Material for PGPSE participants of AFTERSCHOOOL CENTRE FOR SOCIAL ENTREPRENEURSHIP. PGPSE is an entrepreneurship oriented programme, open for all, free for all.

1. QUANTITATIVE TOOL IN MANAGEMENT – CORRELATION, REGRESSION & OTHER TOOLS DR. T.K. JAIN AFTERSCHO ☺ OL CENTRE FOR SOCIAL ENTREPRENEURSHIP WWW.AFTERSCHOOOL.TK PGPSE : online programme for future entrepreneurs World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship OPEN FOR ALL FREE FOR ALL

2. WHAT IS CORRELATION? Relation between two variables is called correlation. Maximum possible value = +1 and minimum possible value = -1

3. Steps ... Calculate average find deviations from mean for each value multiply both the means find the average of the products of dx and dy – this is COVARIANCE devide this by the product of standard deviation of X and Y.

4. STEP 1 FIND MEAN MEAN OF 1,2,3 IS 2, MEAN OF 2,3,4,5, IS 3.5

5. STEP 2 FIND STANDARD DEVIATION FIND DIFFERENCE FOR EACH ITEM 1-2 = -1 2-2=0 3-2=1 SO ON... FOR EACH VALUE FIND DIFFERNCE FROM MEAN, SQUARE THIS DIFFERENCE AND FIND THE AVERAGE OF THIS, THIS IS STANDARD DEVIATION.

6. STEP 3 FIND COVARIANCE MULTIPLY EACH DIFFERENCE (WITHOUT SQUARING) -1 MULTIPLIED TO 1 = 1 THUS YOU GET PRODUCT OF DX (DIFFERENCE OF X FROM MEAN) AND DY. FIND AVERAGE OF THESE VALUES.

7. CALCULATION OF CORRELATION COVARIANCE OF X AND Y / (PRODUCT OF STANDARD DEVIATION OF X AND Y)

8. EXAMPLE

9. CORRELATION STEPS 1. FIND MEAN 2. FIND STANDARD DEVIATION 3. FIND COVARIANCE 4. DIVIDE COVARIANCE BY PRODUCT OF STANDARD DEVIATIONS

10. REGRESSION IT SHOWS RELATION BETWEEN TWO VARIABLES – ONE DEPENDENT AND ONE INDEPENDENT THE DEPENDENT VARIABLE CHANGES WITH INDEPENDENT VARIABLE Y = A + BX HERE REGRESSION ANALYSIS HELPS US IN FINDING VALUES OF A AND B A IS CALLED INTERCEPT B IS CALLED SLOPE

11. FORMULA FOR B (SLOPE) SLOPE CAN BE CALCULATED BY THE FOLLOWING FORMULA : COVARIANCE / VARIANCE OF X THUS IF WE CAN CALCULATE COVARIANCE AND VARIANCE, WE CAN ALSO CALCULATE B OR SLOPE A (INTERCEPT) CAN BE CALCULATED BY THE FORMULA : Y = A+BX