Class 20. Hightower Department
Store
Introduction to
Regression
What we will cover today
• What is a regression line?
• What are two ways to find the equation of a
simple linear regression line (if you have
data)?
• What gets regressed on what and why?
• How to use the regression line to construct a
point forecast?
• What additional assumptions/information do
we need to make a probability forecast?
Case Facts
• Chain of 16 US department stores
• In Late January, Julia Brown went to Germany
to select and order stuffed animals to be sold
in Hightower Department Stores during the
Holiday season.
• For “borderline” animals, Brown ordered a
limited quantity, offered them for sale in only
one store, and used/not used them the
following year based on how they tested.
2011 Test Animals
Leftover units
are sold to
TJMaxx for 80%
of landed cost.
Animal
Landed Cost
Retail Price
Units
Purchased
Units Sold
Closeout
Inventory
Bear
$10.86
$24.95
50
10
40
Pig
$12.46
$26.95
50
4
46
Raccoon
$12.96
$26.95
50
32
18
Which animal(s)
should she “adopt”
for 2012?
If adopted, how
many units will be
sold?
Past Test Results
Year
2000
2001
2001
2002
2003
2003
2004
2005
2005
2006
2006
2006
2007
2007
2008
2009
2009
2009
2010
2010
Animal Landed Cost
Ape
$3.50
Bear
$4.80
Dragon
$3.90
Bird
$4.13
Rabbit
$4.55
Bear
$5.15
Dog
$4.92
Elephant
$4.57
Cat
$5.41
Bear
$6.71
Monkey
$7.64
Dinosaur
$4.76
Skunk
$5.61
Mouse
$8.90
Raccoon
$7.88
Bear
$8.07
Alligator
$11.08
Dog
$9.62
Monkey
$11.36
Bear
$10.15
Price
$7.95
$8.95
$7.95
$8.95
$9.95
$10.95
$9.95
$11.95
$11.95
$14.95
$16.95
$9.95
$9.95
$19.95
$15.95
$17.95
$21.95
$19.95
$24.95
$22.95
Test Sales
27
19
14
7
6
8
12
11
30
13
10
14
4
7
16
23
8
15
8
10
Actual Sales
304
374
234
144
133
209
140
458
245
208
308
47
244
385
269
243
146
259
The
challenge:
Use test
sales to
predict
Actual Sales.
2003 Rabbit
and 2007
Skunk.
What to do
with them?
Let’s go to Excel
What we do will be posted….
Regression..the tool to use to draw a
line through a cloud of points
• We regress Actual Sales on Test Sales
• The regression line is the line that minimizes sum
There is only one line
of squared errors.
that minimizes SSE
– Error = Actual – Predicted
– Predicted is the prediction from the regression line.
• Data Analysis, Regression gives us the equation of
the regression line….and much more.
– You can also get the equation of the regression line by
right clicking on the chart.
To Use the regression line to make a
point forecast…
• Just plug the known X-value (here X is test
sales) into the equation of the regression line.
• Point forecast for the bear which had test
sales of 10 units is……
= 68.088 + 12.398*10
= 192.1 units.
Point
forecast
Predicted
Y
Under certain
assumptions…this is the mean
of Y
𝑌
What we covered today
• What is a regression line?
• What are two ways to find the equation of a
simple linear regression line (if you have
data)?
• What gets regressed on what and why?
• How to use the regression line to construct a
point forecast?
• What additional assumptions/information do
we need to make a probability forecast?
Assignment 22
• No class Monday (no Sunday office hours)
• Assignment 22 due Wed (Tuesday evening
office hours)
– Assignments are 35% of course grade (more than
any exam). Drop lowest two.
• Happy Easter….safe travels.