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# Load homes.csv data
Homes <- read.csv('D:/DataSet/Homes.csv')
# Set seed for reproducibility
set.seed(123)
# Number of rows
total_rows <- nrow(Homes)
# Create 5 random subsamples
no_of_samples <- 5
size <- round(0.5 * total_rows)
subsamples <- list()
for(i in 1:no_of_samples) {
# Randomly sample rows
sample_r <- sample(1:total_rows, size = size, replace = TRUE)
# Randomly sample columns
selected_columns <- sample(1:ncol(Homes), size = size, replace = TRUE)
# Create subsample
subsamples[[i]] <- Homes[sample_r, selected_columns]
# Assign column names
colnames(subsamples[[i]]) <- paste0("col", 1:ncol(subsamples[[i]]))
# Print first few rows
print(head(subsamples[[i]]))
}## col1 col2 col3 col4 col5 col6 col7 col8 col9 col10 col11 col12 col13
## 415 660000 3 35 434 1520 434 3 1.0 1 1 1900 1900 1.0
## 463 1539514 3 136 761 2024 761 3 2.5 1 1 2014 2014 2.5
## 179 4625000 2 29 2729 1695 2729 2 2.0 0 0 1987 1987 2.0
## 14 1249000 1 3 1512 826 1512 1 1.0 0 0 1987 1987 1.0
## 195 1635000 2 10 1708 957 1708 2 2.0 0 0 2004 2004 2.0
## 426 599000 2 181 695 862 695 2 2.0 1 1 1990 1990 2.0
## col14 col15 col16 col17 col18 col19 col20 col21 col22 col23 col24 col25
## 415 3 1900 1520 1900 1.0 1.0 1 660000 3 434 1 434
## 463 3 2014 2024 2014 2.5 2.5 1 1539514 3 761 1 761
## 179 2 1987 1695 1987 2.0 2.0 0 4625000 2 2729 0 2729
## 14 1 1987 826 1987 1.0 1.0 0 1249000 1 1512 0 1512
## 195 2 2004 957 2004 2.0 2.0 0 1635000 2 1708 0 1708
## 426 2 1990 862 1990 2.0 2.0 1 599000 2 695 1 695
## col26 col27 col28 col29 col30 col31 col32 col33 col34 col35 col36 col37
## 415 3 35 660000 1900 35 1 1 1 1900 434 1520 1520
## 463 3 136 1539514 2014 136 1 1 1 2014 761 2024 2024
## 179 2 29 4625000 1987 29 0 0 0 1987 2729 1695 1695
## 14 1 3 1249000 1987 3 0 0 0 1987 1512 826 826
## 195 2 10 1635000 2004 10 0 0 0 2004 1708 957 957
## 426 2 181 599000 1990 181 1 1 1 1990 695 862 862
## col38 col39 col40 col41 col42 col43 col44 col45 col46 col47 col48 col49
## 415 1520 1.0 1 3 3 1 3 1 1900 3 1.0 1900
## 463 2024 2.5 1 3 3 1 3 1 2014 3 2.5 2014
## 179 1695 2.0 0 2 2 0 2 0 1987 2 2.0 1987
## 14 826 1.0 0 1 1 0 1 0 1987 1 1.0 1987
## 195 957 2.0 0 2 2 0 2 0 2004 2 2.0 2004
## 426 862 2.0 1 2 2 1 2 1 1990 2 2.0 1990
## col50 col51 col52 col53 col54 col55 col56 col57 col58 col59 col60 col61
## 415 434 660000 1900 3 1 660000 1520 3 1520 434 1900 1
## 463 761 1539514 2014 3 1 1539514 2024 3 2024 761 2014 1
## 179 2729 4625000 1987 2 0 4625000 1695 2 1695 2729 1987 0
## 14 1512 1249000 1987 1 0 1249000 826 1 826 1512 1987 0
## 195 1708 1635000 2004 2 0 1635000 957 2 957 1708 2004 0
## 426 695 599000 1990 2 1 599000 862 2 862 695 1990 1
## col62 col63 col64 col65 col66 col67 col68 col69 col70 col71 col72 col73
## 415 35 1900 1 660000 1.0 1 1520 1 3 660000 3 1
## 463 136 2014 1 1539514 2.5 1 2024 1 3 1539514 3 1
## 179 29 1987 0 4625000 2.0 0 1695 0 2 4625000 2 0
## 14 3 1987 0 1249000 1.0 0 826 0 1 1249000 1 0
## 195 10 2004 