STAT 503 Quiz VI

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Author:
MRK
ID:
272014
Filename:
STAT 503 Quiz VI
Updated:
2014-05-08 13:48:17
Tags:
ANOVA REgression
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Description:
ANOVA and Regression
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  1. Limits to ANOVA
    • population must be normally distributed
    • samples are independent and random
    • sd of sample = sd of larger population therefore pooled SE
  2. ANOVA Hypothesis
    • H0: u1 = u2 = u3
    • HA: at lease one u is different
  3. n dot
    total number of observations
  4. yij
    observation in j position from group i
  5. SSW
    • sum of squares within
    • (yij - meani)2 + (yij - meani)2 + all js
  6. df within
    n dot - number of categories
  7. MSW
    • mean squares within
    • = SSW/dfW
  8. SSB
    • sum of squares between
    • ni(yi - ygrand)2 + ...
    • Will go up if one mean is higher (reject)
  9. y- double bar
    • overall mean
    • (ni * group mean) + (ni * group mean) / n dot
  10. df between
    I - 1
  11. MSB
    • Mean Squares between
    • = SSB/dfB
  12. SS(total)
    • SS(total) = SSW + SSB
    • df = total observations -1
  13. distance of yij from grand mean
    (yij - yi mean) + (yi mean - grand mean)
  14. Values in ANOVA table
    • df (w & b) total
    • SS (w & b) total
    • MS (w & b) no total
    • Fs
  15. Fs
    • test statistic for ANOVA
    • MSB/MSW
    • High = reject
    • distribution like X2
  16. relationship btw F-test and t-test
    • F2 = ts2
    • using pooled SE
    • Falpha = talpha/22
    • df = n1 + n2 -2
    • non-directional
    • will have same decision
  17. eg
    F(4,20).05
    • F(dfB, dfW)alpha
    • can get I and n-dot from
  18. Conditions of validity for ANOVA
    • Population sds are equal
    • within each group the samples are from normal populations are large n
    • independent and random samples
  19. how to check if sd's are similar
    • residuals:
    • add/subract average - to center on zero
    • want parallel lines
  20. checking for normality?
    plot qq in straight line
  21. response variable
    explanatory variable (controlled)
    • Y
    • X, predictor, co-variate
  22. r
  23. measures strength of relationship X and Y
  24. Hypothosis for correlation btw X and Y
    • H0: rho = 0
    • HA: rho ≠ 0
  25. ts for X, Y correlation
    • t-test
    • = r* √(n-2)/(1-r2)
    • df = n - 2
  26. ei
    • residuals
    • = (yi - bo - mxi)
    • want them to be smallest

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