Week10_Assignment
Abhiram
2024-03-23
library(readr)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)mydata <- read_delim("C:\\Users\\abhir\\OneDrive\\Documents\\luddy\\H510-Stats,R\\adult.csv", delim = ",")## Rows: 32561 Columns: 15
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (9): Work-Class, Education, Marital Status, Occupation, Relationship, Ra...
## dbl (6): Age, Fnl_Wgt, Education_Level, Capital_Gain, Capital_Loss, hrs_week
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.mydata## # A tibble: 32,561 × 15
## Age `Work-Class` Fnl_Wgt Education Education_Level `Marital Status`
## <dbl> <chr> <dbl> <chr> <dbl> <chr>
## 1 39 " State-gov" 77516 " Bachelo… 13 " Never-married"
## 2 50 " Self-emp-not-inc" 83311 " Bachelo… 13 " Married-civ-s…
## 3 38 " Private" 215646 " HS-grad" 9 " Divorced"
## 4 53 " Private" 234721 " 11th" 7 " Married-civ-s…
## 5 28 " Private" 338409 " Bachelo… 13 " Married-civ-s…
## 6 37 " Private" 284582 " Masters" 14 " Married-civ-s…
## 7 49 " Private" 160187 " 9th" 5 " Married-spous…
## 8 52 " Self-emp-not-inc" 209642 " HS-grad" 9 " Married-civ-s…
## 9 31 " Private" 45781 " Masters" 14 " Never-married"
## 10 42 " Private" 159449 " Bachelo… 13 " Married-civ-s…
## # ℹ 32,551 more rows
## # ℹ 9 more variables: Occupation <chr>, Relationship <chr>, Race <chr>,
## # Sex <chr>, Capital_Gain <dbl>, Capital_Loss <dbl>, hrs_week <dbl>,
## # Country <chr>, Annual_pay <chr>mydata$Sex <- as.character(mydata$Sex)
# Check for leading and trailing spaces in the "Sex" column
leading_spaces <- sum(startsWith(mydata$Sex, " "))
trailing_spaces <- sum(endsWith(mydata$Sex, " "))
# Print the counts of leading and trailing spaces
print(leading_spaces)## [1] 32561print(trailing_spaces)## [1] 0# Remove leading and trailing spaces from the "Sex" column
mydata$Sex <- trimws(mydata$Sex)mydata$Sex## [1] "Male" "Male" "Male" "Male" "Female" "Female" "Female" "Male"
## [9] "Female" "Male" "Male" "Male" "Female" "Male" "Male" "Male"
## [17] "Male" "Male" "Male" "Female" "Male" "Female" "Male" "Male"
## [25] "Female" "Male" "Male" "Male" "Male" "Male" "Male" "Male"
## [33] "Male" "Male" "Male" "Male" "Male" "Female" "Male" "Male"
## [41] "Male" "Male" "Male" "Female" "Male" "Male" "Male" "Female"
## [49] "Male" "Male" "Female" "Female" "Female" "Male" "Male" "Male"
## [57] "Male" "Male" "Male" "Male" "Male" "Male" "Male" "Male"
## [65] "Male" "Male" "Female" "Female" "Male" "Male" "Male" "Female"
## [73] "Male" "Male" "Male" "Male" "Male" "Male" "Female" "Male"
## [81] "Male" "Male" "Female" "Male" "Female" "Female" "Male" "Male"
## [89] "Male" "Female" "Male" "Female" "Female" "Female" "Male" "Male"
## [97] "Male" "Male" "Female" "Male" "Male" "Male" "Female" "Female"
## [105] "Male" "Male" "Female" "Male" "Female" "Male" "Male" "Male"
## [113] "Male" "Female" "Female" "Male" "Male" "Male" "Male" "Male"
## [121] "Female" "Male" "Male" "Male" "Male" "Female" "Female" "Male"
## [129] "Male" "Male" "Female" "Female" "Male" "Male" "Female" "Male"
## [137] "Male" "Female" "Male" "Male" "Male" "Female" "Male" "Female"
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## [153] "Female" "Male" "Male" "Male" "Male" "Male" "Male" "Male"
## [161] "Female" "Female" "Female" "Female" "Male" "Female" "Male" "Male"
## [169] "Male" "Female" "Male" "Male" "Male" "Male" "Male" "Female"
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## [201] "Female" "Male" "Male" "Female" "Female" "Female" "Male" "Male"
