PowerPoint Presentation
More on linear regression regression to the meanBaseball
Examples from WebQuartiles
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More on linear regression regression to the meanWhat causes
regression to the mean?What causes the extreme score?Random
variation (chance)?True score?A bit of eachthe more random
variation there is, the more regression to the mean will
occurExample:Think of 2 examsin each of 2 casesCase 1: Exam 1 and
exam 2 scores totally determined by abilityCase 2: Exam 1 and exam
2 scores determined 50% by ability, 50% by chance variation
(feeling good , knew that question, misunderstood a word, etc)KNR
445Regression: slide 212
Exam 1Exam 1Exam 2Exam 22More on linear regression regression to
the meanCorrelate exam 1 with exam 2 in each case:Case 1:Case
2:
KNR 445Regression: slide 31
What if we take z-scores of each variable?More on linear
regression regression to the meanKNR 445Regression: slide
4124Intercept now = 0Slope now = r
563
More on linear regression regression to the meanSo, regression
to the mean is proportional to ruseful to know in situations when
post-test scores and pre-test scores are not perfectly correlated
(all the time!)Means outliers on the pre-test will generally drift
towards the mean on the post-testOriginally demonstrated by Galton
with offspring (taller parents had kids that were in general closer
to mean height)This is actually where the term regression came from
in the procedureSee the sophomore sink and but I regress (web
site)Used in all good fantasy sport estimators1
E.G. Tattoos & workout time
The thing we are trying to predict workout timeThe predictor - #
tattoos12
E.G. - Output
First box is just telling you what you analyzed - 2nd box is
quite informative lets look at that12
E.G. - Output
4. 68% of peoples predicted # hours workout time will fall +/-
3.35 of the value predicted using regression equation3. Adjusts the
R2 value based on sample sizesmall samples tend to overestimate the
ability to predict the DV with the IV1. Pearsons r correlation
between the two variables2. Coefficient of Determination - % of
variance in workout hours accounted for by # tattoos
E.G. Output (continued)
1. ANOVA stuff thats after the midterm. For now, note that the
two procedures give you the same answer2. Still significant...3.
Intercept, slope4. a) Intercept different from 0? b) Is this
relationship reliable (significant, greater than chance,
etc...)?
3E.G. Output (continued)How effectively can we predict a (male)
persons workout hours per week from the number of tattoos he
has?Answer/interpretation:A simple linear regression was calculated
predicting males workout hours per week from their number of
tattoos. A significant regression equation was found (F(1,53) =
7.27, p
