1. Class 20. Hightower Department Store
Introduction to Regression

2. 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?

3. 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.

4. 2011 Test Animals Animal Landed Cost Retail Price Units Purchased
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 4 46
Raccoon
$12.96 32 18
Which animal(s) should she “adopt” for 2012?
If adopted, how many units will be sold?

5. The challenge: Use test sales to predict Actual Sales.
Past Test Results
The challenge: Use test sales to predict Actual Sales.
Year
Animal
Landed Cost
Price
Test Sales
Actual Sales
2000
Ape
$3.50
$7.95 27
304
2001
Bear
$4.80
$8.95 19
374
Dragon
$3.90 14
234
2002
Bird
$4.13 7
144
2003
Rabbit
$4.55
$9.95 6
$5.15
$10.95 8
133
2004
Dog
$4.92 12
209
2005
Elephant
$4.57
$11.95 11
140
Cat
$5.41 30
458
2006
$6.71
$14.95 13
245
Monkey
$7.64
$16.95 10
208
Dinosaur
$4.76
308
2007
Skunk
$5.61 4
Mouse
$8.90
$19.95 47
2008
Raccoon
$7.88
$15.95 16
244
2009
$8.07
$17.95 23
385
Alligator
$11.08
$21.95
269
$9.62 15
243
2010
$11.36
$24.95
146
$10.15
$22.95
259
2003 Rabbit and 2007 Skunk.
What to do with them?

6. What we do will be posted….
Let’s go to Excel
What we do will be posted….

7. 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 of squared errors.
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.
There is only one line that minimizes SSE

8. 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……
= *10
= units.
Under certain assumptions…this is the mean of Y
PredictedY
Point forecast 𝑌

9. 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?

11. 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.