What is Logistic regression?
Logistic regression is used to predict a class, i.e., a probability. Logistic regression can predict a binary outcome accurately.
Imagine you want to predict whether a loan is denied/accepted based on many attributes. The logistic regression is of the form 0/1. y = 0 if a loan is rejected, y = 1 if accepted.
A logistic regression model differs from linear regression model in two ways.
 First of all, the logistic regression accepts only dichotomous (binary) input as a dependent variable (i.e., a vector of 0 and 1).
 Secondly, the outcome is measured by the following probabilistic link function called sigmoid due to its Sshaped.:
The output of the function is always between 0 and 1. Check Image below
The sigmoid function returns values from 0 to 1. For the classification task, we need a discrete output of 0 or 1.
To convert a continuous flow into discrete value, we can set a decision bound at 0.5. All values above this threshold are classified as 1
Learn Java Programming with Beginners Tutorial
How to create Generalized Liner Model (GLM)
Let’s use the adult data set to illustrate Logistic regression. The “adult” is a great dataset for the classification task. The objective is to predict whether the annual income in dollar of an individual will exceed 50.000. The dataset contains 46,033 observations and ten features:
 age: age of the individual. Numeric
 education: Educational level of the individual. Factor.
 marital.status: Marital status of the individual. Factor i.e. Nevermarried, Marriedcivspouse, …
 gender: Gender of the individual. Factor, i.e. Male or Female
 income: Target variable. Income above or below 50K. Factor i.e. >50K, <=50K
amongst others
library(dplyr) data_adult <read.csv(“https://raw.githubusercontent.com/guru99edu/RProgramming/master/adult.csv”) glimpse(data_adult)
Output:
Observations: 48,842 Variables: 10 $ x 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,… $ age 25, 38, 28, 44, 18, 34, 29, 63, 24, 55, 65, 36, 26… $ workclass Private, Private, Localgov, Private, ?, Private,… $ education 11th, HSgrad, Assocacdm, Somecollege, Somecol… $ educational.num 7, 9, 12, 10, 10, 6, 9, 15, 10, 4, 9, 13, 9, 9, 9,… $ marital.status Nevermarried, Marriedcivspouse, Marriedcivsp… $ race Black, White, White, Black, White, White, Black, … $ gender Male, Male, Male, Male, Female, Male, Male, Male,… $ hours.per.week 40, 50, 40, 40, 30, 30, 40, 32, 40, 10, 40, 40, 39… $ income <=50K, <=50K, >50K, >50K, <=50K, <=50K, <=50K, >5…
We will proceed as follow:
 Step 1: Check continuous variables
 Step 2: Check factor variables
 Step 3: Feature engineering
 Step 4: Summary statistic
 Step 5: Train/test set
 Step 6: Build the model
 Step 7: Assess the performance of the model
 step 8: Improve the model
Your task is to predict which individual will have a revenue higher than 50K.
In this tutorial, each step will be detailed to perform an analysis on a real dataset.
Step 1) Check continuous variables
In the first step, you can see the distribution of the continuous variables.
continuous <select_if(data_adult, is.numeric) summary(continuous)
Code Explanation
 continuous < select_if(data_adult, is.numeric): Use the function select_if() from the dplyr library to select only the numerical columns
 summary(continuous): Print the summary statistic
Output:
X age educational.num hours.per.week ## Min. : 1 Min. :17.00 Min. : 1.00 Min. : 1.00 ## 1st Qu.:11509 1st Qu.:28.00 1st Qu.: 9.00 1st Qu.:40.00 ## Median :23017 Median :37.00 Median :10.00 Median :40.00 ## Mean :23017 Mean :38.56 Mean :10.13 Mean :40.95 ## 3rd Qu.:34525 3rd Qu.:47.00 3rd Qu.:13.00 3rd Qu.:45.00 ## Max. :46033 Max. :90.00 Max. :16.00 Max. :99.00
From the above table, you can see that the data have totally different scales and hours.per.weeks has large outliers (.i.e. look at the last quartile and maximum value).
