Summary The term correlation refers to the degree of relationship between two or more variables. Scatter diagram is a graphic device for finding correlation between two variables. Karl Pearson correlation coefficient r ( x , y )= cov X Y v v Correlation coefficient r lies between – and . (i.e) – # r # When r =+ , then the correlation is perfect positive When r =– , then the correlation is perfect negative When r = , then there is no relationship between the variables, (i.e) the variables are uncorrelated.
Rank correlation deals with qualitative characteristics. Spearman’s rank correlation coefficient formula ρ is given by t = – N N h where d = The difference between two ranks = R X – R Y and N = Number of paired observations. Correlation represents linear relationship between the variables but the regression helps to estimate (or predict) one variable by using the other variable. Regression lines of (i) X on Y is X– X = b xy (Y– Y ) (ii) Y on X is Y – Y = b yx ( X – X ) The two regression lines passing through their respective means of X and Y Calculation of the regression coefficients.
b xy = r v v and b yx = r v v The Properties of regression coefficients. (i) r = yx xy (ii) both the regression coefficients cannot be greater than one. (iii) Both the regression coefficients have same sign. - - GLOSSARY (கலைச்சொற்கள்) Abnormal அசாதாரனமான Approximate தோராயமாக Assumed Mean ஊகிக்கப்பட்ட சராசரி Bivariate analysis இருமாறி பகுப்பாய்வு Characteristics பண்புகள் Closeness பொருத்தமுடைய Corrleation ஒட்டுறவு Deviations விலக்கம் Fluctuate ஏற்ற இறக்கம் Interpretation விளக்கம் Negative Correlation எதிர்மறை ஒட்டுறவு Positive Correlation நேரிடை ஒட்டுறவு Random variables சமவாய்ப்பு மாறிகள் Regression analysis தொடர்பு போக்கு ஆய்வு Relative Variable சார்ந்த மாறி Univariate analysis ஒருமாறி பகுப்பாய்வு - - Correlation and Regression analysis Step Browse in the link th Business Mathematics and Statistics (or) scan the QR Code