Statistics Graduate Level Quiz
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ADVANCED TOPICS IN GRADUATE STATISTICS
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A simple linear regression is fitted to n=25n=25 observations. The residual standard error is s=2s=2, the predictor mean is xˉ=10\bar{x}=10, and Sxx=∑i=1n(xi−xˉ)2=100S_{xx}=\sum_{i=1}^{n}(x_i-\bar{x})^2=100. At x0=14x_0=14, the fitted response is y^0=18\hat{y}_0=18. Assume the usual Gaussian linear-model conditions, and use t0.975,23=2.064t_{0.975,23}=2.064.
Which interval is the approximate 95%95\% prediction interval for a single new response at x0=14x_0=14?
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