Transcript squared - Campbell County Schools

3.2 - LeastSquares
Regression
Where else have we
seen
“residuals?”
Sx = data point - mean
(observed - predicted)
z-scores = observed - expected
• * note: this is just the
numerator of these calculations
Remember:
AP
Below is the LSRL for sprint time (seconds) and the long jump distance (inches)
Find and interpret the residual for John who had a time of 8.09 seconds and a
jump of 151 inches.
•
predicted long jump distance = 304.56 - 27.63(sprint time)
residual = observed - predicted
residual
=- 69.97
151
81.03inches
John jumped much farther than what
was predicted by our least squares
regression line. He jumped almost 70
inches farther, based on his sprint
time.
So why least squared
regression line?
://bcs.whfreeman.com/tps4e/#628644__66639
Residual Plots
a scatterplot of the residuals
against the explanatory
variable.
Use to help assess the
strength of your regression
line
with Normal Probability Plots
we want the graphs to be
linear to support the Normality
of our data.
with Residual Plots we want
the residuals to be very
scattered so our data is can
be model with a linear
Remember:
regression.
Residual Plots
Correlation does NOT assess
linearity, just strength and direct
What’s a Good
Residual
Plot?
No
obvious pattern
- the LSRL
would be in the middle of the
data, some data above and
some below
Relatively small residuals - the
data points are close to the
LSRL
Do the following residual plots support
or refute a linear model?
http://content.ebscohost.com/pdf23_24/pdf/2009/D8Y/01Sep09/43669525.pdf?T=P&P=AN&K=43669525&S=R&D=aph&EbscoContent=dGJyMNHX8kSeqK84yOvqOLCmr0qep7RSs6%2B4S7aWxWXS&ContentCustomer=
ssk2xqLJNuePfgeyx44Hy
How
to
Graph?
Take each data point and
determine the residual
Plot the residuals versus the
explanatory variable
• i.e. (explanatory data, residual)
residual
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
use the same numbers as your scatterplot
explanatory variable
Calculator
Construction
have a lot of data, follow the instructions on pag
to construct your residual plot
also have to have done the technology corner o
What is Standard
Deviation?
the average squared distance
a data point is from the mean
Is there a sx? Is there a sy?
So why not s? (standard
deviation of residuals)
Standard Deviation of
Residuals
gives the approximate size of
an “average” or “typical”
prediction error from our LSRL
formula on page 177
Why divide by n-2?