22 + pixel23 + pixel24 + pixel25 + pixel26 + pixel27 + pixel28 + pixel29 + pixel30 + pixel31 + pixel32 + pixel33 + pixel34 + pixel35, house_train2)
summary(model_house2)##
## Call:
## lm(formula = label ~ pixel0 + pixel1 + pixel2 + pixel3 + pixel4 +
## pixel5 + pixel6 + pixel7 + pixel8 + pixel9 + pixel10 + pixel11 +
## pixel12 + pixel13 + pixel14 + pixel15 + pixel16 + pixel17 +
## pixel18 + pixel19 + pixel20 + pixel21 + pixel22 + pixel23 +
## pixel24 + pixel25 + pixel26 + pixel27 + pixel28 + pixel29 +
## pixel30 + pixel31 + pixel32 + pixel33 + pixel34 + pixel35,
## data = house_train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4564 -2.4564 -0.4564 2.5436 4.5436
##
## Coefficients: (30 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.45641 0.01409 316.219 <2e-16 ***
## pixel0 NA NA NA NA
## pixel1 NA NA NA NA
## pixel2 NA NA NA NA
## pixel3 NA NA NA NA
## pixel4 NA NA NA NA
## pixel5 NA NA NA NA
## pixel6 NA NA NA NA
## pixel7 NA NA NA NA
## pixel8 NA NA NA NA
## pixel9 NA NA NA NA
## pixel10 NA NA NA NA
## pixel11 NA NA NA NA
## pixel12 0.04252 0.04276 0.994 0.320
## pixel13 -0.01334 0.01493 -0.893 0.372
## pixel14 NA NA NA NA
## pixel15 NA NA NA NA
## pixel16 NA NA NA NA
## pixel17 NA NA NA NA
## pixel18 NA NA NA NA
## pixel19 NA NA NA NA
## pixel20 NA NA NA NA
## pixel21 NA NA NA NA
## pixel22 NA NA NA NA
## pixel23 NA NA NA NA
## pixel24 NA NA NA NA
## pixel25 NA NA NA NA
## pixel26 NA NA NA NA
## pixel27 NA NA NA NA
## pixel28 NA NA NA NA
## pixel29 NA NA NA NA
## pixel30 NA NA NA NA
## pixel31 NA NA NA NA
## pixel32 -0.29252 1.72876 -0.169 0.866
## pixel33 0.13242 0.58530 0.226 0.821
## pixel34 -0.01162 0.03988 -0.291 0.771
## pixel35 0.01172 0.01581 0.741 0.459
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.888 on 41993 degrees of freedom
## Multiple R-squared: 6.981e-05, Adjusted R-squared: -7.306e-05
## F-statistic: 0.4886 on 6 and 41993 DF, p-value: 0.8174plot(model_house2)## Warning: not plotting observations with leverage one:
## 19297, 20740, 35364
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
# Using only significant columns
model_house3 <- lm(label ~ pixel0 + pixel1 + pixel2 + pixel3 + pixel4 + pixel5 + pixel6 + pixel7 + pixel8 + pixel9 + pixel10 + pixel11 + pixel12 + pixel13 + pixel14 + pixel15 + pixel16 + pixel17 + pixel18 + pixel19 + pixel20 + pixel21 + pixel22 + pixel23 + pixel24 + pixel25 + pixel26 + pixel27 + pixel28 + pixel29 + pixel30, house_train2)
summary(model_house3)##
## Call:
## lm(formula = label ~ pixel0 + pixel1 + pixel2 + pixel3 + pixel4 +
## pixel5 + pixel6 + pixel7 + pixel8 + pixel9 + pixel10 + pixel11 +
## pixel12 + pixel13 + pixel14 + pixel15 + pixel16 + pixel17 +
## pixel18 + pixel19 + pixel20 + pixel21 + pixel22 + pixel23 +
## pixel24 + pixel25 + pixel26 + pixel27 + pixel28 + pixel29 +
## pixel30, data = house_train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4567 -2.4567 -0.4567 2.5433 4.5433
##
## Coefficients: (29 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.45666 0.01409 316.273 <2e-16 ***
## pixel0 NA NA NA NA
## pixel1 NA NA NA NA
## pixel2 NA NA NA NA
## pixel3 NA NA NA NA
## pixel4 NA NA NA NA
## pixel5 NA NA NA NA
## pixel6 NA NA NA NA
## pixel7 NA NA NA NA
## pixel8 NA NA NA NA
## pixel9 NA NA NA NA
## pixel10 NA NA NA NA
## pixel11 NA NA NA NA
## pixel12 0.04252 0.04276 0.994 0.320
## pixel13 -0.01334 0.01493 -0.893 0.372
## pixel14 NA NA NA