You can create a scatter plot based on a theoretical model and add it to the plot with the `lines`

function. Consider the example of the following block of code as illustration.

```
# Data. Model: Y = X ^ 2
set.seed(54)
x <- seq(0, 10, by = 0.05)
y <- x ^ 2 + rnorm(length(x), sd = 20)
# Scatter plot and underlying model
plot(x, y, pch = 16)
lines(x, x ^ 2, col = 2, lwd = 3)
# Text
text(2, 70, expression(Y == X ^ 2))
```

You can add a regression line to a scatter plot passing a `lm`

object to the `abline`

function. Recall that `coef`

returns the coefficients of an estimated linear model.

```
# Data. Model: Y = X ^ 2
set.seed(54)
x <- seq(0, 10, by = 0.05)
y <- x ^ 2 + rnorm(length(x), sd = 20)
# Scatter plot and linear regression line
plot(x, y, pch = 16)
abline(lm(y ~ x), col = 4, lwd = 3)
# Text
coef <- round(coef(lm(y ~ x)), 2)
text(2, 70, paste("Y = ", coef[1], "+", coef[2], "x"))
```

The LOWESS smoother uses locally-weighted polynomial regression. This non-parametric regression can be estimated with `lowess`

function.

```
# Data. Model: Y = X ^ 2
set.seed(54)
x <- seq(0, 10, by = 0.05)
y <- x ^ 2 + rnorm(length(x), sd = 20)
# Scatter plot and LOWESS regression curve
plot(x, y, pch = 16)
lines(lowess(x, y), col = 3, lwd = 3)
```

See also