Linear Regression is the process of finding a “best fit” line for a data set. This line may not directly pass through any data points, but it can be used as a somewhat reliable tool to predict values in the data by going to the corresponding \(x\) or \(y\) value and seeing where that point falls on the best fit line.

• Easy to compute, can often be done on a calculator and does not need much computing power

• Allows extrapolation based on the best fit line to imagine what other data points might look like

• Can be done with any amount of data points, however more points will produce a more accurate best fit line

-Generates an easy to follow line using the formula \(y=mx+b\) where m is the slope, and b is the y-intercept.

#This code generates a plotly plot showing the best fit line between city 
#mileage and cylinders in the engine as a scatter plot.
mod = lm(mpg$cty~mpg$cyl)
x = mpg$cyl
y = mpg$cty

xax = list(
  title = "Cylinders"
)

yax = list(
  title = "MPG (City)"
)

plot_ly(x = x, y = y, type = "scatter", mode = "markers", name = "data") %>%
  add_lines(x = x, y = fitted(mod), name = "fitted") %>%
  layout(xaxis = xax, yaxis = yax)

ggplot(data = mpg, aes(x = cyl, y = hwy)) + geom_smooth()

## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

Interestingly, the best fit line between the number of cylinders a car has in its engine and the miles per gallon it gets stays almost the exact same shape whether talking about the city or the highway.