You can deal with it following two steps:
 1: Plot the distribution of hours.per.week
 2: Standardize the continuous variables
 Plot the distribution
Let’s look closer at the distribution of hours.per.week
Histogram with kernel density curve library(ggplot2) ggplot(continuous, aes(x = hours.per.week)) + geom_density(alpha = .2, fill = “#FF6666”)
Output:
The variable has lots of outliers and not welldefined distribution. You can partially tackle this problem by deleting the top 0.01 percent of the hours per week.
Basic syntax of quantile:
quantile(variable, percentile) arguments: variable: Select the variable in the data frame to compute the percentile percentile: Can be a single value between 0 and 1 or multiple value. If multiple, use this format: c(A,B,C, ...) 
A,
B,
Cand
…` are all integer from 0 to 1.
We compute the top 2 percent percentile
top_one_percent < quantile(data_adult$hours.per.week, .99) top_one_percent
Code Explanation
 quantile(data_adult$hours.per.week, .99): Compute the value of the 99 percent of the working time
Output:
99% ## 80
98 percent of the population works under 80 hours per week.
You can drop the observations above this threshold. You use the filter from the dplyr library.
data_adult_drop <data_adult %>% filter(hours.per.week<top_one_percent) dim(data_adult_drop)
Output:
[1] 45537 10
 Standardize the continuous variables
You can standardize each column to improve the performance because your data do not have the same scale. You can use the function mutate_if from the dplyr library. The basic syntax is:
mutate_if(df, condition, funs(function)) arguments: df
: Data frame used to compute the function  condition
: Statement used. Do not use parenthesis  funs(function): Return the function to apply. Do not use parenthesis for the function
You can standardize the numeric columns as follow:
data_adult_rescale < data_adult_drop % > % mutate_if(is.numeric, funs(as.numeric(scale(.)))) head(data_adult_rescale)
Code Explanation
 mutate_if(is.numeric, funs(scale)): The condition is only numeric column and the function is scale
Output:
X age workclass education educational.num ## 1 1.732680 1.02325949 Private 11th 1.22106443 ## 2 1.732605 0.03969284 Private HSgrad 0.43998868 ## 3 1.732530 0.79628257 Localgov Assocacdm 0.73162494 ## 4 1.732455 0.41426100 Private Somecollege 0.04945081 ## 5 1.732379 0.34232873 Private 10th 1.61160231 ## 6 1.732304 1.85178149 Selfempnotinc Profschool 1.90323857 ## marital.status race gender hours.per.week income ## 1 Nevermarried Black Male 0.03995944 <=50K ## 2 Marriedcivspouse White Male 0.86863037 <=50K ## 3 Marriedcivspouse White Male 0.03995944 >50K ## 4 Marriedcivspouse Black Male 0.03995944 >50K ## 5 Nevermarried White Male 0.94854924 <=50K ## 6 Marriedcivspouse White Male 0.76683128 >50K
Step 2) Check factor variables
This step has two objectives:
 Check the level in each categorical column
 Define new levels
We will divide this step into three parts:
 Select the categorical columns
 Store the bar chart of each column in a list
 Print the graphs
We can select the factor columns with the code below:
Select categorical column factor < data.frame(select_if(data_adult_rescale, is.factor)) ncol(factor)
Code Explanation
 data.frame(select_if(data_adult, is.factor)): We store the factor columns in factor in a data frame type. The library ggplot2 requires a data frame object.
Output:
[1] 6
The dataset contains 6 categorical variables
The second step is more skilled. You want to plot a bar chart for each column in the data frame factor. It is more convenient to automatize the process, especially in situation there are lots of columns.
library(ggplot2) # Create graph for each column graph < lapply(names(factor), function(x) ggplot(factor, aes(get(x))) + geom_bar() + theme(axis.text.x = element_text(angle = 90)))
Code Explanation
 lapply(): Use the function lapply() to pass a function in all the columns of the dataset. You store the output in a list
 function(x): The function will be processed for each x. Here x is the columns
 ggplot(factor, aes(get(x))) + geom_bar()+ theme(axis.text.x = element_text(angle = 90)): Create a bar char chart for each x element. Note, to return x as a column, you need to include it inside the get()
The last step is relatively easy. You want to print the 6 graphs.