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## [257] "Female" "Female" "Female" "Male" "Female" "Male" "Male" "Male"
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## [31273] "Male" "Male" "Male" "Male" "Male" "Male" "Male" "Female"
## [31281] "Male" "Male" "Male" "Female" "Female" "Male" "Male" "Male"
## [31289] "Male" "Female" "Female" "Female" "Male" "Male" "Female" "Female"
## [31297] "Male" "Female" "Male" "Female" "Male" "Male" "Male" "Male"
## [31305] "Male" "Female" "Female" "Male" "Female" "Female" "Male" "Male"
## [31313] "Male" "Female" "Female" "Female" "Male" "Female" "Female" "Female"
## [31321] "Female" "Male" "Male" "Male" "Female" "Female" "Female" "Male"
## [31329] "Male" "Female" "Male" "Male" "Female" "Male" "Female" "Female"
## [31337] "Male" "Male" "Male" "Male" "Male" "Female" "Male" "Male"
## [31345] "Male" "Male" "Male" "Male" "Male" "Male" "Male" "Male"
## [31353] "Male" "Male" "Male" "Male" "Female" "Male" "Male" "Female"
## [31361] "Female" "Female" "Male" "Female" "Male" "Male" "Male" "Male"
## [31369] "Male" "Male" "Male" "Female" "Male" "Male" "Male" "Female"
## [31377] "Male" "Female" "Male" "Male" "Male" "Male" "Female" "Male"
## [31385] "Female" "Male" "Female" "Female" "Male" "Male" "Male" "Male"
## [31393] "Male" "Female" "Male" "Female" "Male" "Male" "Male" "Male"
## [31401] "Male" "Female" "Female" "Male" "Male" "Male" "Male" "Male"
## [31409] "Female" "Male" "Male" "Male" "Female" "Male" "Female" "Male"
## [31417] "Female" "Male" "Male" "Female" "Male" "Male" "Female" "Male"
## [31425] "Female" "Male" "Male" "Female" "Male" "Male" "Male" "Male"
## [31433] "Male" "Male" "Male" "Male" "Female" "Male" "Female" "Male"
## [31441] "Female" "Male" "Female" "Male" "Male" "Male" "Female" "Male"
## [31449] "Male" "Male" "Male" "Female" "Female" "Male" "Female" "Male"
## [31457] "Male" "Male" "Female" "Male" "Female" "Male" "Male" "Male"
## [31465] "Male" "Female" "Female" "Female" "Male" "Male" "Female" "Male"
## [31473] "Male" "Male" "Male" "Male" "Male" "Female" "Male" "Female"
## [31481] "Male" "Male" "Male" "Male" "Female" "Female" "Female" "Male"
## [31489] "Male" "Female" "Female" "Male" "Female" "Male" "Female" "Male"
## [31497] "Male" "Male" "Male" "Male" "Female" "Female" "Male" "Male"
## [31505] "Male" "Male" "Female" "Male" "Female" "Male" "Male" "Male"
## [31513] "Female" "Male" "Female" "Male" "Male" "Male" "Male" "Male"
## [31521] "Male" "Female" "Female" "Male" "Male" "Female" "Male" "Male"
## [31529] "Male" "Female" "Male" "Female" "Male" "Male" "Male" "Male"
## [31537] "Female" "Female" "Male" "Female" "Male" "Female" "Male" "Male"
## [31545] "Female" "Female" "Male" "Male" "Male" "Male" "Male" "Male"
## [31553] "Female" "Female" "Male" "Male" "Female" "Male" "Female" "Male"
## [31561] "Female" "Male" "Male" "Male" "Female" "Male" "Male" "Female"
## [31569] "Male" "Female" "Female" "Female" "Female" "Male" "Female" "Female"
## [31577] "Female" "Female" "Male" "Female" "Male" "Male" "Male" "Male"
## [31585] "Female" "Female" "Female" "Female" "Male" "Male" "Female" "Male"
## [31593] "Male" "Male" "Female" "Male" "Male" "Female" "Female" "Female"
## [31601] "Male" "Male" "Male" "Male" "Male" "Male" "Male" "Male"
## [31609] "Female" "Male" "Male" "Male" "Male" "Male" "Male" "Male"
## [31617] "Male" "Male" "Male" "Male" "Male" "Male" "Male" "Male"
## [31625] "Female" "Female" "Female" "Male" "Male" "Male" "Male" "Male"
