# Load necessary libraries
library(ggplot2)
library(plotly)

Attaching package: 'plotly'

The following object is masked from 'package:ggplot2':

    last_plot

The following object is masked from 'package:stats':

    filter

The following object is masked from 'package:graphics':

    layout

# Step 1: Generate made-up data
set.seed(42)  # For reproducibility
n <- 200
x1 <- rnorm(n)
x2 <- rnorm(n)
z <- -0.5 + 1.2 * x1 + 1.5 * x2  # Linear combination
prob <- 1 / (1 + exp(-z))  # Logistic function for probabilities
class <- rbinom(n, 1, prob)  # Generate binary classes (0 or 1)

# Combine into a data frame
data <- data.frame(x1 = x1, x2 = x2, class = factor(class))

# Step 2: Fit a logistic regression model
model <- glm(class ~ x1 + x2, data = data, family = binomial)

# Step 3: Create a grid for predictions
grid_x1 <- seq(min(data$x1) - 0.5, max(data$x1) + 0.5, length.out = 100)
grid_x2 <- seq(min(data$x2) - 0.5, max(data$x2) + 0.5, length.out = 100)
grid <- expand.grid(x1 = grid_x1, x2 = grid_x2)
grid$prob <- predict(model, newdata = grid, type = "response")

# Step 4: Decision boundary
decision_boundary <- grid[abs(grid$prob - 0.5) < 0.02, ]

# Step 5: Plot 1 - Decision boundary with probabilities
plot1 <- ggplot() +
  geom_tile(data = grid, aes(x = x1, y = x2, fill = prob), alpha = 0.8) +
  scale_fill_gradient(low = "blue", high = "red", name = "P(Class 1)") +
  geom_contour(data = grid, aes(x = x1, y = x2, z = prob), breaks = 0.5, color = "black", size = 1.2) +
  labs(
    title = "Decision Boundary with Probability Gradient",
    x = "Predictor x1",
    y = "Predictor x2"
  ) +
  theme_minimal()

Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.

# Step 6: Plot 2 - Example data with decision threshold
plot2 <- ggplot(data, aes(x = x1, y = x2)) +
  geom_tile(data = grid, aes(x = x1, y = x2, fill = prob), alpha = 0.8) +
  scale_fill_gradient(low = "blue", high = "red", name = "P(Class 1)") +
  geom_point(aes(shape = class, color = class), size = 3, alpha = 0.7) +
  #scale_color_manual(values = c("cyan", "red"), name = "Class") +
  geom_contour(data = grid, aes(x = x1, y = x2, z = prob), breaks = 0.5, color = "black", size = 1.2) +
  labs(
    title = "Example Data with Decision Threshold",
    x = "Predictor x1",
    y = "Predictor x2"
  ) +
  theme_minimal()

# Step 7: Plot 3 - 3D surface using plotly
z_matrix <- matrix(grid$prob, nrow = length(grid_x1), ncol = length(grid_x2))
plot3 <- plot_ly(
  x = grid_x1,
  y = grid_x2,
  z = z_matrix,
  type = "surface",
  colors = c("blue", "yellow")
) %>%
  layout(
    title = "3D Logistic Surface Plot",
    scene = list(
      xaxis = list(title = "Predictor x1"),
      yaxis = list(title = "Predictor x2"),
      zaxis = list(title = "P(Class 1)")
    )
  )

# Step 8: Display plots
print(plot1)  # 2D decision boundary with probabilities

print(plot2)  # 2D decision threshold with example data

plot3         # Interactive 3D surface plot