Print the graph graph
Output:
[[1]]
## [[2]]
## [[3]]
## [[4]]
## [[5]]
## [[6]]
Note: Use the next button to navigate to the next graph
Step 3) Feature engineering
Recast education
From the graph above, you can see that the variable education has 16 levels. This is substantial, and some levels have a relatively low number of observations. If you want to improve the amount of information you can get from this variable, you can recast it into higher level. Namely, you create larger groups with similar level of education. For instance, low level of education will be converted in dropout. Higher levels of education will be changed to master.
Here is the detail:
Old level  New level 

Preschool  dropout 
10th  Dropout 
11th  Dropout 
12th  Dropout 
1st4th  Dropout 
5th6th  Dropout 
7th8th  Dropout 
9th  Dropout 
HSGrad  HighGrad 
Somecollege  Community 
Assocacdm  Community 
Assocvoc  Community 
Bachelors  Bachelors 
Masters  Masters 
Profschool  Masters 
Doctorate  PhD 
recast_data < data_adult_rescale % > % select(X) % > % mutate(education = factor(ifelse(education == “Preschool”  education == “10th”  education == “11th”  education == “12th”  education == “1st4th”  education == “5th6th”  education == “7th8th”  education == “9th”, “dropout”, ifelse(education == “HSgrad”, “HighGrad”, ifelse(education == “Somecollege”  education == “Assocacdm”  education == “Assocvoc”, “Community”, ifelse(education == “Bachelors”, “Bachelors”, ifelse(education == “Masters”  education == “Profschool”, “Master”, “PhD”)))))))
Code Explanation
 We use the verb mutate from dplyr library. We change the values of education with the statement ifelse
In the table below, you create a summary statistic to see, on average, how many years of education (zvalue) it takes to reach the Bachelor, Master or PhD.
recast_data % > % group_by(education) % > % summarize(average_educ_year = mean(educational.num), count = n()) % > % arrange(average_educ_year)
Output:
# A tibble: 6 x 3 ## education average_educ_year count ## ## 1 dropout 1.76147258 5712 ## 2 HighGrad 0.43998868 14803 ## 3 Community 0.09561361 13407 ## 4 Bachelors 1.12216282 7720 ## 5 Master 1.60337381 3338 ## 6 PhD 2.29377644 557
Recast Maritalstatus
It is also possible to create lower levels for the marital status. In the following code you change the level as follow:
Old level  New level 

Nevermarried  Notmarried 
Marriedspouseabsent  Notmarried 
MarriedAFspouse  Married 
Marriedcivspouse  
Separated  Separated 
Divorced  
Widows  Widow 
Change level marry recast_data < recast_data % > % mutate(marital.status = factor(ifelse(marital.status == “Nevermarried”  marital.status == “Marriedspouseabsent”, “Not_married”, ifelse(marital.status == “MarriedAFspouse”  marital.status == “Marriedcivspouse”, “Married”, ifelse(marital.status == “Separated”  marital.status == “Divorced”, “Separated”, “Widow”)))))
You can check the number of individuals within each group.
table(recast_data$marital.status)
Output:
## Married Not_married Separated Widow ## 21165 15359 7727 1286
Step 4) Summary Statistic
It is time to check some statistics about our target variables. In the graph below, you count the percentage of individuals earning more than 50k given their gender.
Plot gender income ggplot(recast_data, aes(x = gender, fill = income)) + geom_bar(position = “fill”) + theme_classic()
Output:
Next, check if the origin of the individual affects their earning.
