Homework VIII
Question 1.
The following question is designed to give you a better understanding of how regression
works and how to use and interpret the regression output from Minitab. Imagine that you
want to predict the number of walkins each night based on the number of canceled
flights before 6:00PM at the local airport.
Observation
Number of Walkins
Number of Canceled Flights Before 6:00PM
1
3
18
2
5
22
3
8
26
4
14
31
Please
SHOW ALL
of your work clearly and by hand. It is perfectly appropriate to use
Minitab to check your answers. (STAT >REGRESSION > REGRESSION)
a.
Is this a regression problem or a correlation problem? Explain in two sentences or
less. If a regression problem, explicitly define the predictor variable and the
response variable.
This is a regression because we expect the number of cancelled flights to have an
influence upon the number of walkins (there’s a causeeffect outcome).
The
predictor variable is the number of cancelled flights and the response variable is the
number of walkins.
b.
Compute and interpret
the slope of this linear regression, using the formula
∑
∑
=
=



=
4
1
2
4
1
1
)
(
)
)(
(
i
i
i
i
i
x
x
y
y
x
x
b
. (Or you may use the computational formula.)
xbar= 97/4=24.25
ybar= 30/4=7.5
numerator:
78.5
denominator: 92.75
b1= 78.5/92.75=0.846
Obs
Y
X
Yiybar
Xixbar
numerator
denominator
1
3
18
4.5
6.25
28.125
39.0625
2
5
22
2.5
2.25
5.625
5.0625
3
8
26
0.5
1.75
0.875
3.0625
4
14
31
6.5
6.75
43.875
45.5625
SUM: 30
97
78.5
92.75
This tells us that as the number of cancelled flights before 6pm increase by 1, we would
expect on average the number of walkins to increase by about 0.846.
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H ADM 201
Homework VIII
Spring 2006
c.
Compute and interpret
the intercept of the estimated regression equation using the
formula
x
b
y
b
o
1

=
. Is the interpretation of this parameter realistic given the
specifics of this problem? Why is this so?
B0= 7.50.846*24.25=13.02
This is not a realistic parameter because this would mean that we would actually have a
negative number of walk ins if there were no cancelled flights.
Obviously this doesn’t
make sense.
This occurs because we are attempting to extrapolate way further then the
given data permits; the range of X values here is 18 to 31, and we are extrapolating back
to x = 0.
d.
Using the estimated regression equation, compute the predicted values
i
y
ˆ
, and the
residual, e
i
= y
i

i
y
ˆ
, for each
i
x
in the data set.
Obs
x
i
walkin (y
i
)
Yihat
ei
1
18
3
2.2112
0.7888
2
22
5
5.5968
0.5968
3
26
8
8.9824
0.9824
4
31
14
13.2144
0.7856
e.
Compute the estimate for the variance around the line, the MSE. Use this to
compute
and interpret
the estimated standard deviation around the line.
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 Spring '06
 RLLOYD
 Statistics, Regression Analysis, Errors and residuals in statistics, segment profit

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