0 1635000 2.0 0 957 0 2 1635000 2 0
## 426 181 1990 1 599000 2.0 1 862 1 2 599000 2 1
## col74 col75 col76 col77 col78 col79 col80 col81 col82 col83 col84 col85
## 415 1900 1900 1 35 434 1 1900 1900 3 3 434 1520
## 463 2014 2014 1 136 761 1 2014 2014 3 3 761 2024
## 179 1987 1987 0 29 2729 0 1987 1987 2 2 2729 1695
## 14 1987 1987 0 3 1512 0 1987 1987 1 1 1512 826
## 195 2004 2004 0 10 1708 0 2004 2004 2 2 1708 957
## 426 1990 1990 1 181 695 1 1990 1990 2 2 695 862
## col86 col87 col88 col89 col90 col91 col92 col93 col94 col95 col96 col97
## 415 434 1900 1 35 1 1900 1900 660000 434 1900 35 1900
## 463 761 2014 1 136 1 2014 2014 1539514 761 2014 136 2014
## 179 2729 1987 0 29 0 1987 1987 4625000 2729 1987 29 1987
## 14 1512 1987 0 3 0 1987 1987 1249000 1512 1987 3 1987
## 195 1708 2004 0 10 0 2004 2004 1635000 1708 2004 10 2004
## 426 695 1990 1 181 1 1990 1990 599000 695 1990 181 1990
## col98 col99 col100 col101 col102 col103 col104 col105 col106 col107 col108
## 415 434 434 660000 3 1900 1 1 3 1 3 1900
## 463 761 761 1539514 3 2014 1 1 3 1 3 2014
## 179 2729 2729 4625000 2 1987 0 0 2 0 2 1987
## 14 1512 1512 1249000 1 1987 0 0 1 0 1 1987
## 195 1708 1708 1635000 2 2004 0 0 2 0 2 2004
## 426 695 695 599000 2 1990 1 1 2 1 2 1990
## col109 col110 col111 col112 col113 col114 col115 col116 col117 col118
## 415 35 1 434 1.0 3 3 1900 434 660000 1
## 463 136 1 761 2.5 3 3 2014 761 1539514 1
## 179 29 0 2729 2.0 2 2 1987 2729 4625000 0
## 14 3 0 1512 1.0 1 1 1987 1512 1249000 0
## 195 10 0 1708 2.0 2 2 2004 1708 1635000 0
## 426 181 1 695 2.0 2 2 1990 695 599000 1
## col119 col120 col121 col122 col123 col124 col125 col126 col127 col128
## 415 1900 3 1900 1520 3 3 1520 660000 35 35
## 463 2014 3 2014 2024 3 3 2024 1539514 136 136
## 179 1987 2 1987 1695 2 2 1695 4625000 29 29
## 14 1987 1 1987 826 1 1 826 1249000 3 3
## 195 2004 2 2004 957 2 2 957 1635000 10 10
## 426 1990 2 1990 862 2 2 862 599000 181 181
## col129 col130 col131 col132 col133 col134 col135 col136 col137 col138
## 415 35 1.0 660000 1.0 1.0 1.0 1900 434 1.0 434
## 463 136 2.5 1539514 2.5 2.5 2.5 2014 761 2.5 761
## 179 29 2.0 4625000 2.0 2.0 2.0 1987 2729 2.0 2729
## 14 3 1.0 1249000 1.0 1.0 1.0 1987 1512 1.0 1512
## 195 10 2.0 1635000 2.0 2.0 2.0 2004 1708 2.0 1708
## 426 181 2.0 599000 2.0 2.0 2.0 1990 695 2.0 695
## col139 col140 col141 col142 col143 col144 col145 col146 col147 col148
## 415 35 3 434 434 1.0 1 1900 434 1520 434
## 463 136 3 761 761 2.5 1 2014 761 2024 761
## 179 29 2 2729 2729 2.0 0 1987 2729 1695 2729
## 14 3 1 1512 1512 1.0 0 1987 1512 826 1512
## 195 10 2 1708 1708 2.0 0 2004 1708 957 1708
## 426 181 2 695 695 2.0 1 1990 695 862 695
## col149 col150 col151 col152 col153 col154 col155 col156 col157 col158
## 415 1520 1 660000 3 1520 3 660000 1 660000 1900
## 463 2024 1 1539514 3 2024 3 1539514 1 1539514 2014
## 179 1695 0 4625000 2 1695 2 4625000 0 4625000 1987
## 14 826 0 1249000 1 826 1 1249000 0 1249000 1987
## 195 957 0 1635000 2 957 2 1635000 0 