NA
## pixel15 NA NA NA NA
## pixel16 NA NA NA NA
## pixel17 NA NA NA NA
## pixel18 NA NA NA NA
## pixel19 NA NA NA NA
## pixel20 NA NA NA NA
## pixel21 NA NA NA NA
## pixel22 NA NA NA NA
## pixel23 NA NA NA NA
## pixel24 NA NA NA NA
## pixel25 NA NA NA NA
## pixel26 NA NA NA NA
## pixel27 NA NA NA NA
## pixel28 NA NA NA NA
## pixel29 NA NA NA NA
## pixel30 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.888 on 41997 degrees of freedom
## Multiple R-squared: 2.403e-05, Adjusted R-squared: -2.359e-05
## F-statistic: 0.5047 on 2 and 41997 DF, p-value: 0.6037plot(model_house3)## Warning: not plotting observations with leverage one:
## 19297, 20740
# Removing 5 more columns
model_house4 <- lm(label ~ pixel0 + pixel1 + pixel2 + pixel3 + pixel4 + pixel5 + pixel6 + pixel7 + pixel8 + pixel9 + pixel10 + pixel11 + pixel12 + pixel13 + pixel14 + pixel15 + pixel16 + pixel17 + pixel18 + pixel19 + pixel20 + pixel21 + pixel22 + pixel23 + pixel24 + pixel25, house_train2)
summary(model_house4)##
## Call:
## lm(formula = label ~ pixel0 + pixel1 + pixel2 + pixel3 + pixel4 +
## pixel5 + pixel6 + pixel7 + pixel8 + pixel9 + pixel10 + pixel11 +
## pixel12 + pixel13 + pixel14 + pixel15 + pixel16 + pixel17 +
## pixel18 + pixel19 + pixel20 + pixel21 + pixel22 + pixel23 +
## pixel24 + pixel25, data = house_train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4567 -2.4567 -0.4567 2.5433 4.5433
##
## Coefficients: (24 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.45666 0.01409 316.273 <2e-16 ***
## pixel0 NA NA NA NA
## pixel1 NA NA NA NA
## pixel2 NA NA NA NA
## pixel3 NA NA NA NA
## pixel4 NA NA NA NA
## pixel5 NA NA NA NA
## pixel6 NA NA NA NA
## pixel7 NA NA NA NA
## pixel8 NA NA NA NA
## pixel9 NA NA NA NA
## pixel10 NA NA NA NA
## pixel11 NA NA NA NA
## pixel12 0.04252 0.04276 0.994 0.320
## pixel13 -0.01334 0.01493 -0.893 0.372
## pixel14 NA NA NA NA
## pixel15 NA NA NA NA
## pixel16 NA NA NA NA
## pixel17 NA NA NA NA
## pixel18 NA NA NA NA
## pixel19 NA NA NA NA
## pixel20 NA NA NA NA
## pixel21 NA NA NA NA
## pixel22 NA NA NA NA
## pixel23 NA NA NA NA
## pixel24 NA NA NA NA
## pixel25 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.888 on 41997 degrees of freedom
## Multiple R-squared: 2.403e-05, Adjusted R-squared: -2.359e-05
## F-statistic: 0.5047 on 2 and 41997 DF, p-value: 0.6037# Using model_house4 we'll create a scatterplot
plot(model_house4)## Warning: not plotting observations with leverage one:
## 19297, 20740
# Predict prices for test data
house_test <- read.csv("C:/Users/Ivan/OneDrive/Desktop/test.csv/test.csv")
house_test2 <- house_test %>%
dplyr::select_if(is.numeric) %>%
replace(is.na(.), 0)
prediction <- predict(model_house4, house_test2, type = "response")## Warning in predict.lm(model_house4, house_test2, type = "response"): prediction
## from a rank-deficient fit may be misleadinghead(prediction)## 1 2 3 4 5 6
## 4.456665 4.456665 4.456665 4.456665 4.456665 4.456665# Prepare data frame for submission
kaggle_prediction <- data.frame(pixel50 = house_test2$pixel50 , label = prediction)
head(kaggle_prediction)## pixel50 label
## 1 0 4.456665
## 2 0 4.456665
## 3 0 4.456665
## 4 0 4.456665
## 5 0 4.456665
## 6 0 4.456665General References https://stackoverflow.com/questions/16496210/rotate-a-matrix-in-r-by-90-degrees-clockwise https://www.rdocumentation.org/packages/igraph/versions/1.3.1/topics/graph_from_adjacency_matrix