Class 21 Notes

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Transcript Class 21 Notes

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 Pig Raccoon $10.86

$12.46

$12.96

$24.95

$26.95

50 50 50 10 4 32 40 46 18 Which animal(s) should she “adopt” for 2012?

If adopted, how many units will be sold?

Year

2000 2001 2001 2002 2003 2003 2004 2005 2005 2006 2006 2006 2007 2007 2008 2009 2009 2009 2010 2010

Animal

Ape Bear Dragon Bird Rabbit Bear Dog Elephant Cat Bear Monkey Dinosaur Skunk Mouse Raccoon Bear Alligator Dog Monkey Bear

Landed Cost

$3.50 $4.80 $3.90 $4.13 $4.55 $5.15 $4.92 $4.57 $5.41 $6.71 $7.64 $4.76 $5.61 $8.90 $7.88 $8.07 $11.08 $9.62 $11.36 $10.15

Past Test Results

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 23 8 15 8 10 11 30 13 10 14 4 7 16

Actual Sales

304 374 234 144 47 244 385 269 243 146 259 133 209 140 458 245 208 308 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 of squared errors.

There is only one line 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.

Under certain assumptions…this is the mean of Y Predicted Y Point forecast

What we covered today