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"url": "https://numbas.mathcentre.ac.uk/api/questions/11867/?format=api",
"name": "Multiple and partial correlation(old)",
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"full_name": "Newcastle University Mathematics and Statistics",
"pk": 697,
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"notes": "<p>The correlation coefficients are generated by $Y$ a random sample of 10 numbers between 5 and 20, $X_1$ obtained from $Y$ by adding on some noise and similarly for $X_2$. The correlation coefficients are then worked out from these samples.</p>",
"licence": "Creative Commons Attribution 4.0 International",
"description": "<p>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 $X_1$.</p>"
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