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# 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:-

1. What is regression?

2. What is smoothing?

3. Uses.

6. Example.

7. 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.

• Easy to use

• Simple

• Flexible

• Shows trend

• 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")```