Abs regression
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Transcript of Abs regression
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.