Plot origin income ggplot(recast_data, aes(x = race, fill = income)) + geom_bar(position = “fill”) + theme_classic() + theme(axis.text.x = element_text(angle = 90))
Output:
The number of hours work by gender.
box plot gender working time ggplot(recast_data, aes(x = gender, y = hours.per.week)) + geom_boxplot() + stat_summary(fun.y = mean, geom = “point”, size = 3, color = “steelblue”) + theme_classic()
Output:
The box plot confirms that the distribution of working time fits different groups. In the box plot, both genders do not have homogeneous observations.
You can check the density of the weekly working time by type of education. The distributions have many distinct picks. It can probably be explained by the type of contract in the US.
Plot distribution working time by education ggplot(recast_data, aes(x = hours.per.week)) + geom_density(aes(color = education), alpha = 0.5) + theme_classic()
Code Explanation
 ggplot(recast_data, aes( x= hours.per.week)): A density plot only requires one variable
 geom_density(aes(color = education), alpha =0.5): The geometric object to control the density
Output:
To confirm your thoughts, you can perform a oneway ANOVA test:
anova < aov(hours.per.week~education, recast_data) summary(anova)
Output:
Df Sum Sq Mean Sq F value Pr(>F) ## education 5 1552 310.31 321.2 <2e16 *** ## Residuals 45531 43984 0.97 ## — ## Signif. codes: 0 ‘’ 0.001 '’ 0.01 '’ 0.05 ‘.’ 0.1 ’ ’ 1
The ANOVA test confirms the difference in average between groups.
Nonlinearity
Before you run the model, you can see if the number of hours worked is related to age.
library(ggplot2) ggplot(recast_data, aes(x = age, y = hours.per.week)) + geom_point(aes(color = income), size = 0.5) + stat_smooth(method = ‘lm’, formula = y~poly(x, 2), se = TRUE, aes(color = income)) + theme_classic()
Code Explanation
 ggplot(recast_data, aes(x = age, y = hours.per.week)): Set the aesthetic of the graph
 geom_point(aes(color= income), size =0.5): Construct the dot plot
 stat_smooth(): Add the trend line with the following arguments:
 method=‘lm’: Plot the fitted value if the linear regression
 formula = y~poly(x,2): Fit a polynomial regression
 se = TRUE: Add the standard error
 aes(color= income): Break the model by income
Output:
In a nutshell, you can test interaction terms in the model to pick up the nonlinearity effect between the weekly working time and other features. It is important to detect under which condition the working time differs.
Correlation
The next check is to visualize the correlation between the variables. You convert the factor level type to numeric so that you can plot a heat map containing the coefficient of correlation computed with the Spearman method.
library(GGally) # Convert data to numeric corr < data.frame(lapply(recast_data, as.integer)) # Plot the graphggcorr(corr, method = c(“pairwise”, “spearman”), nbreaks = 6, hjust = 0.8, label = TRUE, label_size = 3, color = “grey50”)
Code Explanation
 data.frame(lapply(recast_data,as.integer)): Convert data to numeric
 ggcorr() plot the heat map with the following arguments:
 method: Method to compute the correlation
 nbreaks = 6: Number of break
 hjust = 0.8: Control position of the variable name in the plot
 label = TRUE: Add labels in the center of the windows
 label_size = 3: Size labels
 color = “grey50”): Color of the label
Output:
Step 5) Train/test set
Any supervised machine learning task require to split the data between a train set and a test set. You can use the “function” you created in the other supervised learning tutorials to create a train/test set.
set.seed(1234) create_train_test < function(data, size = 0.8, train = TRUE) { n_row = nrow(data) total_row = size * n_row train_sample < 1: total_row if (train == TRUE) { return (data[train_sample, ]) } else { return (data[train_sample, ]) } } data_train < create_train_test(recast_data, 0.8, train = TRUE) data_test < create_train_test(recast_data, 0.8, train = FALSE) dim(data_train)
Output:
[1] 36429 9
dim(data_test)
Output:
[1] 9108 9
Step 6) Build the model
To see how the algorithm performs, you use the glm() package. The Generalized Linear Model is a collection of models. The basic syntax is:
glm(formula, data=data, family=linkfunction() Argument:  formula: Equation used to fit the model data: dataset used  Family:  binomial: (link = “logit”)  gaussian: (link = “identity”)  Gamma: (link = “inverse”)  inverse.gaussian: (link = “1/mu^2”)  poisson: (link = “log”)  quasi: (link = “identity”, variance = “constant”)  quasibinomial: (link = “logit”)  quasipoisson: (link = “log”)
You are ready to estimate the logistic model to split the income level between a set of features.
formula < income~. logit < glm(formula, data = data_train, family = ‘binomial’) summary(logit)
Code Explanation
 formula < income ~ .: Create the model to fit
 logit < glm(formula, data = data_train, family = ‘binomial’): Fit a logistic model (family = ‘binomial’) with the data_train data.
 summary(logit): Print the summary of the model
Output:
## Call: ## glm(formula = formula, family = “binomial”, data = data_train) ## ## Deviance Residuals: ## Min 1Q Median 3Q Max ## 2.6456 0.5858 0.2609 0.0651 3.1982 ## ## Coefficients: ## Estimate Std. Error z value Pr(>z) ## (Intercept) 0.07882 0.21726 0.363 0.71675 ## age 0.41119 0.01857 22.146 < 2e16 *** ## workclassLocalgov 0.64018 0.09396 6.813 9.54e12 *** ## workclassPrivate 0.53542 0.07886 6.789 1.13e11 *** ## workclassSelfempinc 0.07733 0.10350 0.747 0.45499 ## workclassSelfempnotinc 1.09052 0.09140 11.931 < 2e16 *** ## workclassStategov 0.80562 0.10617 7.588 3.25e14 *** ## workclassWithoutpay 1.09765 0.86787 1.265 0.20596 ## educationCommunity 0.44436 0.08267 5.375 7.66e08 *** ## educationHighGrad 0.67613 0.11827 5.717 1.08e08 *** ## educationMaster 0.35651 0.06780 5.258 1.46e07 *** ## educationPhD 0.46995 0.15772 2.980 0.00289 ** ## educationdropout 1.04974 0.21280 4.933 8.10e07 *** ## educational.num 0.56908 0.07063 8.057 7.84e16 *** ## marital.statusNot_married 2.50346 0.05113 48.966 < 2e16 *** ## marital.statusSeparated 2.16177 0.05425 39.846 < 2e16 *** ## marital.statusWidow 2.22707 0.12522 17.785 < 2e16 *** ## raceAsianPacIslander 0.08359 0.20344 0.411 0.68117 ## raceBlack 0.07188 0.19330 0.372 0.71001 ## raceOther 0.01370 0.27695 0.049 0.96054 ## raceWhite 0.34830 0.18441 1.889 0.05894 . ## genderMale 0.08596 0.04289 2.004 0.04506 * ## hours.per.week 0.41942 0.01748 23.998 < 2e16 *** ## —## Signif. codes: 0 ‘’ 0.001 '’ 0.01 '’ 0.05 ‘.’ 0.1 ’ ’ 1 ## ## (Dispersion parameter for binomial family taken to be 1) ## ## Null deviance: 40601 on 36428 degrees of freedom ## Residual deviance: 27041 on 36406 degrees of freedom ## AIC: 27087 ## ## Number of Fisher Scoring iterations: 6
The summary of our model reveals interesting information. The performance of a logistic regression is evaluated with specific key metrics.
 AIC (Akaike Information Criteria): This is the equivalent of R2 in logistic regression. It measures the fit when a penalty is applied to the number of parameters. Smaller AIC values indicate the model is closer to the truth.
 Null deviance: Fits the model only with the intercept. The degree of freedom is n1. We can interpret it as a Chisquare value (fitted value different from the actual value hypothesis testing).