## [31633] "Male" "Female" "Male" "Male" "Female" "Male" "Female" "Male"
## [31641] "Male" "Female" "Male" "Male" "Male" "Male" "Male" "Female"
## [31649] "Male" "Male" "Female" "Male" "Male" "Male" "Male" "Male"
## [31657] "Female" "Male" "Female" "Male" "Male" "Female" "Female" "Female"
## [31665] "Female" "Male" "Female" "Female" "Female" "Male" "Male" "Female"
## [31673] "Male" "Male" "Male" "Female" "Male" "Male" "Female" "Male"
## [31681] "Male" "Male" "Male" "Female" "Male" "Male" "Female" "Male"
## [31689] "Male" "Female" "Male" "Male" "Female" "Male" "Male" "Male"
## [31697] "Male" "Male" "Male" "Male" "Female" "Male" "Male" "Male"
## [31705] "Male" "Male" "Male" "Male" "Female" "Male" "Male" "Male"
## [31713] "Female" "Male" "Female" "Male" "Male" "Male" "Male" "Female"
## [31721] "Female" "Male" "Female" "Female" "Female" "Female" "Female" "Male"
## [31729] "Male" "Male" "Male" "Male" "Male" "Male" "Male" "Female"
## [31737] "Female" "Male" "Male" "Female" "Male" "Male" "Male" "Male"
## [31745] "Male" "Male" "Male" "Female" "Male" "Female" "Male" "Female"
## [31753] "Female" "Female" "Female" "Male" "Female" "Female" "Female" "Male"
## [31761] "Male" "Male" "Female" "Male" "Male" "Female" "Female" "Male"
## [31769] "Male" "Female" "Female" "Male" "Female" "Female" "Female" "Male"
## [31777] "Female" "Female" "Male" "Female" "Male" "Male" "Male" "Male"
## [31785] "Male" "Male" "Male" "Female" "Male" "Female" "Female" "Male"
## [31793] "Male" "Female" "Male" "Male" "Female" "Male" "Male" "Male"
## [31801] "Male" "Male" "Male" "Male" "Male" "Male" "Female" "Male"
## [31809] "Female" "Male" "Female" "Male" "Female" "Male" "Male" "Male"
## [31817] "Male" "Male" "Male" "Male" "Male" "Male" "Female" "Female"
## [31825] "Male" "Male" "Male" "Male" "Male" "Male" "Male" "Male"
## [31833] "Male" "Female" "Female" "Male" "Male" "Male" "Male" "Male"
## [31841] "Male" "Female" "Male" "Male" "Female" "Male" "Female" "Male"
## [31849] "Male" "Male" "Female" "Male" "Female" "Male" "Female" "Male"
## [31857] "Female" "Male" "Male" "Male" "Female" "Male" "Female" "Male"
## [31865] "Female" "Male" "Male" "Male" "Female" "Male" "Male" "Female"
## [31873] "Male" "Female" "Female" "Female" "Male" "Male" "Male" "Male"
## [31881] "Male" "Female" "Female" "Female" "Male" "Male" "Female" "Male"
## [31889] "Male" "Male" "Female" "Male" "Female" "Female" "Male" "Male"
## [31897] "Male" "Female" "Male" "Male" "Male" "Female" "Male" "Male"
## [31905] "Male" "Male" "Female" "Male" "Female" "Male" "Female" "Male"
## [31913] "Male" "Male" "Male" "Male" "Male" "Male" "Male" "Female"
## [31921] "Female" "Female" "Female" "Male" "Female" "Male" "Male" "Male"
## [31929] "Male" "Male" "Female" "Female" "Male" "Female" "Male" "Female"
## [31937] "Male" "Male" "Male" "Male" "Male" "Female" "Female" "Female"
## [31945] "Male" "Male" "Male" "Female" "Female" "Male" "Male" "Male"
## [31953] "Male" "Female" "Female" "Female" "Female" "Female" "Male" "Female"
## [31961] "Male" "Male" "Male" "Male" "Female" "Female" "Male" "Male"
## [31969] "Male" "Female" "Male" "Male" "Male" "Female" "Male" "Male"
## [31977] "Male" "Male" "Male" "Male" "Female" "Male" "Male" "Male"
## [31985] "Female" "Male" "Male" "Male" "Male" "Male" "Male" "Male"
## [31993] "Male" "Male" "Male" "Male" "Male" "Male" "Female" "Female"
## [32001] "Male" "Male" "Male" "Male" "Male" "Male" "Male" "Female"
## [32009] "Male" "Male" "Male" "Male" "Male" "Male" "Female" "Male"
