MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Civil and Environmental Engineering
1.017 Computing and Data Analysis for Environmental Applications
Quiz 3
Thursday, December 4, 2003
Please answer all questions on a separate piece(s) of paper with your name clearly identified:
Problem 1 ( 30 points)
Consider the following model of temporal fluctuations in air temperature:
y
(
t
) =
a
1
+
a
2
cos[
π
t
/12]cos[
π
t
/4380] +
e
Where
y
(
t
) is temperature in degrees C,
t
is the number of hours from midnight Dec 31,
a
1
and
a
2
are unknown regression coefficients, and
e
is assumed to be a zero mean normally random residual
error with an unknown standard deviation
σ
e
.
The first cosine function accounts for daily (diurnal)
fluctuations while the second cosine function accounts for seasonal fluctuations.
Suppose that you
have a file called
temp.txt
that consists of a column of daily temperature measurements taken
over a 2 year period.
Write a MATLAB program, using the internal MATLAB
regress
function, to perform a
regression analysis for this problem.
Make sure that your program does the following:
a) Computes leastsquares estimates of
a
1
and
a
2
from the data in
temp.txt
.
b)
Plots a regression curve on the same axes as the temperature measurements.
c)
Plots on the same axes as the regression curve and temperature measurements a pair of 95%
confidence interval curves for the predicted temperature, over the 2 year measurement
period.
The MATLAB documentation for the
regress
function is attached at the end of this exam.
Problem 2 ( 10 points)
Consider the regression ANOVA table presented below.
Indicate whether the regression is
significant at the 95% confidence level.
Compute the
R
2
value.
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 Spring '05
 GeorgeKocur
 Normal Distribution, Environmental Engineering, Massachusetts, Normal probability plot, cosine function accounts, test statistic CDF

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