This preview shows pages 1–2. Sign up to view the full content.
Spring 2008
Homework #3
(due Friday, February 8, by 4:00 p.m.)
1.
An employee claims that drinking beer has no effect on the amount of time it takes for
him to perform a particular task. The following data show how many seconds he took
to perform the task after consuming various quantities of beer, measured in ounces:
Beer
Consumption,
x
Time,
y
0
62
12
50
24
59
36
74
48
59
60
83
72
68
Σ
x
= 252,
Σ
y
= 455,
Σ
x
2
= 13,104,
Σ
y
2
= 30,295,
Σ
x
y
= 17,388,
Σ
(
x
–
x
)
2
= 4032,
Σ
(
y
–
y
)
2
= 720,
Σ
(
x
–
x
)
(
y
–
y
) =
Σ
(
x
–
x
)
y
= 1,008.
Consider the model
Y
i
=
β
0
+
β
1
x
i
+
ε
i
., where
ε
i
’s are i.i.d.
N
(
0,
σ
2
).
a)
Find the equation of the leastsquares regression line.
b)
Give an estimate for
σ
, the standard deviation of the observations about the true
regression line?
c)
What proportion of observed variation in time needed to perform the task is explained
by a straightline relationship with the amount of beer consumed?
d)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 STEPANOV
 Statistics

Click to edit the document details