# LOCALLY ESTIMATED SCATTERPLOT SMOOTHING

Author : Amritha Varma

Locally Estimated Scatterplot Smoothing (LOESS) is a regression tool which help us to create a smooth line between the scatter plot. It helps us to show the relation between the variables and trends of variables. It is a non parametric regression method which combines multiple regression in K-nearest neighbor. Non parametric regression finds a curve without assuming data. This smoothing function captures general patterns and it makes assumptions about relationship among variables. The result of LOESS is a line moving through central tendency. It is mainly used to show the relationship between two variables with large data sets.

**Content:-**

What is regression?

What is smoothing?

Uses.

Advantages.

Disadvantages.

Example.

Reference.

**WHAT IS REGRESSION:-**

Regression is a mathematical function which show the relationship between one dependent variable and one more variable. The obtained function is called regression equation.

**WHAT IS SMOOTHING:-**

Smoothing is a technique to group variables with similar expectations and fit a suitable curve. It helps to decrease the volatility in data series. Therefore trend can be observed clearly.

**USES:-**

Fitting a line to a scatter plot where noisy data values with your ability to see a line of best fit.

Linear regression where least squares fitting does not create a line of good fit

Data explorations in social science.

**ADVANTAGES:-**

Easy to use

Simple

Flexible

Shows trend

**DISADVANTAGES:-**

Complex in nature

Difficult for explaining result

No on hand formula so it is difficult to transport results.

**EXAMPLE:-**

**Figure-1**

Here the scatterplot will be displayed on the basis of car dataset with box plots in the margins and non-parametric regression smooth.

```
x <- mtcars$wt
y <- mtcars$mpg
plot(x, y, main = "Main title",
xlab = "X axis title", ylab = "Y axis title",
pch = 19, frame = FALSE)
lines(lowess(x, y), col = "green")
```