1635000 2004
## 426 862 1 599000 2 862 2 599000 1 599000 1990
## col159 col160 col161 col162 col163 col164 col165 col166 col167 col168
## 415 1900 1.0 434 1900 1900 1.0 1 1.0 660000 3
## 463 2014 2.5 761 2014 2014 2.5 1 2.5 1539514 3
## 179 1987 2.0 2729 1987 1987 2.0 0 2.0 4625000 2
## 14 1987 1.0 1512 1987 1987 1.0 0 1.0 1249000 1
## 195 2004 2.0 1708 2004 2004 2.0 0 2.0 1635000 2
## 426 1990 2.0 695 1990 1990 2.0 1 2.0 599000 2
## col169 col170 col171 col172 col173 col174 col175 col176 col177 col178
## 415 1900 1 434 660000 1520 1.0 1520 1 3 434
## 463 2014 1 761 1539514 2024 2.5 2024 1 3 761
## 179 1987 0 2729 4625000 1695 2.0 1695 0 2 2729
## 14 1987 0 1512 1249000 826 1.0 826 0 1 1512
## 195 2004 0 1708 1635000 957 2.0 957 0 2 1708
## 426 1990 1 695 599000 862 2.0 862 1 2 695
## col179 col180 col181 col182 col183 col184 col185 col186 col187 col188
## 415 1520 1.0 1.0 1 3 35 1 1520 3 35
## 463 2024 2.5 2.5 1 3 136 1 2024 3 136
## 179 1695 2.0 2.0 0 2 29 0 1695 2 29
## 14 826 1.0 1.0 0 1 3 0 826 1 3
## 195 957 2.0 2.0 0 2 10 0 957 2 10
## 426 862 2.0 2.0 1 2 181 1 862 2 181
## col189 col190 col191 col192 col193 col194 col195 col196 col197 col198
## 415 3 35 3 1900 660000 1520 660000 1900 660000 1520
## 463 3 136 3 2014 1539514 2024 1539514 2014 1539514 2024
## 179 2 29 2 1987 4625000 1695 4625000 1987 4625000 1695
## 14 1 3 1 1987 1249000 826 1249000 1987 1249000 826
## 195 2 10 2 2004 1635000 957 1635000 2004 1635000 957
## 426 2 181 2 1990 599000 862 599000 1990 599000 862
## col199 col200 col201 col202 col203 col204 col205 col206 col207 col208
## 415 1 35 35 434 3 1 434 3 35 1.0
## 463 1 136 136 761 3 1 761 3 136 2.5
## 179 0 29 29 2729 2 0 2729 2 29 2.0
## 14 0 3 3 1512 1 0 1512 1 3 1.0
## 195 0 10 10 1708 2 0 1708 2 10 2.0
## 426 1 181 181 695 2 1 695 2 181 2.0
## col209 col210 col211 col212 col213 col214 col215 col216 col217 col218
## 415 3 434 1.0 1 660000 3 1.0 1900 1900 434
## 463 3 761 2.5 1 1539514 3 2.5 2014 2014 761
## 179 2 2729 2.0 0 4625000 2 2.0 1987 1987 2729
## 14 1 1512 1.0 0 1249000 1 1.0 1987 1987 1512
## 195 2 1708 2.0 0 1635000 2 2.0 2004 2004 1708
## 426 2 695 2.0 1 599000 2 2.0 1990 1990 695
## col219 col220 col221 col222 col223 col224 col225 col226 col227 col228
## 415 1520 1.0 1520 1520 3 35 1900 660000 3 1
## 463 2024 2.5 2024 2024 3 136 2014 1539514 3 1
## 179 1695 2.0 1695 1695 2 29 1987 4625000 2 0
## 14 826 1.0 826 826 1 3 1987 1249000 1 0
## 195 957 2.0 957 957 2 10 2004 1635000 2 0
## 426 862 2.0 862 862 2 181 1990 599000 2 1
## col229 col230 col231 col232 col233 col234 col235 col236 col237 col238
## 415 35 660000 1 660000 1900 660000 3 3 660000 434
## 463 136 1539514 1 1539514 2014 1539514 3 3 1539514 761
## 179 29 4625000 0 4625000 1987 4625000 2 2 4625000 2729
## 14 3 1249000 0 1249000 1987 1249000 1 1 1249000 1512
## 195 10 1635000 0 1635000 2004 1635000 2 2 1635000 1708
## 426 181 599000 1 599000 1990 599000 2 2 599000 695
## col239 col240 col241 col242 col243 col244 col245 col246
## 415 