Demo Presentation on Linear Regression

Nishant Upadhyay
21/11/2015 2.30 pm

Relationships between 2 variables

  • Correlation—Correlation is a bivariate analysis that describes the strength of linear association between two numerical variables.

  • Correlations has two properties: strength and direction.

Correlation is not causation

  • Ice cream sales are positively correlated with shark attacks on swimmers

causationimpliescausation

"Regression Towards Mediocrity"

  • Sir Francis Galton

francisgalton

It's a Basket---yay!

Let's take Shaquille O'Neal as an example. Shaq is really tall, 7 ft 1 in to be exact (for you metric fans that's about 2.2 meters)

Shakiloniel

  • How tall would be be his son Turns out this is the case: Shaq's son is pretty tall (6 ft 7 in), but not nearly as tall as his dad.

Simple Linear Regression

Galton called this phenomenon regression, as in “A father's son's height tends to regress (or drift towards) the mean (average) height.”

Linear regression is an approach to model a relationship between a dependent variable (y) and one or more independent variables (x).

\[ Y_i=\beta_0 + \beta_1 X_i \]

Digging the Regression Dirt

A very simple example to understand how the relationship between two variables work. We will explore a relationship between Father's heigth and Son's height.

scatter1

Regression technique tries to fit a single line through a scatter plot by the principle of minimising the squared sum of errors.

What does Best Fit Line mean?

  • A critical question to ask at this point is why this red line?—why not green or blue line

  • how can we claim that this line is the best and what it means to be the best fit line?

scatter2

What next?

  • Linear regression is a powerful tool that you can do some really cool stuff with.From just this example you could estimate how tall a man's son will be before he has one, determine which of your friends is freakishly tall with respect to their dad, or even compare different groups of men and their sons over time to analyze trends.

One day, Simba, you will be 4' 10".

lionking

Its NOT the End-Its just the begining!

Concepts at this stage will be confusing/nagging– which is a good thing…..explore..read…ask…collaborate

cause its Friday, andR can be molesting sometime

Refer books:

  • S C Gupta for Statistics
  • Basics Econometrics by Damodar Gujrati,5ed