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REGRESSION

REGRESSION. 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.

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REGRESSION

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  1. REGRESSION

  2. 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

  3. 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.

  4. 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

  5. diagram

  6. 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.

  7. CONTND…..

  8. 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 αAND β

  9. 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 byx FOR THE REGRESSION LINE Y ON X

  10. TO FIND a FOR y=a+bX LINE

  11. THANK YOU

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