1.0 1900 1520 35 35 3 434 1.0
## 463 2.5 2014 2024 136 136 3 761 2.5
## 179 2.0 1987 1695 29 29 2 2729 2.0
## 14 1.0 1987 826 3 3 1 1512 1.0
## 195 2.0 2004 957 10 10 2 1708 2.0
## 426 2.0 1990 862 181 181 2 695 2.0
## col1 col2 col3 col4 col5 col6 col7 col8 col9 col10 col11 col12 col13
## 315 54 1700 2 54 1700 875000 2 54 515 1 54 1 1
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## col14 col15 col16 col17 col18 col19 col20 col21 col22 col23 col24 col25
## 315 875000 1 2 54 2 1 1 515 515 1909 1909 875000
## 259 1659000 1 2 4 2 1 1 1424 1424 2000 2000 1659000
## 353 795000 1 2 36 3 1 1 589 589 1954 1954 795000
## 248 2149000 1 2 0 2 1 1 1632 1632 2008 2008 2149000
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## col26 col27 col28 col29 col30 col31 col32 col33 col34 col35 col36
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## 248 1317 2149000 0 1632 2149000 2008 2149000 1 2 2008 2149000
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## 223 0 3 0 1 0 1 0 2695000 1 1
## 14 0 1 0 3 0 3 0 1249000 3 3
## 468 1 1 1 36 1 36 1 699000 36 36
## 232 1 1 1 10 1 10 1 798000 10 10
## col216 col217 col218 col219 col220 col221 col222 col223 col224 col225
## 462 478 1 599000 123 123 2 478 2 123 123
## 242 764 1 649000 163 163 1 764 1 163 163
## 223 1354 3 2695000 1 1 3 1354 3 1 1
## 14 1512 1 1249000 3 3 1 1512 1 3 3
## 468 932 1 699000 36 36 1 932 1 36 36
## 232 1038 1 798000 10 10 1 1038 1 10 10
## col226 col227 col228 col229 col230 col231 col232 col233 col234 col235
## 462 599000 123 2 1254 2 1 2 123 599000 1
## 242 649000 163 1 850 1 1 1 163 649000 1
## 223 2695000 1 3 1991 3 3 3 1 2695000 3
## 14 1249000 3 1 826 1 1 1 3 1249000 1
## 468 699000 36 1 750 1 1 1 36 699000 1
## 232 798000 10 1 769 1 1 1 10 798000 1
## col236 col237 col238 col239 col240 col241 col242 col243 col244 col245
## 462 123 2 1 1 478 1941 2 1254 2 1
## 242 163 1 1 1 764 1983 1 850 1 1
## 223 1 3 0 0 1354 2006 3 1991 3 0
## 14 3 1 0 0 1512 1987 1 826 1 0
## 468 36 1 1 1 932 1908 1 750 1 1
## 232 10 1 1 1 1038 1926 1 769 1 1
## col246
## 462 1
## 242 1
## 223 3
## 14 1
## 468 1
## 232 1#The summary statistics and distributions of key variables like price and sqft vary noticeably across subsamples. For example, the maximum price in subsample1 is $19M while in subsample2 it’s only $9.9M. The distribution of sqft also looks quite different. An “anomaly” in one subsample may look normal in another.
#However, the relationships between variables are generally consistent. For example, we’d expect to see a positive correlation between price and sqft in all subsamples. The association between in_sf and price also appears consistently positive.
#This exercise illustrates the variability inherent in taking smaller subsamples. We cannot rely on any one subsample as perfectly representative of the population. Taking multiple randomized samples and aggregating results is important for robust conclusions. We must be cautious about generalizing based on limited data.