Lab 2, assignment 1: OLS regression of electricity consumption on temperature at 53 sites

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Lab 2, assignment 1 OLS regression of
electricity consumption on temperature at 53 sites
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SAS code for ridge regression
proc reg datamining.dailytemperature outest
dtempbeta ridge0 to 10 by 1 model
daily_consumption stockholm g_teborg malm_
/p output outolsoutput predolspred proc print
datadtempbeta run
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Estimated regression parameters in ridge
regression
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Predicted vs observed values in OLS regression
and ridge regression- trade-off between variance
and bias
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Fat content vs absorbance in different channels
(wavelengths)
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OLS regression fat vs channel10, channel30,
channel50, channel70, channel90
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OLS regression fat vs channel1 channel 100
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OLS regression fat vs channel1 channel 100
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OLS regression with strongly correlated predictors
If the XTX matrix has not full rank (some
X-variables are linearly dependent) the mean
square solution is not unique If the X-variables
are strongly correlated, then (i) the
regression coefficients will be uncertain (ii)
the predictions may be OK
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Principal Component Analysis of lake survey data
Some variables vary much more than others How
does this influence principal components derived
from the covariance and correlation matrices,
respectively?
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Principal Component Analysis of lake survey
data- score plot derived from the correlation
matrix
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Principal Component Analysis of lake survey
data- eigenvectors derived from the correlation
matrix
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Principal Component Analysis of lake survey data
with outliers removed- score plot derived from
the correlation matrix
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Principal Component Analysis of lake survey data
with outliers removed - eigenvectors derived
from the correlation matrix
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Principal Component Analysis of lake survey data
with outliers removed- MINITAB score plot
derived from the correlation matrix
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Principal Component Analysis of lake survey data
with outliers removed - MINITAB loading plot
derived from the correlation matrix
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Regression of an indicator matrix
Find a linear function which is (on average) one
for objects in class 1 and otherwise (on average)
zero Find a linear function which is (on
average) one for objects in class 1 and otherwise
(on average) zero
Assign a new object to class 1 if
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Discriminant analysis- decision border
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3D-plot of an indicator matrix for class 1
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3D-plot of an indicator matrix for class 2
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Regression of an indicator matrix-
discriminating function
Estimate discriminant functions for each class,
and then classify a new object to the class with
the largest value for its discriminant function
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Linear discriminant analysis (LDA)
LDA is an optimal classification method when the
data arise from Gaussian distributions with
different means and a common covariance matrix