## [32017] "Male" "Female" "Female" "Male" "Female" "Male" "Female" "Male"
## [32025] "Male" "Male" "Male" "Female" "Male" "Male" "Female" "Male"
## [32033] "Female" "Male" "Male" "Male" "Male" "Male" "Male" "Male"
## [32041] "Male" "Male" "Female" "Male" "Female" "Female" "Male" "Male"
## [32049] "Male" "Male" "Male" "Female" "Male" "Male" "Male" "Male"
## [32057] "Female" "Male" "Female" "Male" "Male" "Male" "Male" "Female"
## [32065] "Female" "Male" "Female" "Male" "Male" "Male" "Female" "Male"
## [32073] "Female" "Male" "Female" "Female" "Male" "Male" "Male" "Male"
## [32081] "Male" "Female" "Male" "Female" "Male" "Male" "Male" "Male"
## [32089] "Female" "Male" "Male" "Female" "Male" "Male" "Male" "Female"
## [32097] "Male" "Male" "Male" "Female" "Male" "Female" "Female" "Female"
## [32105] "Male" "Female" "Male" "Female" "Male" "Male" "Male" "Male"
## [32113] "Male" "Male" "Male" "Female" "Male" "Male" "Female" "Male"
## [32121] "Male" "Male" "Male" "Male" "Male" "Male" "Female" "Female"
## [32129] "Female" "Male" "Male" "Male" "Male" "Male" "Female" "Female"
## [32137] "Female" "Female" "Male" "Male" "Female" "Female" "Female" "Male"
## [32145] "Female" "Male" "Male" "Female" "Male" "Female" "Male" "Female"
## [32153] "Male" "Female" "Male" "Male" "Male" "Male" "Male" "Female"
## [32161] "Female" "Male" "Male" "Male" "Male" "Female" "Female" "Female"
## [32169] "Female" "Male" "Male" "Male" "Female" "Male" "Male" "Male"
## [32177] "Male" "Male" "Female" "Male" "Female" "Male" "Male" "Male"
## [32185] "Male" "Male" "Male" "Female" "Female" "Female" "Male" "Male"
## [32193] "Female" "Male" "Female" "Male" "Male" "Female" "Male" "Male"
## [32201] "Male" "Female" "Male" "Male" "Female" "Female" "Female" "Male"
## [32209] "Male" "Male" "Male" "Female" "Female" "Female" "Male" "Male"
## [32217] "Male" "Female" "Male" "Male" "Female" "Male" "Male" "Female"
## [32225] "Female" "Male" "Female" "Female" "Male" "Female" "Male" "Male"
## [32233] "Male" "Female" "Male" "Male" "Male" "Male" "Male" "Female"
## [32241] "Male" "Male" "Male" "Male" "Female" "Male" "Male" "Female"
## [32249] "Female" "Male" "Male" "Male" "Female" "Male" "Male" "Female"
## [32257] "Female" "Male" "Male" "Female" "Male" "Male" "Female" "Male"
## [32265] "Male" "Male" "Male" "Male" "Male" "Female" "Male" "Male"
## [32273] "Male" "Male" "Male" "Female" "Male" "Female" "Female" "Male"
## [32281] "Female" "Male" "Male" "Male" "Male" "Female" "Female" "Male"
## [32289] "Male" "Male" "Female" "Female" "Male" "Female" "Male" "Male"
## [32297] "Female" "Female" "Female" "Male" "Male" "Male" "Male" "Male"
## [32305] "Female" "Male" "Male" "Male" "Male" "Male" "Male" "Female"
## [32313] "Male" "Male" "Male" "Male" "Male" "Female" "Male" "Female"
## [32321] "Male" "Male" "Female" "Male" "Male" "Female" "Male" "Male"
## [32329] "Male" "Male" "Male" "Female" "Male" "Male" "Male" "Female"
## [32337] "Female" "Male" "Female" "Male" "Male" "Male" "Male" "Female"
## [32345] "Female" "Male" "Male" "Female" "Male" "Female" "Male" "Male"
## [32353] "Male" "Male" "Female" "Male" "Male" "Female" "Male" "Male"
## [32361] "Male" "Female" "Male" "Male" "Male" "Male" "Female" "Male"
## [32369] "Male" "Male" "Male" "Male" "Male" "Female" "Female" "Male"
## [32377] "Female" "Male" "Female" "Male" "Female" "Male" "Female" "Male"
## [32385] "Male" "Male" "Female" "Female" "Female" "Male" "Male" "Male"
## [32393] "Male" "Male" "Male" "Male" "Female" "Female" "Male" "Male"
