Multiple Correlation - Thiyagu

Multiple Correlation - Thiyagu

• 1.
  Multiple Correlation K.THIYAGU, AssistantProfessor, Department of Education, Central University of Kerala, Kasaragod
• 2.
  Multiple Correlation Coefficient denoting acorrelation of one variable with multiple other variables. The multiple correlation coefficient is denoted as RA. BCD…K Which denotes that A is correlated with B,C,D up to K variables
• 3.
  The Multiple Correlation Coefficient,R, is a measure of the strength of the association between the independent (explanatory) variables and the one dependent (prediction) variable. R value Interpretation* 1 Perfect linear relationship 0 No linear relationship R value Interpretation 0.9 Strong association 0.5 Moderate association 0.25 Weak association Multiple Correlation Coefficient
• 4.
  The R2 isthe percentage of variance in DV explained by the linear combination of IVs
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  R = 0 R=  0.2 R =  0.4 R2 = 0 R2 = 0.04 R2 = 0.16 Variance = 0 % Variance = 4 % Variance = 16 % X Y X Y X Y
• 6.
  R = 0.8 R =  1 R2 = 36 R2 = 0.64 R2 = 1 Variance = 36 % Variance = 64 % Variance = 100 % X Y R =  0.6 X X Y Y
• 7.
  Anxiety X Academic Achievement Y Intelligence Z RAcademic Achievement (Y). Anxiety (X) Intelligence (Z) Correlation can be represented as
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  Academic Achievement IntelligenceAnxiety
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  Eg: If we takethe case of one’s academic achievement, it may be found associated with or dependent on variables like intelligence, socio-economic status, education of the parents, the methods of teaching, the quality of teachers, aptitude, interest, environmental setup, number of hours spent on studies and so on. In many studies related to education and psychology, we find that the variable is dependent on a number of other variables called independent variables.
• 10.
  Interpretation of R Strengthof the Association: The strength of the association is measured by the Multiple Correlation Coefficient, R. R can be any value from 0 to +1. • The closer R is to one, the stronger the linear association is. • If R equals zero, then there is no linear association between the dependent variable and the independent variables. Unlike the simple correlation coefficient, r, which tells both the strength and direction of the association, R tells only the strength of the association. R is never a negative value. This can be seen from the formula below, since the square root of this value indicates the positive root.
• 11.
  Given variables x,y and z, we define the multiple correlation coefficient
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  Example: In a study,a researcher wanted to know the impact of a person’s intelligence and his socio-economic stats on his academic success. For computing the coefficient of multiple correlation, he collected the required data and computed the following intercorrelations: r12=0.60; r13=0.40; r23=0.50 Where 1,2,3 represent the variables ‘Academic Success’, ‘Intelligence’ and ‘socio-economic status’ respectively. In this case, find out the required multiple correlation coefficient.
• 15.
  r12=0.60; r13=0.40; r23=0.50 Where1,2,3 represent the variables ‘Academic Success’, ‘Intelligence’ and ‘socio-economic status’ respectively. In this case, find out the required multiple correlation coefficient.
• 16.
  Thank You K.THIYAGU, Assistant Professor, Departmentof Education, Central University of Kerala, Kasaragod