PSTAT 120C:
Practice Midterm
May 2, 2006
The midterm will be Thursday May 4 form 9:30 to 10:45. Please bring
•
Textbook,
•
One page (8
1
2
×
11) with whatever formulas you decide are necessary,
•
Calculator, and
•
Blue book for writing all your answers.
Please come early on Thursday because the exam will begin promptly at 9:30 to give everyone as
much time as possible.
Here are a couple of practice questions. I hope to publish the solutions on Wednesday.
1. Suppose that
Y
1
, . . . , Y
n
are independent normal observations with standard deviation
σ
and
expectations
E
(
Y
i
) =
β
0
+
β
1
x
i
for some known values of
x
i
. Let ˆ
y
i
be the leastsquares predicted value of the mean at
x
i
.
Calculate Cov(ˆ
y
i
, y
i
).
2. The Goleta Surfboard Company wants to predict the size of the waves based on the speed
of the wind at the coast.
They checked back through historical records for the 365 days of
last year and found that the wind averaged 15 mph with a standard deviation of
s
wind
= 10
mph. The average size of the waves is 2 feet with a standard deviation of
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 Spring '07
 idk
 Statistics, Normal Distribution, Regression Analysis, Standard Deviation, Goleta Surfboard Company

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