Presented by,
Saravanan L
(13UTA30)
Karthikeya B
(13UTA17)
Ashwin sankar
(13UTA06)
Bharath VS
(13UTA08)
Sathiyaseelun A RM...
Objectives:
1.Meaning
2.Definition
3.Simple linear regression
4. Nature of regression lines
5. Equation
6. Properties
7. W...






Study of finding a functional relationship between
the variables.
Simple regression – study of functional relatio...
Simple
Linear

Multiple
Regression
NonLinear

Simple
Multiple
Simple Regression:
A regression model is a mathematical
equation that describes the relationship between two or
more varia...
Linear regression:
A (simple) regression model that gives
straight-line relationship between two variables called
linear r...
Simple Linear Regression

Dependent variable (y)

SIMPLE LINEAR REGRESSION

є

y’ = b0 + b1X ± є

b0 (y intercept)

B1 = s...
Simple Linear Regression

SIMPLE LINEAR REGRESSION

Dependent variable

Observation: y
Prediction: ^
y

Zero
Independent v...
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


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


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









The correlation co-efficient is the geometric mean of the
regression co-efficient.
r = √ byx.bxy .
Both the...





Regression
analysis
allows
you
to
model,
examine,
and
explore
spatial
relationships, and can help explain the fact...
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Abs regression

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  • The term Regression was first used by Sir Fransis Galton (1822-1911), who studied relationship between the heights of children and the height of their parents
  • .
  • Abs regression

    1. 1. Presented by, Saravanan L (13UTA30) Karthikeya B (13UTA17) Ashwin sankar (13UTA06) Bharath VS (13UTA08) Sathiyaseelun A RM (13UTA45)
    2. 2. Objectives: 1.Meaning 2.Definition 3.Simple linear regression 4. Nature of regression lines 5. Equation 6. Properties 7. Where it used?
    3. 3.    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.
    4. 4. Simple Linear Multiple Regression NonLinear Simple Multiple
    5. 5. 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. 
    6. 6. Linear regression: A (simple) regression model that gives straight-line relationship between two variables called linear regression model  Non – Linear regression A (Simple) regression model that gives curve-line relationship between two variables called non-linear regression model.  a a a a
    7. 7. Simple Linear Regression Dependent variable (y) SIMPLE LINEAR REGRESSION є y’ = b0 + b1X ± є b0 (y intercept) B1 = slope = ∆y/ ∆x Independent variable (x) 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.
    8. 8. Simple Linear Regression SIMPLE LINEAR REGRESSION Dependent variable Observation: y Prediction: ^ y Zero Independent variable (x) The function will make a prediction for each observed data point. The observation is denoted by y and the prediction is denoted by y. ^
    9. 9. NATURE OF REGRESSION LINES 1.Perfect Correlation (r=+1 or r=-1) 2.No Correlation ( r=0 )
    10. 10. 3.Strong & Weak Correlation 4.Point of intersection & nature of slope
    11. 11.  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
    12. 12.  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
    13. 13.       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.
    14. 14.    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.
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