Skip to content
Projects
Groups
Snippets
Help
Loading...
Help
Support
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
E
Evaluating Networked Systems
Project
Project
Details
Activity
Releases
Cycle Analytics
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Charts
Issues
0
Issues
0
List
Boards
Labels
Milestones
Merge Requests
0
Merge Requests
0
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Charts
Create a new issue
Commits
Issue Boards
Open sidebar
Robert Ricci
Evaluating Networked Systems
Commits
e0afb25b
Commit
e0afb25b
authored
Mar 03, 2014
by
Robert Ricci
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Finish Chapter 14 contents, still need lab stuff
parent
b9642f00
Changes
1
Hide whitespace changes
Inline
Sidebyside
Showing
1 changed file
with
43 additions
and
0 deletions
+43
0
lectures/lecture14/lecturenotes.tex
lectures/lecture14/lecturenotes.tex
+43
0
No files found.
lectures/lecture14/lecturenotes.tex
View file @
e0afb25b
...
...
@@ 57,6 +57,49 @@
\2
In the end, gives us
$
b
_
1
=
\frac
{
s
^
2
_{
xy
}}{
s
_
x
^
2
}$
\3
Correlation of
$
x
$
and
$
y
$
divided by variance of
$
x
$
\3
$
\frac
{
\sum
{
xy
}

n
\overline
{
x
}
\overline
{
y
}}{
\sum
{
x
^
2
}

n
(
\overline
{
x
}
)
^
2
}$
\1
SS*
\2
SSE = Sum of squared errors
\2
SST = total sum of squares (TSS): difference from mean
\2
SS0 = square
$
\overline
{
y
}$
$
n
$
times
\2
SSY = square of all
$
y
$
, so SST = SSY  SS0
\2
SSR = Error explained by regression: SST  SSE
\1
Point of above: we can talk about two sources that explain variance: sum of
squared difference from mean, and sum of errors
\2
$
R
^
2
=
\frac
{
SSR
}{
SST
}$
\2
The ratio is the amount that was explained by the regression  close to 1 is good (1 is max possible)
\2
If the regression sucks, SSR will be close to 0
\1
Remember, our error terms and
$
b
$
s are random variables
\2
We can calculate stddev, etc. on them
\2
Variance is
$
s
_
e
^
2
=
\frac
{
SSE
}{
n

2
}$
 MSE, mean squared error
\2
Confidence intervals, too
\2
\textit
{
What do confidence intervals tell us in this case?
}
\3
A: Our confidence in how close to the true slope our estimate is
\3
For example: How sure are we that two slopes are actually different
\2
\textit
{
When would we want to show that the confidence interval for
$
b
_
1
$
includes zero?
}
\1
Confidence intervals for predictions
\2
Confidence intervals tightest near middle of sample
\2
If we go far out, our confidence is low, which makes intuitive sense
\2
$
s
_
e
\big
(
\frac
{
1
}{
m
}
+
\frac
{
1
}{
n
}
+
\frac
{
(
x
_
p

\overline
{
x
}^
2
)
}{
\sum
_{
x
^
2
}

n
\overline
{
x
}^
2
}
\big
)
^
\frac
{
1
}{
2
}$
\2
$
s
_
e
$
is sttdev of error
\2
$
m
$
is how many predictions we are making
\2
$
p
$
is value at which we are predicting (
$
x
$
)
\2
$
x
_
p

\overline
{
x
}$
is capturing difference from center of sample
\2
\textit
{
Why is it smaller for more
$
m
$}
?
\3
Accounts for variance, assumption of normal distribution
\1
Residuals
\2
AKA error values
\2
We can expect several things from them if our assumptions about regressions are correct
\2
They will not show trends:
\textit
{
why would this be a problem
}
\3
Tells us that an assumption has been violated
\3
If not randomly distributed for different
$
x
$
, tells us there is a systematic error at high or low values  error and predictor not independent
\2
QQ plot of error distribution vs. normal ditribution
\2
Want the spread of stddev to be constant across range
\1
For next time
\end{outline}
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment