me May 21, 2026
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union# Make random number generation reproducible
set.seed(123)
# Number of observations/rows to generate
data_size <- 100# create the dataframe
df <- data.frame(
age = round(rnorm(data_size, 35, 10)),
income = round(rnorm(data_size, 50000, 15000)),
education_years = sample(8:18, data_size, replace = TRUE),
purchased = sample(c("No", "Yes"), data_size, replace = TRUE, prob = c(0.7, 0.3))
)
# Ensure the dependent variable is a factor
df$purchased <- as.factor(df$purchased)
# Check the structure of the data
str(df)## 'data.frame': 100 obs. of 4 variables:
## $ age : num 29 33 51 36 36 52 40 22 28 31 ...
## $ income : num 39344 53853 46300 44787 35726 ...
## $ education_years: int 14 10 16 14 16 11 9 13 17 16 ...
## $ purchased : Factor w/ 2 levels "No","Yes": 2 1 1 1 1 2 1 1 1 1 ...## age income education_years purchased
## Min. :12.00 Min. :19201 Min. : 8.00 No :63
## 1st Qu.:30.00 1st Qu.:37983 1st Qu.:10.00 Yes:37
## Median :36.00 Median :46613 Median :13.00
## Mean :35.93 Mean :48387 Mean :12.85
## 3rd Qu.:42.00 3rd Qu.:57018 3rd Qu.:16.00
## Max. :57.00 Max. :98616 Max. :18.00## age income education_years purchased
## 1 29 39344 14 Yes
## 2 33 53853 10 No
## 3 51 46300 16 No
## 4 36 44787 14 No
## 5 36 35726 16 No
## 6 52 49325 11 Yes
## 7 40 38226 9 No
## 8 22 24981 13 No
## 9 28 44297 17 No
## 10 31 63785 16 NoBuilding logistic model using glm(family = “binomial”)
Try to predict purchased based on age, income, and education_years:
#build regression model,
#purchased ~ age + income + education_years
model <- glm(purchased ~ age + income + education_years,
data=df, family = 'binomial')
#model <- glm(purchased ~ ., data = df, family = "binomial") if you want all variables, use a dot (.)Summarizing and interpreting the model.
Deviace Residuals: indicate how well the mdoel is fit to the data, smaller is better.
Coefficients Estimates are log-odds. Highr log-odd estimate means that as predictor variable increases, so does the probability of a postive/“Yes” categorization from the model
std. Error is the standard error of the coefficient estimate (log-odds)
z-value, Wald Z-Stat, testing the significance of each coefficient/predictor
Pr(>|z|), the p-value. Default significance is 0.05, if its less than that then the model has shown the predictor is statistically significant.
Null Deviance: deviance of the model with only its intercept
Residual Deviance: deviance of the fitted model. if this value is significantly smaller than null deviance, then the predictors are suggested to be good for the model
AIC measure of fitness, penalizes model for complexity. lower AIC is indicative of a good model
##
## Call:
## glm(formula = purchased ~ age + income + education_years, family = "binomial",
## data = df)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.417e+00 1.455e+00 -0.974 0.330
## age 3.298e-02 2.348e-02 1.405 0.160
## income -1.393e-05 1.525e-05 -0.913 0.361
## education_years 2.768e-02 6.301e-02 0.439 0.660
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 131.79 on 99 degrees of freedom
## Residual deviance: 128.57 on 96 degrees of freedom
## AIC: 136.57
##
## Number of Fisher Scoring iterations: 4Interpret log-odds as odd ratios: Odds ratio > 1 means that per one-unit increase in the predictor, the odds of the outcome (“Yes”) increases by such a factor.
Odds ratio < 1 means the odds decrese
For example, an odds ratio of 1.2 means the odds increase by 20% for every one-unit increase in the predictor.
## Odds Ratios:## (Intercept) age income education_years
## 0.2423756 1.0335288 0.9999861 1.0280621##
##
## Confidence Intervals:## Waiting for profiling to be done...
## 2.5 % 97.5 %
## (Intercept) 0.0127716 4.015293
## age 0.9877914 1.083886
## income 0.9999549 1.000015
## education_years 0.9085221 1.164756We’ve built the model and interpreted the performance. Now, predictions.
# Creating data for predictions
new_data <- data.frame(
age = c(40, 25, 60),
income = c(60000, 30000, 80000),
education_years = c(16, 12, 18)
)
# Predictions, when we let type="response", we get a binary possibility
pred <- predict(model, newdata = new_data, type = 'response')
cat("Predictions:\n")## Predictions:## 1 2 3
## 0.3796879 0.3366023 0.4863865# now, convert the probabilities into binary outcomes:
pred_classes <- ifelse(pred > 0.5, 'Yes', 'No')
cat("Binary Predictions:\n")## Binary Predictions:## 1 2 3
## "No" "No" "No"Evaluation of model performance. For binary classification, a confusion matrix is common.
CM shows the counts of true/false positives/negatives. This allows us to calculate accuracy statistics like accuracy, precision, revall, F1.
# build CM
# Get predictions from original dataset
predictions_on_df <- predict(model, type="response")
# make those og predicitons binary
predicted_classes_df <- ifelse(predictions_on_df > 0.5, "Yes", "No")
# ensure pred_og is a factor w/ the same levels as the df
predicted_classes_df <- factor(predicted_classes_df , levels = levels(df$purchased))
# cm
cm <- table(Actual = df$purchased, Predicted = predicted_classes_df)
cat("Confusion Matrix:\n\n")## Confusion Matrix:## Predicted
## Actual No Yes
## No 56 7
## Yes 34 3#accuracy stats from cm
accuracy <- sum(diag(cm))/sum(cm)
cat("Model Accuracy: ", round(accuracy, 4), "\n")## Model Accuracy: 0.59