 Residual Deviance: Model with all the variables. It is also interpreted as a Chisquare hypothesis testing.
 Number of Fisher Scoring iterations: Number of iterations before converging.
The output of the glm() function is stored in a list. The code below shows all the items available in the logit variable we constructed to evaluate the logistic regression.
The list is very long, print only the first three elements
lapply(logit, class)[1:3]
Output:
$coefficients ## [1] “numeric” ## ## $residuals ## [1] “numeric” ## ## $fitted.values ## [1] “numeric”
Each value can be extracted with the $ sign follow by the name of the metrics. For instance, you stored the model as logit. To extract the AIC criteria, you use:
logit$aic
Output:
[1] 27086.65
Step 7) Assess the performance of the model
Confusion Matrix
The confusion matrix is a better choice to evaluate the classification performance compared with the different metrics you saw before. The general idea is to count the number of times True instances are classified are False.
To compute the confusion matrix, you first need to have a set of predictions so that they can be compared to the actual targets.
predict < predict(logit, data_test, type = ‘response’) # confusion matrix table_mat < table(data_test$income, predict > 0.5) table_mat
Code Explanation
 predict(logit,data_test, type = ‘response’): Compute the prediction on the test set. Set type = ‘response’ to compute the response probability.
 table(data_test$income, predict > 0.5): Compute the confusion matrix. predict > 0.5 means it returns 1 if the predicted probabilities are above 0.5, else 0.
Output:
## FALSE TRUE ## <=50K 6310 495 ## >50K 1074 1229
Each row in a confusion matrix represents an actual target, while each column represents a predicted target. The first row of this matrix considers the income lower than 50k (the False class): 6241 were correctly classified as individuals with income lower than 50k ( True negative ), while the remaining one was wrongly classified as above 50k ( False positive ). The second row considers the income above 50k, the positive class were 1229 ( True positive ), while the True negative was 1074.
You can calculate the model accuracy by summing the true positive + true negative over the total observation
accuracy_Test < sum(diag(table_mat)) / sum(table_mat) accuracy_Test
Code Explanation
 sum(diag(table_mat)): Sum of the diagonal
 sum(table_mat): Sum of the matrix.
Output:
[1] 0.8277339
The model appears to suffer from one problem, it overestimates the number of false negatives. This is called the accuracy test paradox . We stated that the accuracy is the ratio of correct predictions to the total number of cases. We can have relatively high accuracy but a useless model. It happens when there is a dominant class. If you look back at the confusion matrix, you can see most of the cases are classified as true negative. Imagine now, the model classified all the classes as negative (i.e. lower than 50k). You would have an accuracy of 75 percent (6718/6718+2257). Your model performs better but struggles to distinguish the true positive with the true negative.
In such situation, it is preferable to have a more concise metric. We can look at:
 Precision=TP/(TP+FP)
 Recall=TP/(TP+FN)
Precision vs Recall
Precision looks at the accuracy of the positive prediction. Recall is the ratio of positive instances that are correctly detected by the classifier;
You can construct two functions to compute these two metrics
 Construct precision
precision < function(matrix) { # True positive tp < matrix[2, 2] # false positive fp < matrix[1, 2] return (tp / (tp + fp)) }
Code Explanation
 mat[1,1]: Return the first cell of the first column of the data frame, i.e. the true positive
 mat[1,2]; Return the first cell of the second column of the data frame, i.e. the false positive
recall < function(matrix) { # true positive tp < matrix[2, 2]# false positive fn < matrix[2, 1] return (tp / (tp + fn)) }
Code Explanation
 mat[1,1]: Return the first cell of the first column of the data frame, i.e. the true positive
 mat[2,1]; Return the second cell of the first column of the data frame, i.e. the false negative
You can test your functions
prec < precision(table_mat) prec rec < recall(table_mat) rec
Output:
[1] 0.712877 ## [2] 0.5336518
When the model says it is an individual above 50k, it is correct in only 54 percent of the case, and can claim individuals above 50k in 72 percent of the case.
