Announcements
!
Our final exam is Wednesday December 10 from 710pm (room
assignments will be announced when I know).
!
If you have a time conflict with another exam (i.e. Calculus), you must bring
the proper form to me personally and I will add you to my list.
!
The last day to contact me personally about a makeup exam is Monday
December 1
st
after class.
(Tuesday, Dec. 2 for the TTh sections.)
!
The time of the makeup exam is Thursday December 11 from 112pm.
Unless you have a schedule conflict, you must take the exam during it’s
regularly scheduled time.
If this time does not work for someone with a
conflict, you must arrange a makeup with your other class.
!
During the week of November 2428, there are no classes, discussions, stat
labs, or quizzes.
All activities will resume Monday 12/1.
Information
!
We can partition the total sum of squares into two
sources of variation.
!
If we are looking at the deviation between y
i
and ybar, it
can be split into two parts.
Question
!
How do the y
i
values vary around ybar?
!
Some of the difference is due to the difference between y
hat
i
and ybar.
"
This difference is accounted for by the difference between x
i
and xbar.
!
The rest of the difference is due to the difference between
y
i
and yhat
i
"
This difference is unexplained by the variation in x.
"
Represents variables not otherwise represented by the
model
Visualizing Errors in the Simple Model
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View Full DocumentUnderstanding Variation
!
Looking at the past equation as sums of squares…
We see
Variation in y = SSE + SSR
!
SSE measures the amount of variation in y that remains unexplained
!
SSR (SSM) measures the amount of variation in y that is explained by the
variation in the independent variable x.
Coefficient of determination,
r
2
The coefficient of determination,
r
2
,
square of the correlation
coefficient,
is the percentage of the variance in
y
(vertical scatter
from the regression line)
that can be explained by changes in
x
.
r
2
=
variation in
y
caused by
x
(i.e., the regression line)
total variation in observed
y
values around the mean
Procedure
1)
Develop a model theoretically and
set a response and
explanatory variable.
2)
Collect data for the two variables (try to conduct an experiment).
3)
Draw a scatter plot to see if a linear model is appropriate (also
consider correlation)
4)
Determine regression equation.
5)
Calculate residuals and examine the residuals plot to determine if
we have constant variance of the error term.
6)
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 Spring '08
 HOLT
 Coefficient Of Determination, Regression Analysis, explanatory variables

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