Outline
This presentation is the property of its rightful owner.
Sponsored Links
1 / 13

Outline PowerPoint PPT Presentation


  • 61 Views
  • Uploaded on
  • Presentation posted in: General

Outline. When X’s are Dummy variables EXAMPLE 1: USED CARS EXAMPLE 2: RESTAURANT LOCATION Modeling a quadratic relationship Restaurant Example. Qualitative Independent Variables. In many real-life situations one or more independent variables are qualitative.

Download Presentation

Outline

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Outline

Outline

  • When X’s are Dummy variables

    • EXAMPLE 1: USED CARS

    • EXAMPLE 2: RESTAURANT LOCATION

  • Modeling a quadratic relationship

    • Restaurant Example


Qualitative independent variables

Qualitative Independent Variables

  • In many real-life situations one or more independent variables are qualitative.

  • Including qualitative variables in a regression analysis model is done via indicator variables.

  • An indicator variable (I) can assume one out of two values, “zero” or “one”.

1 if a degree earned is in Finance

0 if a degree earned is not in Finance

1 if the temperature was below 50o

0 if the temperature was 50o or more

1 if a first condition out of two is met

0 if a second condition out of two is met

1 if data were collected before 1980

0 if data were collected after 1980

I=


Example 1

1 if the color is white

0 if the color is not white

I1 =

1 if the color is silver

0 if the color is not silver

I2 =

Example 1

  • The dealer believes that color is a variable that affects a car’s price.

  • Three color categories are considered:

    • White

    • Silver

    • Other colors

  • Note: Color is a qualitative variable.

And what about “Other colors”? Set I1 = 0 and I2 = 0


Outline

To represent a qualitative variable that has

m possible categories (levels), we must create

m-1 indicator variables.

  • Solution

    • the proposed model is y = b0 + b1(Odometer) + b2I1 + b3I2 + e

    • The data

White car

Other color

Silver color


Outline

There is insufficient evidence

to infer that a white color car and

a car of “Other color” sell for a

different auction price.

There is sufficient evidence

to infer that a silver color car

sells for a larger price than a

car of the “Other color” category.


Outline

Price

6498 - .0278(Odometer)

6395.2 - .0278(Odometer)

6350 - .0278(Odometer)

Odometer

From Excel we get the regression equation

PRICE = 6350-.0278(ODOMETER)+45.2I1+148I2

For one additional mile the auction price

decreases by 2.78 cents.

A white car sells, on the average,

for $45.2 more than a car of the “Other color” category

A silver color car sells, on the average,

for $148 more than a car of the “Other color” category

The equation for a

car of silver color

Price = 6350 - .0278(Odometer) + 45.2(0) + 148(1)

The equation for a

car of white color

The equation for a

car of the “Other color”

category.

Price = 6350 - .0278(Odometer) + 45.2(1) + 148(0)

Price = 6350 - .0278(Odometer) + 45.2(0) + 148(0)


Example 2 location for a new restaurant

Example 2 Location for a new restaurant

  • A fast food restaurant chain tries to identify new locations that are likely to be profitable.

  • The primary market for such restaurants is middle-income adults and their children (between the age 5 and 12).

  • Which regression model should be proposed to predict the profitability of new locations?


Outline

Revenue

Revenue

Income

age

Low Middle High

Low Middle High

  • Solution

    • The dependent variable will be Gross Revenue

  • There are quadratic relationships between Revenue and each predictor variable. Why?

  • Members of middle-class families are more likely to visit a fast food family than members of poor or wealthy families.

Revenue = b0 + b1Income + b2Age

+ b3Income2 +b4Age2 + b5(Income)(Age) +e

  • Families with very young or older kids will not visit the restaurant as frequent as families with mid-range ages of kids.


Example 2

Example 2

  • To verify the validity of the model proposed in example 19.1, 25 areas with fast food restaurants were randomly selected.

  • Data collected included (see Xm19-02.xls):

    • Previous year’s annual gross sales.

    • Mean annual household income.

    • Mean age of children


Outline

The model provides a good fit


Outline

The model can be used to make predictions.

However, do not interpret the coefficients or test them.

Multicollinearity is a problem!!

In excel: Tools > Data Analysis > Correlation


Outline

Regression results of the modified model

Multicolinearity is not a problem anymore


  • Login