STAT212regression

STAT212regression - Simple linear regression The...

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Simple linear regression: The coefficient of determination, r^2 , measures the proportion of variability in y that is explained by x. Each SRS is drawn from a distinct subpopulation (explanatory variable). One SRS, with multiple measurements (fixed x value) y^= bo + b1x µy= ßo + ß1x (where ß1= µb1) yi= ßo + ß1x + ei (0, ∂) - Linearity as µy connects subpopulation means. - Constant spread- ∂ doesn’t depend on x. - Normality - Each is bell shaped within a subpopulation. Formulas for regression standard error s and SEb1 are given. Ho: ß1= 0 (Ha would be 1 or 2 sided) t= b1/SEb1 (n-2 degrees of freedom) CI- b1 +- tSEb1 NOTE on robustness- A moderate lack of normality may be tolerated but outliers may be problematic. r is the sample correlation, p is the population correlation. Ho: p= 0 (against Ha 1 or 2 sided) - Calculate other form of test statistic t and use n-2 df. Confidence interval for y^ (estimate from µy= ßo + ß1x.) y^ +- tSEµ^ Predicted interval for y^ (prediction for y) y^+- tSEy^ (Larger due to greater uncertainty) Total MS = SST/DFT= sy^2 MSR = SSR/DFR= (n-1)r^2sy^2 MSE = SSE/DFE= s^2
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