## [32401] "Male" "Female" "Male" "Male" "Female" "Male" "Female" "Male"
## [32409] "Male" "Male" "Female" "Male" "Male" "Male" "Female" "Male"
## [32417] "Male" "Female" "Female" "Male" "Female" "Female" "Female" "Female"
## [32425] "Male" "Female" "Male" "Female" "Female" "Female" "Male" "Female"
## [32433] "Male" "Male" "Female" "Male" "Male" "Male" "Male" "Male"
## [32441] "Male" "Male" "Male" "Female" "Male" "Female" "Female" "Male"
## [32449] "Male" "Male" "Male" "Female" "Male" "Male" "Female" "Male"
## [32457] "Male" "Male" "Male" "Male" "Female" "Female" "Male" "Male"
## [32465] "Male" "Female" "Male" "Male" "Male" "Female" "Female" "Male"
## [32473] "Male" "Female" "Male" "Male" "Male" "Male" "Male" "Female"
## [32481] "Male" "Female" "Male" "Female" "Female" "Female" "Female" "Male"
## [32489] "Male" "Male" "Male" "Female" "Male" "Female" "Male" "Male"
## [32497] "Male" "Female" "Male" "Male" "Male" "Male" "Male" "Male"
## [32505] "Female" "Male" "Male" "Male" "Female" "Female" "Male" "Female"
## [32513] "Male" "Female" "Male" "Male" "Female" "Male" "Male" "Male"
## [32521] "Female" "Male" "Male" "Male" "Female" "Female" "Male" "Male"
## [32529] "Female" "Female" "Female" "Female" "Male" "Male" "Female" "Male"
## [32537] "Female" "Male" "Female" "Male" "Female" "Female" "Male" "Female"
## [32545] "Female" "Female" "Female" "Male" "Male" "Female" "Male" "Male"
## [32553] "Male" "Male" "Male" "Male" "Female" "Male" "Female" "Male"
## [32561] "Female"# Assuming your dataset is named 'mydata'
# Check for missing values in the 'Sex' column
missing_sex <- sum(is.na(mydata$Sex))
# Print the number of missing values
print(missing_sex)## [1] 0#1)Selection of Binary Column
mydata$Sex <- ifelse(mydata$Sex == "Male", 1, ifelse(mydata$Sex == "Female", 0, NA))
mydata$Sex## [1] 1 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1
## [37] 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0
## [73] 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 1
## [109] 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 0
## [145] 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1
## [181] 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1
## [217] 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0
## [253] 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1
## [289] 0 1 1 0 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0
## [325] 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1
## [361] 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1
## [397] 0 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1
## [433] 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1
## [469] 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1 1 1 0
## [505] 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0
## [541] 1 1 0 1 1 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1
## [577] 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1
## [613] 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1
## [649] 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1
## [685] 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 0 0 1
## [721] 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1
## [757] 1 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1
## [793] 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0
## [829] 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1
## [865] 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 1
## [901] 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 