del Assumptions o what are they? ____ 1. E(Yit) = m + t(i) 2. outliers? 3. independence? 4. constant variance? 5. normality? o why important? o what if violated? o offer mainly visual/grahic Residual Analysis techniques and some tests o obtain residuals _____ - e(it) = Y(it) - Y (i.) - standardized are Z(it) = e(it) / sqrt (MSE) ala Dean Z(it) = e(it)/sqrt (SSE/(n-1)) - for us: Dean Y(it) z(it) L(it) Z(it) 100 -.48 64 -.55 93 -.78 76 -.90 140 1.26 72 1.45 105 1.16 79 1.34 45 -1.45 71 -1.67 85 .29 70 .34 35 -.10 77 -.12 40 .12 70 .13 37 -.01 75 -.02 o proper model? - plot z(it) vs. L(it) and check for pattern - plot z(it) vs. Y(it) and check for pattern o outlier - 95% within 2 st.dev - recording errors? o independence - if data collected sequentially or in proximity to each other the plot z(it) in order - check for pattern o equal variance - graphical: plot z(it) in each treatment and view ranges - ad hoc test is max(sample variance) ----------------------------- min (sample variance) is less than 3