1 / 13

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

rosalyn-sweet
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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Outline • When X’s are Dummy variables • EXAMPLE 1: USED CARS • EXAMPLE 2: RESTAURANT LOCATION • Modeling a quadratic relationship • Restaurant Example

  2. 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=

  3. 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

  4. 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

  5. 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.

  6. 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)

  7. 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?

  8. 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.

  9. 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

  10. The model provides a good fit

  11. 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

  12. Regression results of the modified model Multicolinearity is not a problem anymore

More Related