Simple linear regression models a graph between a dependent variable, normally y, and an independent variable, normally x.

The equation for a simple linear regression is: \[ y = a + bx \]

where a is the intercept and b is the slope.

You use the sum of squared errors, or SSE, to find the best-fitting line for the regression model. The equation for SSE is:

\[ SSE = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 \]

y_i is the actual value of y, while {y}_i is the predicted value of y from the model. Using those values in the equation above gives the best-fitting line for the regression model.

A dataset is created manually with 6 points:

x <- c(10, 11, 12, 13, 14, 15)
y <- c(7, 10, 15, 18, 19, 23)

data = data.frame(x,y)

There are multiple ways of plotting a simple linear regression in R. For example, you can use ggplot2, which will be the first way shown.

Implement ggplot2.

library(ggplot2)

Then plot.

ggplot(data, aes(x=x, y=y)) +
  geom_point(color="maroon", size=3) +
  geom_smooth(method="lm", color="gold", se=FALSE) +
  labs(title="Simple Linear Regression", x="x", y="y") +theme_minimal()

ggplot(data, aes(x=x, y=y)) +
  geom_point(color="purple", size=3) +
  labs(title="Scatter Plot", x="x", y="y") +
  theme_minimal()

Another main way of plotting graphs in R is by using plotly.

Implement plotly and make a z variable for 3D plotting.

library(plotly)
data$z <- rep(1, length(data$x))

Then plot.

plot_ly(data, x = ~x, y = ~y, z = ~z, type = "scatter3d", mode = "markers") %>%
  layout(title = "3D Scatter Plot",
         scene = list(xaxis = list(title = "x"),
                      yaxis = list(title = "y"),
                      zaxis = list(title = "Constant Z")))

plot_ly(data, x = ~x, y = ~y, type = "scatter", mode = "markers+lines") %>%
  layout(title = "Interactive 2D Scatter Plot",
         xaxis = list(title = "x"),
         yaxis = list(title = "y"))