A scatter plot displaying the relationship between two numeric variables with a fitted polynomial regression curve (degree 2-4). This visualization extends beyond linear regression to capture non-linear relationships in data, making it ideal for modeling curved trends, parabolic patterns, and complex data relationships where a straight line would not adequately represent the underlying pattern.
#' anyplot.ai
#' scatter-regression-polynomial: Scatter Plot with Polynomial Regression
#' Library: ggplot2 3.5.1 | R 4.4.1
#' Quality: 90/100 | Created: 2026-08-11
library(ggplot2)
library(ragg)
set.seed(42)
# --- Theme tokens -------------------------------------------------------
THEME <- Sys.getenv("ANYPLOT_THEME", "light")
PAGE_BG <- if (THEME == "light") "#FAF8F1" else "#1A1A17"
ELEVATED_BG <- if (THEME == "light") "#FFFDF6" else "#242420"
INK <- if (THEME == "light") "#1A1A17" else "#F0EFE8"
INK_SOFT <- if (THEME == "light") "#4A4A44" else "#B8B7B0"
# Imprint categorical palette — 8 hues, theme-independent
IMPRINT_PALETTE <- c(
"#009E73", # 1 — brand green (ALWAYS first series)
"#C475FD", # 2 — lavender
"#4467A3", # 3 — blue (used here for the fitted curve)
"#BD8233", # 4 — ochre
"#AE3030", # 5 — matte red
"#2ABCCD", # 6 — cyan
"#954477", # 7 — rose
"#99B314" # 8 — lime
)
# --- Data -----------------------------------------------------------------
# Nitrogen fertilizer applied to a corn field vs. resulting yield — a classic
# diminishing-returns relationship: yield climbs with more nitrogen, then
# plateaus and declines once over-fertilization sets in (quadratic pattern).
n <- 120
fertilizer_kg_ha <- runif(n, min = 0, max = 300)
noise <- rnorm(n, mean = 0, sd = 0.8)
corn_yield_t_ha <- -0.00018 * fertilizer_kg_ha^2 +
0.075 * fertilizer_kg_ha +
2.5 +
noise
df <- tibble::tibble(
fertilizer_kg_ha = fertilizer_kg_ha,
corn_yield_t_ha = corn_yield_t_ha
)
# Fit the degree-2 polynomial to report R² and the equation coefficients
poly_fit <- lm(corn_yield_t_ha ~ poly(fertilizer_kg_ha, 2, raw = TRUE), data = df)
r_squared <- summary(poly_fit)$r.squared
coefs <- coef(poly_fit)
annotation_label <- paste0(
sprintf("y = %.5fx² + %.3fx + %.2f", coefs[3], coefs[2], coefs[1]),
"\n",
sprintf("R² = %.3f", r_squared)
)
ann_x <- min(df$fertilizer_kg_ha) + 0.03 * diff(range(df$fertilizer_kg_ha))
ann_y <- max(df$corn_yield_t_ha) - 0.02 * diff(range(df$corn_yield_t_ha))
# --- Plot -------------------------------------------------------------------
title_text <- "Corn Yield vs. Nitrogen Fertilizer · scatter-regression-polynomial · r · ggplot2 · anyplot.ai"
p <- ggplot(df, aes(x = fertilizer_kg_ha, y = corn_yield_t_ha)) +
geom_smooth(
method = "lm",
formula = y ~ poly(x, 2, raw = TRUE),
se = TRUE,
color = IMPRINT_PALETTE[3],
fill = IMPRINT_PALETTE[3],
alpha = 0.18,
linewidth = 1.2
) +
geom_point(color = IMPRINT_PALETTE[1], size = 2.5, alpha = 0.65) +
annotate(
"text",
x = ann_x, y = ann_y,
label = annotation_label,
hjust = 0, vjust = 1,
size = 3.2, lineheight = 1.15,
color = INK
) +
labs(
title = title_text,
x = "Nitrogen Fertilizer (kg/ha)",
y = "Corn Yield (t/ha)"
) +
theme_minimal(base_size = 8) +
theme(
plot.background = element_rect(fill = PAGE_BG, color = PAGE_BG),
panel.background = element_rect(fill = PAGE_BG, color = NA),
panel.grid.major = element_line(color = INK_SOFT, linewidth = 0.15),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
axis.title = element_text(color = INK, size = 10),
axis.text = element_text(color = INK_SOFT, size = 8),
axis.line = element_line(color = INK_SOFT),
axis.ticks = element_blank(),
plot.title = element_text(color = INK, size = 9, face = "bold"),
plot.margin = margin(t = 12, r = 20, b = 10, l = 10)
)
# --- Save -------------------------------------------------------------------
ggsave(
filename = sprintf("plot-%s.png", THEME),
plot = p,
device = ragg::agg_png,
width = 8,
height = 4.5,
units = "in",
dpi = 400
)
Part of Scatter Plot with Polynomial Regression on anyplot.ai.