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Multiple and partial correlation(old)
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Multiple correlation question. Given the correlation coefficent of $Y$ with $X_1$ is $r_{01}$ , the correlation coefficent of $Y$ with $X_2$ is $r_{02}$ and the correlation coefficent of $X_1$ with $X_2$ is $r_{12}$ then explain the proportion of variablity of $Y$ . Also find the partial corr coeff between $Y$ and $X_2$ after fitting $X_1$ and find how much of the remaining variability in $Y$ is explained by $X_2$ after fitting $X_1$ .