Question

Using the simple linear model with normal errors in an engineering safety experiment, a researcher found...

Using the simple linear model with normal errors in an engineering safety experiment, a researcher found for the first 10 cases that R2 was zero. Is it possible that for the complete set of 30 cases R2 will not be zero? Could R2 not be zero for the first 10 cases, yet equal zero for all 30 cases? Explain.

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Answer #1

Is it possible that for the complete set of 30 cases R^{2} will not be zero?

Yes, if the R^2 of the next 20 cases is not 0, then that will be the case.
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Could R^{2} not be zero for the first 10 cases, yet equal zero for all 30 cases? Explain

Yes, if the correlation of the next 20 cases exactly cancels the correlation due to the first 20 cases. In such a case, it is necessary that the sign of R for the first 10 is opposite of the sign of the next 20 cases.

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