Problem 4. Instead of plotting the residuals versus the fitted values Y to look for dependencies...

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Problem 4. Instead of plotting the residuals versus the fitted values Y to look for dependencies of the variance on the magnitude of Y, one might think of plotting residuals versus the Y; values. (a) When y = X + , a model including an intercept term, is fitted by least squares, show that the sample correlation between the least-squares residuals, 1, ..., En, and Y, ..., Yn is 1 R2, where R is the square of the coefficient of determination (also known as multiple correlation coefficient). (b) Does the result in part (a) depends on assumptions about the errors 1, ..., En in the model y = X+e? 1 Problem 4. Instead of plotting the residuals versus the fitted values Y to look for dependencies of the variance on the magnitude of Y, one might think of plotting residuals versus the Y; values. (a) When y = X + , a model including an intercept term, is fitted by least squares, show that the sample correlation between the least-squares residuals, 1, ..., En, and Y, ..., Yn is 1 R2, where R is the square of the coefficient of determination (also known as multiple correlation coefficient). (b) Does the result in part (a) depends on assumptions about the errors 1, ..., En in the model y = X+e? 1