STAT 420
Examples for 10/18/2007
Spring 2007
1.
The marketing manager of a large supermarket chain would like to determine the
effect of shelf space and whether the product was placed at the front or back of the
aisle on the sales of pet food. A random sample of 12 equalsized stores is selected
with the following results:
Store
Shelf
Space
(feet)
Location
Weekly
Sales
(hundreds
of dollars)
1
5
Back
1.6
2
5
Front
2.2
3
5
Back
1.4
4
10
Back
1.9
5
10
Back
2.4
6
10
Front
2.6
7
15
Back
2.3
8
15
Back
2.7
9
15
Front
2.8
10
20
Back
2.6
11
20
Back
2.9
12
20
Front
3.1
Consider the model
Y =
β
0
+
β
1
x
1
+
β
2
x
2
+
e
, where the dummy variable
x
2
is the indicator for the front of the aisle
(
i.e.,
x
2
= 1 for front,
x
2
= 0 for back
).
For the back of the aisle:
Y =
β
0
+
β
1
x
1
+
e
.
For the front of the aisle:
Y =
β
0
+
β
1
x
1
+
β
2
+
e
=
(
β
0
+
β
2
) +
β
1
x
1
+
e
.
The dummy variable splits the regression relationship into two parallel lines, one for
each level
(
0 or 1
) of the qualitative dummy variable. The distance between the two
parallel lines
(
measured as the distance between the two yintercepts
) is equal to the
estimated coefficient of the dummy variable
x
2
.
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View Full Document> x1 < c( 5, 5, 5, 10, 10, 10, 15, 15, 15, 20, 20, 20)
> x2 < c( 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1)
> y < c(1.6,2.2,1.4,1.9,2.4,2.6,2.3,2.7,2.8,2.6,2.9,3.1)
> petfood < lm(y ~ x1 + x2)
> summary(petfood)
Call:
lm(formula = y ~ x1 + x2)
Residuals:
Min 1Q Median 3Q Max
0.2700 0.1325 0.0650 0.1125 0.3600
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 Spring '07
 STEPANOV
 Degrees Of Freedom, Normal Distribution, Regression Analysis, Errors and residuals in statistics, Residual standard error, freedom Multiple Rsquared

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