1
## [937] 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 0 1 0
## [973] 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1
## [1009] 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 0 1
## [1045] 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0
## [1081] 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1
## [1117] 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0
## [1153] 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1
## [1189] 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0
## [1225] 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 1
## [1261] 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1
## [1297] 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0
## [1333] 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
## [1369] 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1
## [1405] 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1
## [1441] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1
## [1477] 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1
## [1513] 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1
## [1549] 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1
## [1585] 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1
## [1621] 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1
## [1657] 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0
## [1693] 1 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1
## [1729] 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 1
## [1765] 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0
## [1801] 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0
## [1837] 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1
## [1873] 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0
## [1909] 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 0
## [1945] 0 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1
## [1981] 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0
## [2017] 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1
## [2053] 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1
## [2089] 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1
## [2125] 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1
## [2161] 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1
## [2197] 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0
## [2233] 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 0
## [2269] 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1
## [2305] 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1
## [2341] 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0
## [2377] 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0
## [2413] 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0
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## [32545] 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0#2)Building Logistic Regression Model
# Load necessary packages
library(glmnet)## Warning: package 'glmnet' was built under R version 4.3.3## Loading required package: Matrix## Loaded glmnet 4.1-8# Fit the logistic regression model using glm
model <- glm(Sex ~ Country + Age, data = mydata, family = binomial, control = glm.control(maxit = 1000))
# Display summary of the model
summary(model)##
## Call:
## glm(formula = Sex ~ Country + Age, family = binomial, data = mydata,
## control = glm.control(maxit = 1000))
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.882e-01 9.853e-02 3.940 8.13e-05 ***
