Problem 13 dealt with how to form a confidence interval for the value of a line at a poi...

Problem 13 dealt with how to form a confidence interval for the value of a line at a point x₀. Suppose that instead we want to predict the value of a new observation, Y₀, at x₀,

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Suppose that a line is fit by the method of least squares to n points, that the standard statistical model holds, and that we want to estimate the line at a new point, x₀. Denoting the value on the line by μ₀, the estimate is