Use the following steps to establish a relationship between the coefficient of determination and the correlation coefficient.
Question:
Use the following steps to establish a relationship between the coefficient of determination and the correlation coefficient.
a. Show that \(\widehat{y}_{i}-\bar{y}=b_{1}\left(x_{i}-\bar{x}\right)\).
b. Use part (a) to show that Regress \(S S=\sum_{i=1}^{n}\left(\widehat{y}_{i}-\bar{y}\right)^{2}=b_{1}^{2} s_{x}^{2}(n-1)\).
c. Use part (b) to establish \(R^{2}=r^{2}\).
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Regression Modeling With Actuarial And Financial Applications
ISBN: 9780521135962
1st Edition
Authors: Edward W. Frees
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