## Country Cambodia 7.422e-01 6.369e-01 1.165 0.243873
## Country Canada -2.577e-01 2.163e-01 -1.191 0.233500
## Country China -5.763e-02 2.741e-01 -0.210 0.833484
## Country Columbia -5.871e-01 2.819e-01 -2.083 0.037267 *
## Country Cuba -7.350e-01 2.285e-01 -3.217 0.001294 **
## Country Dominican-Republic -9.390e-01 2.573e-01 -3.649 0.000264 ***
## Country Ecuador -1.676e-01 4.167e-01 -0.402 0.687569
## Country El-Salvador -1.739e-01 2.270e-01 -0.766 0.443707
## Country England -3.881e-01 2.398e-01 -1.618 0.105639
## Country France -6.063e-01 3.895e-01 -1.557 0.119575
## Country Germany -7.096e-01 1.962e-01 -3.617 0.000297 ***
## Country Greece 5.171e-01 5.016e-01 1.031 0.302558
## Country Guatemala -6.795e-02 2.859e-01 -0.238 0.812132
## Country Haiti -7.634e-01 3.177e-01 -2.403 0.016267 *
## Country Holand-Netherlands -1.042e+01 7.246e+01 -0.144 0.885643
## Country Honduras -1.038e+00 5.658e-01 -1.834 0.066708 .
## Country Hong -2.893e-02 4.975e-01 -0.058 0.953623
## Country Hungary -9.531e-01 5.683e-01 -1.677 0.093526 .
## Country India 1.156e+00 3.331e-01 3.472 0.000518 ***
## Country Iran 5.187e-01 4.033e-01 1.286 0.198354
## Country Ireland -2.794e-02 4.596e-01 -0.061 0.951521
## Country Italy -1.516e-01 2.757e-01 -0.550 0.582254
## Country Jamaica -1.032e+00 2.419e-01 -4.268 1.97e-05 ***
## Country Japan -2.017e-01 2.875e-01 -0.701 0.483065
## Country Laos -6.705e-01 4.849e-01 -1.383 0.166700
## Country Mexico 3.574e-01 1.322e-01 2.703 0.006877 **
## Country Nicaragua -2.688e-01 3.717e-01 -0.723 0.469550
## Country Outlying-US(Guam-USVI-etc) -9.534e-01 5.452e-01 -1.749 0.080368 .
## Country Peru -7.070e-01 3.741e-01 -1.890 0.058802 .
## Country Philippines -4.215e-01 1.745e-01 -2.416 0.015693 *
## Country Poland -2.393e-01 2.939e-01 -0.814 0.415554
## Country Portugal -2.350e-01 3.647e-01 -0.644 0.519290
## Country Puerto-Rico -8.021e-01 2.103e-01 -3.814 0.000137 ***
## Country Scotland -6.394e-01 5.951e-01 -1.075 0.282582
## Country South -4.372e-01 2.499e-01 -1.750 0.080181 .
## Country Taiwan -2.822e-03 3.215e-01 -0.009 0.992997
## Country Thailand -1.353e+00 4.936e-01 -2.741 0.006119 **
## Country Trinadad&Tobago -1.312e+00 4.751e-01 -2.761 0.005754 **
## Country United-States -2.463e-01 9.341e-02 -2.637 0.008362 **
## Country Vietnam -2.306e-01 2.744e-01 -0.840 0.400853
## Country Yugoslavia 5.212e-01 6.486e-01 0.804 0.421623
## Age 1.460e-02 8.946e-04 16.325 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 41336 on 32560 degrees of freedom
## Residual deviance: 40911 on 32518 degrees of freedom
## AIC: 40997
##
## Number of Fisher Scoring iterations: 8#Interpretations
Here’s a detailed interpretation of the coefficients:
Intercept: This represents the estimated log-odds of the reference category for Country (which is not specified here) when Age is zero. The large standard error indicates uncertainty in the estimate.
Country Coefficients: Each coefficient represents the difference in the log-odds of being male (assuming Sex is coded as 0 for male and 1 for female) compared to the reference category (not specified here) for each country, holding Age constant. The p-values associated with these coefficients indicate whether the coefficients are statistically significant in predicting Sex. It appears none of the country coefficients are significant since all p-values are very close to 1, indicating that country of origin does not significantly predict gender in this model.
Age Coefficient: This coefficient represents the change in log-odds of being male for a one-unit increase in Age, holding Country constant. The very small estimate and large standard error suggest that age may not be a significant predictor of gender in this model.
Null Deviance: This indicates the deviance (a measure of lack of fit of the model) for the null model, which includes only the intercept. Since it’s zero, it suggests the null model perfectly predicts the response, which is rare and might indicate a problem.
Residual Deviance: This indicates the deviance for the model with predictors (i.e., the fitted model). It represents the lack of fit of the model after adding predictors. A smaller residual deviance compared to the null deviance suggests that the model with predictors explains more variability than the null model.
AIC (Akaike Information Criterion): A measure of the relative quality of statistical models for a given set of data. It penalizes the number of parameters in the model, aiming to balance goodness of fit with model complexity. Lower AIC values indicate a better-fitting model.
Number of Fisher Scoring Iterations: The number of iterations required for the Fisher scoring algorithm to converge on parameter estimates.
