Formulas for Inference in Simple Linear Regression - Notes | STAT 305, Study notes of Statics

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Statistics 305: Formulas for Inference in Simple Linear Regression © Model: ys = Bo + fits t+ & Least squares estimates: estimates of the slope and intercept are the least squares slope and intercept from Section 4.1 Estimate of o?: 1 1 2 _g?a2— ye Sir = 5 LY fy = aah Re Residuals: as in Section 4.1 & = Yi e Standardized residuals: ¢ Inference for {: confidence interval SLE yu -#)? by +t + test of Hy: f= # P= (1 -— #)yYd (e - 2)? SLF e Inference for pyje = Po + fiz: confidence interval a grt: sur ats t test of Ho : Uyje = # =# Suri +a > 1 («—#)? Gxt: spr. l+o+ Sec « Simple Regression and ANOVA: SSE =o (y-9)' = (n-2)stp SSR = SSTot — SSE =~ (9-9) 2 _ SSR SSTot T= beep 3 * Prediction intervals: For testing Ho : f; =0 SSR/1 MSR = 35E/m—y ~ Ms #