STA 371G Lecture Notes - Lecture 13: Prediction Interval, The Intercept
Document Summary
Goal: measure accuracy of forecast/ how much uncertainty there is in forecast. Prediction interval: probable range of y values for a given x: need conditional distribution of y given x. Probability model: "with 95% probability the prediction error will be within +/- ,000. " For sqft = 2: y = 40 + 45(2) + e, y = 130 + e (y|x = 2) ~ n(130, 10^2, 95% prediction interval: 110 < y < 150. B0 and b1 determine the linear relationship btwn x and the mean of y given x. Sigma determines the spread/variation of the realized values around the line. We use least squares to estimate b0 and b1: b1hat = b1 = corr(x,y) * (sdy/sdx, b0hat = b0. S^2 = (1/n-2) * sum(e^2) = sse/n-2: usually use s = sqrt(sse/(n-2)) --> regression standard error. Describes how estimator b1 = b1hat varies over different samples with the x values fitted sb1 = standard error of b1.