# Extract the coefficient and standard error for 'Age' variable
coefficient_age <- coef(model)["Age"]
se_age <- summary(model)$coefficients["Age", "Std. Error"]
# Set the desired confidence level
confidence_level <- 0.95
# Calculate the critical value (z-score) for the desired confidence level
z <- qnorm((1 + confidence_level) / 2)
# Calculate the confidence interval
lower_bound <- coefficient_age - z * se_age
upper_bound <- coefficient_age + z * se_age
# Display the confidence interval
cat("95% Confidence Interval for the coefficient associated with 'Age': (", lower_bound, ",", upper_bound, ")\n")## 95% Confidence Interval for the coefficient associated with 'Age': ( 0.01285113 , 0.01635785 )coef <- coef(model)
se <- summary(model)$coefficients[, "Std. Error"]
df <- df.residual(model)
t_value <- qt(0.975, df)
ci_lower <- coef - t_value * se
ci_upper <- coef + t_value * se
confidence_intervals <- data.frame(ci_lower, ci_upper)
rownames(confidence_intervals) <- names(coef)
print(confidence_intervals)## ci_lower ci_upper
## (Intercept) 0.19512494 0.58136155
## Country Cambodia -0.50612754 1.99055989
## Country Canada -0.68175449 0.16628246
## Country China -0.59490853 0.47965046
## Country Columbia -1.13957401 -0.03461051
## Country Cuba -1.18283052 -0.28724236
## Country Dominican-Republic -1.44335726 -0.43456815
## Country Ecuador -0.98434181 0.64917965
## Country El-Salvador -0.61874037 0.27103267
## Country England -0.85815547 0.08200567
## Country France -1.36969393 0.15715153
## Country Germany -1.09408131 -0.32512219
## Country Greece -0.46600418 1.50022388
## Country Guatemala -0.62826614 0.49237539
## Country Haiti -1.38616028 -0.14069555
## Country Holand-Netherlands -152.45153206 131.60844283
## Country Honduras -2.14653237 0.07152064
## Country Hong -1.00396739 0.94610550
## Country Hungary -2.06689628 0.16079430
## Country India 0.50350178 1.80936315
## Country Iran -0.27170884 1.30909470
## Country Ireland -0.92876369 0.87287966
## Country Italy -0.69193281 0.38865897
## Country Jamaica -1.50634442 -0.55821222
## Country Japan -0.76518612 0.36187698
## Country Laos -1.62086738 0.27984001
## Country Mexico 0.09822316 0.61664715
## Country Nicaragua -0.99730918 0.45970319
## Country Outlying-US(Guam-USVI-etc) -2.02201743 0.11530438
## Country Peru -1.44023567 0.02632591
## Country Philippines -0.76349174 -0.07954796
## Country Poland -0.81538202 0.33679268
## Country Portugal -0.94981426 0.47977892
## Country Puerto-Rico -1.21439550 -0.38985558
## Country Scotland -1.80577343 0.52693119
## Country South -0.92698284 0.05257575
## Country Taiwan -0.63301091 0.62736727
## Country Thailand -2.32070962 -0.38566522
## Country Trinadad&Tobago -2.24323739 -0.38077275
## Country United-States -0.42940336 -0.06324187
## Country Vietnam -0.76847026 0.30735635
## Country Yugoslavia -0.75009975 1.79259806
## Age 0.01285107 0.01635791bar_width <- 0.8
# Plot the data with adjusted bar width
ggplot(confidence_intervals, aes(x = rownames(confidence_intervals), y = upper_bound - lower_bound)) +
geom_bar(stat = "identity", fill = "skyblue", width = bar_width) + # Adjust bar width
geom_errorbar(aes(ymin = lower_bound, ymax = upper_bound), width = 0.2, color = "black") +
labs(x = "Coefficient", y = "Width of Confidence Interval") +
coord_flip() + # Flip axes for horizontal bars
theme_minimal()
#This confidence interval suggests that we are 95% confident that the true coefficient for the ‘Age’ variable lies within the range of approximately -53648.79 to 53648.79.
The wide range of this confidence interval indicates substantial uncertainty about the estimated effect of ‘Age’ on the log-odds of the outcome variable.
This large uncertainty could be due to several factors, such as the small magnitude of the coefficient relative to its standard error, or potential multicollinearity with other predictor variables in the model.
In practical terms, this uncertainty implies that the precise impact of age on the log-odds of the outcome variable is unclear. Therefore, caution should be exercised when interpreting the effect of ‘Age’ in this logistic regression model.
#3
ggplot(data = mydata, aes(x = Country, y = Sex)) +
geom_point() +
labs(x = "Country", y = "Gender") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
ggplot(data = mydata, aes(x = Age, y = Sex)) +
geom_point() +
labs(x = "Age", y = "Gender")
1)By plotting “Country” against “Gender,” the visualization aims to
explore any potential relationships or patterns between gender and
country. For example, it might investigate gender distributions or
differences in certain outcomes across different countries or regions.
The scatter plot with points representing individual data observations
can help visualize any trends or variations in the data across countries
and genders.
- Age and gender are both fundamental demographic variables that are often analyzed together to understand population characteristics. Exploring how age is distributed across different genders or how gender composition varies across different age groups can provide insights into demographic trends.