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Perremnan W correlation and “LOrre lation is a statistical teconique that Ws wsed to measure ONG ARCrIVE the relationship between two varianles (the Variables are observed Os they eaist, NO manipuiarion) * The Characteristics of @ relationship “_Unt_dovecton_og the reianeny nip * Positive correlation, tend to change In the same direc: ___ ton (@.g. * increase, Yintrease) A Negative correlation, tend 10 go in the opposite direction Cinverse relanonship, eg. x intwease, Y decrease) “Tne form of Ine relanonsiip Climear iy the most Conimon) _ TINE anvengrh_or_consisvency of_the_velone nship + Exo ple, fora linear telanionsnip the data point coud — PETEeCtly Fit PETERCNY on A Straight ne, everytime x increasea By 4 point, the value of Y alse changer by _ _Q consistent and predicabie amount __* A perfect correlation always is identipied by o correlation Of 1.00 and INdiCOres a pergectiy consiment relationship + Examples of diggerent values for linear coreeanon Secure (-0.40) Karunatitta Pamphary 21020-0190-0004 3 Reqresion * ~_Compurarionar gor mune (ax)? —- §92-x? - SP 2-LxY— uxt | ae * carculotion of the pearson correlanon ~ Rano comparing the covariobitity of X and Y (numerator) with tne variability of x andY separorely (denominator) * Correlation and tne patrern of dato point 7_Adding fsupstrouing a constant som each x and/or Y_ __VO\We does Mot change the partern of dara point noe the correlation — =_Mulsiptying / dividing each » ot Y vowe py a positiv' Oo TONt does Mot Change the pattern nor the value Of the corretarion ~_ Multiplying by oO negative Constant produces a mirroe _Amage of the pattern and changes the sign o¢ tne __torretarion * Pearson correlation and 2- Scores _ Formula for Sampie > _Formuya gor popyiation ~ Ltt | feeetey mouneat ston poritiNe _tniead Larionyhip used with aaa fcale/ranns relativeny wear negative from an erainat ) Pergect __ negative 2. The Pearson Correlation ( ThE PeAriON correlanon meosures the degree andthe direc- _tion of the jinear relorionship between two variables * Formula ee ee covariabitity of ¥ and Y vortability of X and Y separatelt _* Pergect linear relationship = Every changes in X hos a corresponding change in Y _ = corretatvon will be - 1.00 014 1.00 __7_ Similar to SS, it measures the amount of covoriapility | between two variapres = DdeFiNitional formurd — (n-1) __twhert_and why correjarions ore used Prediqtion = volidiey Retinbivey _ 2 Theory verification Interpreting correlations |_* COFTEIATION Simply describe relationship between two vor., Mt does not demonstrate causation 7 _VOIMe OF COrrelAriOn is affected by the 1ange of Stores in the data = _Extreme points (ourtiers) Mave an impact on me varue __= Cortelarion cannot be interpreted of a proportion, to show Ls STy [se 2 (K-Mx) OY My) | the shared variapility. you need to square the correlation Scanned with CamScanner 
