# See for visualization
# https://r-graph-gallery.com/

# Correlation and Regression

# Village Weaver Data

# Set working directory and Import data
weaver <- read.csv("villageweaver.csv")


# -------------------------------------------------------------

# CORRELATION

# -------------------------------------------------------------

# Check whether wing length and weight are correlated.

  ## Step 1: Check the variables

summary(weaver$wing)
summary(weaver$weight)

  
  ## Step 2: Plot the relationship (Scatterplot)

library(ggplot2)
ggplot(weaver, aes(x = wing, y = weight)) +
  geom_point() +
  labs(x = "Wing Length (mm)",
       y = "Weight (g)") +
  theme_classic()
  
  ## Step 3: Calculate correlation

shapiro.test(weaver$weight)

cor(weaver$wing, weaver$weight, method = "spearman")
cor.test(weaver$wing, weaver$weight, method = "spearman")

### Interpretation

# Correlation coefficient (r)
  # r > 0 : positive relationship
  # r < 0 : negative relationship
  # r = 0 : no relationship

# There is a positive correlation between wing length and weight (r = 0.63, p < 0.001).
# Birds with longer wings tend to be heavier.
# -------------------------------------------------------------

# 3. LINEAR REGRESSION

# -------------------------------------------------------------

### Goal: Predict weight from wing length.

  ## Step 1: Fit a linear regression model
  
model1 <- lm(weight ~ wing, data = weaver)
summary(model1)

### Look at:
  # Estimate for wing → slope
  # p-value → significance of effect
  # R-squared → how much variation is explained

# Wing length significantly predicts weight (p < 0.001).
# The model explains about 54% of the variation in weight.
# For each 1 mm increase in wing length, weight increases by about 0.88 g.
  
  ## Step 2: Plot regression line with ggplot

ggplot(weaver, aes(x = wing, y = weight)) +
  geom_point() +
  geom_smooth(method = "lm") +
  labs(x = "Wing Length (mm)",
       y = "Weight (g)") +
  theme_classic()


# -------------------------------------------------------------

# 4. MULTIPLE REGRESSION

# -------------------------------------------------------------

### Predict weight using wing and sex.

model2 <- lm(weight ~ wing + sex, data = weaver)
summary(model2)

ggplot(weaver, aes(x = wing, y = weight, colour=sex)) +
  geom_point() +
  geom_smooth(method = "lm") +
  labs(x = "Wing Length (mm)",
       y = "Weight (g)") +
  theme_classic()