REGRESSION

REGRESSIO

N

MEANING OF REGRESSION

WE KNOW HOW TO FIND THE CORRELATION BETWEEN 2 VARIABLES.

WHEN THE CORRELATION IS STRONG POSITIVE OR STRONG NEGATIVE, WE CAN GO AHED WITH THE REGRESSION ANALYSIS OF THE 2 VARIABLES.

CORRELATION GIVES US THE BEHAVIOR OF THE 2 VARIABLES WHILE REGRESSION WILL HELP US TO FIND THE VALUE OF ONE VARIABLE WHEN THE VALUE OF THE OTHER IS KNOWN.

DEFINATION : REGRESSION IS THE THEORY OF ESTIMATION OF UNKNOWN

VALUE OF A VARIABLE WITH THE HELP OF KNOWN VALUE OF OTHER VARIABLES

LINEAR & NON-LINEAR REGRESSION

THE RELATIONSHIP BETWEEN 2 VARIABLES CAN BE LINEAR OR NON-LINEAR.

WE WILL CONSIDER ONLY LINEAR REGRESSION IN 2 VARIABLES.

LET ‘X’ AND ‘Y’ BE THE 2 VARIABLES SAY X= MASS AND Y= LENGTH OF THE SPRING

LET US FIX, ‘X’ AND FIND THE VALUES OF ‘Y’ EXPERIMENTALLY.

‘X’ IS CALLED INDEPENDENT VARIABLE AND ‘Y’ IS CALLED DEPENDENT VARIABLE.

SCATTER DIAGRAM FOR REGRESSION

CONSIDER;

PLOT THE INDEPENDENT VARIABLE(X) ON X-AXIS AND DEPENDENT VARIABLE(Y) ON Y-AXIS AND TRY TO GET A SCATTER DIAGRAM

THE RESULT IS SHOWN ON NEXT SLIDE

X(MASS IN KGS) 20 40 60 80 100

Y(LENGTH OF STRING IN CMS)

48 55.1

56.3

61.2

68

DIAGRAM

CONTND

YOU CAN SEE THAT STRAIGHT LINES CAN NOT BE DRAWN PASSING THROUGH ALL POINTS LINEAR (REGRESSION).

THIS IS DUE TO ERRORS IN ‘Y’

A LINE IS MADE TO PASS THROUGH ALL POINTS IN SUCH A WAY THAT EQUAL NO. OF POINTS LIE ABOVE AND BELOW THIS LINE.

THE SUM OF THE SQUARED OF THE VERTICAL DISTANCE BETWEEN THE LINE AND THE POINTS(∑) IS MINIMUM.

SUCH A LINE IS CALLED A REGRESSION LINE.

NEXT SLIDE SHOWS SUCH A LINE.

CONTND…..

CONTND……

LINE OF BAST FIT OR REGRESSION LINE

Y = a + bX IS THE EQUATION OF REGRESSION LINE

POINT (Xi, Yi) WHICH LIES AT A DISTANCE OF ri ABOVE THIS LINE.

Yi = α + βXi + ri

ri = Yi - α + βXi

a AND b OF REGRESSION LINE ARE ESTIMATES OF α AND β

TO FIND byx FOR THE REGRESSION LINE Y ON X

ACCORDING TO LEAST SQUARES LAW MUST BE MINIMUM THIS HAPPENS WHEN

b IS CALLED REGRESSION COEFFICIENT OF Y ON X DENOTED BY byx

TO FIND a FOR y=a+bX LINE

THANK YOU