REGRESSION

Presented by,

Saravanan L (13UTA30)

Karthikeya B (13UTA17)

Ashwin sankar (13UTA06)

Bharath VS (13UTA08)

Sathiyaseelun A RM (13UTA45)

REGRESSIONObjectives:

1.Meaning

2.Definition

3.Simple linear regression

4. Nature of regression lines

5. Equation

6. Properties

7. Where it used?

MEANING

Study of finding a functional relationship between the variables.

Simple regression – study of functional relationship between two variables.

Multiple regression – Study of functional relationship between more then two numbers.

TYPES

Regression

LinearSimple

Multiple

Non-Linear

Simple

Multiple

DEFINITION

Simple Regression:

A regression model is a mathematical equation that describes the relationship between two or more variables. A simple regression model includes two variables; one is Independent and one Dependent. The dependent variable is the one being explained, and independent variable is the one used to explain the variation in the dependent variable.

DEFINITION

Linear regression:

A (simple) regression model that gives a straight-line relationship between two variables called a linear regression model Non – Linear regression

A (Simple) regression model that gives a curve-line relationship between two variables called a non-linear regression model.

Simple Linear Regression

Independent variable (x)

Depend

ent

vari

able

(y

)

The output of a regression is a function that predicts the dependent variable based upon values of the independent variables.

Simple regression fits a straight line to the data.

y’ = b0 + b1X ± є

b0 (y intercept)

B1 = slope= ∆y/ ∆x

є

SIMPLE LINEAR REGRESSION

Simple Linear Regression

Independent variable (x)

Depend

ent

vari

able

The function will make a prediction for each observed data point.

The observation is denoted by y and the prediction is denoted by y.

Zero

Prediction: y

Observation: y

^

^

SIMPLE LINEAR REGRESSION

NATURE OF REGRESSION LINES

1.Perfect Correlation (r=+1 or r=-1)

2.No Correlation ( r=0 )

3.Strong & Weak Correlation

4.Point of intersection & nature of slope

REGRESSION EQUATION

Equation for Y on X :

Y = a+b.X , a,b are constants

byx = Regression co-efficient of Y on X

byx = r.σY/σX

REGRESSION EQUATION

Equation of X on Y

X = a0 + b0.Y , a0 & b0 are constants

bxy = Regression Co-efficient of X on Y

bxy = r.σx/σy

Properties of Regression co-efficients

The correlation co-efficient is the geometric mean of the regression co-efficient.

r = √ byx.bxy . Both the regression co-efficient are either positive or negative. Correlation coefficient has the same sign as that of regression

co-efficient If one regression co-efficient is greater then 1, the other must be

less then 1. Shift of origin does not affect the regression co-efficients, but

shift in scale affects. Arithmetic mean of regression co-efficients is greater than or

equal to correlation coefficient.

WHERE IT USED?

Regression analysis allows you to model, examine, and explore spatial relationships, and can help explain the factors behind observed spatial patterns. Regression analysis is also used for prediction.

Eg. to predict rainfall where there are no rain gauges It provides a global model of the variable or process

you are trying to understand or predict.