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.
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. 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. 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. 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. NATURE OF REGRESSION LINES
1.Perfect Correlation (r=+1 or r=-1)
2.No Correlation ( r=0 )
10. 3.Strong & Weak Correlation
4.Point of intersection & nature of slope
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.
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.
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.
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