You can create the score based on the precision and recall. The is a harmonic mean of these two metrics, meaning it gives more weight to the lower values.
f1 < 2 * ((prec * rec) / (prec + rec)) f1
Output:
[1] 0.6103799
Precision vs Recall tradeoff
It is impossible to have both a high precision and high recall.
If we increase the precision, the correct individual will be better predicted, but we would miss lots of them (lower recall). In some situation, we prefer higher precision than recall. There is a concave relationship between precision and recall.
 Imagine, you need to predict if a patient has a disease. You want to be as precise as possible.
 If you need to detect potential fraudulent people in the street through facial recognition, it would be better to catch many people labeled as fraudulent even though the precision is low. The police will be able to release the nonfraudulent individual.
The ROC curve
The Receiver Operating Characteristic curve is another common tool used with binary classification. It is very similar to the precision/recall curve, but instead of plotting precision versus recall, the ROC curve shows the true positive rate (i.e., recall) against the false positive rate. The false positive rate is the ratio of negative instances that are incorrectly classified as positive. It is equal to one minus the true negative rate. The true negative rate is also called specificity . Hence the ROC curve plots sensitivity (recall) versus 1specificity
To plot the ROC curve, we need to install a library called RORC. We can find in the conda library. You can type the code:
conda install c r rrocr yes
We can plot the ROC with the prediction() and performance() functions.
library(ROCR) ROCRpred < prediction(predict, data_test$income) ROCRperf < performance(ROCRpred, ‘tpr’, ‘fpr’) plot(ROCRperf, colorize = TRUE, text.adj = c(0.2, 1.7))
Code Explanation
 prediction(predict, data_test$income): The ROCR library needs to create a prediction object to transform the input data
 performance(ROCRpred, ‘tpr’,‘fpr’): Return the two combinations to produce in the graph. Here, tpr and fpr are constructed. Tot plot precision and recall together, use “prec”, “rec”.
Output:
Step 8) Improve the model
You can try to add nonlinearity to the model with the interaction between
 age and hours.per.week
 gender and hours.per.week.
You need to use the score test to compare both model
formula_2 < income~age: hours.per.week + gender: hours.per.week + . logit_2 < glm(formula_2, data = data_train, family = ‘binomial’) predict_2 < predict(logit_2, data_test, type = ‘response’) table_mat_2 < table(data_test$income, predict_2 > 0.5) precision_2 < precision(table_mat_2) recall_2 < recall(table_mat_2) f1_2 < 2 * ((precision_2 * recall_2) / (precision_2 + recall_2)) f1_2
Output:
[1] 0.6109181
The score is slightly higher than the previous one. You can keep working on the data a try to beat the score.
Summary
We can summarize the function to train a logistic regression in the table below:
Package  Objective  function  argument 

  Create train/test dataset  create_train_set()  data, size, train 
glm  Train a Generalized Linear Model  glm()  formula, data, family* 
glm  Summarize the model  summary()  fitted model 
base  Make prediction  predict()  fitted model, dataset, type = ‘response’ 
base  Create a confusion matrix  table()  y, predict() 
base  Create accuracy score  sum(diag(table())/sum(table()  
ROCR  Create ROC : Step 1 Create prediction  prediction()  predict(), y 
ROCR  Create ROC : Step 2 Create performance  performance()  prediction(), ‘tpr’, ‘fpr’ 
ROCR  Create ROC : Step 3 Plot graph  plot()  performance() 
The other GLM type of models are:

binomial: (link = “logit”)

gaussian: (link = “identity”)

Gamma: (link = “inverse”)

inverse.gaussian: (link = “1/mu^2”)

poisson: (link = “log”)

quasi: (link = “identity”, variance = “constant”)

quasibinomial: (link = “logit”)

quasipoisson: (link = “log”)