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# Outline - PowerPoint PPT Presentation

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.

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Presentation Transcript

• When X’s are Dummy variables

• EXAMPLE 1: USED CARS

• EXAMPLE 2: RESTAURANT LOCATION

• Restaurant Example

• 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=

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

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

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.

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)

• 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?

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.

• 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

However, do not interpret the coefficients or test them.

Multicollinearity is a problem!!

In excel: Tools > Data Analysis > Correlation

Multicolinearity is not a problem anymore