Qualitative Independent (Dummy) 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”. I= 1 if a degree earned is in Finance 0 if a degree earned is not in Finance
Example—Car Sale Price 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. I 1 = 1 if the color is white 0 if the color is not white I 2 = 1 if the color is silver 0 if the color is not silver And what about “Other colors”? Set I 1 = 0 and I 2 = 0
To represent a qualitative variable that has m possible categories (levels), we must create m-1 indicator variables. Solution – the proposed model is y = 0 + 1 (Odometer) + 2 I 1 + 3 I 2 + – The data White car Other color Silver color
Price = 6350 -.0278(Odometer) + 45.2(0) + 148(1) Price = 6350 -.0278(Odometer) + 45.2(1) + 148(0) Price = 6350 -.0278(Odometer) + 45.2(0) + 148(0) From Excel we get the regression equation PRICE = 6350-.0278(ODOMETER)+45.2I 1 +148I 2 For one additional mile the auction price decreases by 2.78 cents. Odometer Price A white car sells, on the average, for $45.2 more than a car of the “Other color” category 6350 -.0278(Odometer) 6395.2 -.0278(Odometer) 6498 -.0278(Odometer) 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 the “Other color” category. The equation for a car of white color The equation for a car of silver color
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.
Create and identify indicator variables to represent the following qualitative variables. Religious affiliation (Christian, Hindu, Jew, Muslim, Other) Working shift (8:00am to 4:00pm, 4:00pm to 12:00 midnight, 12:00 midnight to 8:00am) Supervisor (Ringo Star, Rondal Gondarfshkitka, Seymour Heinne, and Billy Bob Thorton) 1. Assume there are no other supervisors 2. Assume there are other supervisors Example
1. What should the following apartment rent for? It has the following amenities: dishwasher, tennis court, yearly leases, it is in a good neighborhood, utilities are provided, it is furnished, 1 bath per bedroom, 300 square feet per bedroom, it is located 7.7 miles from downtown, and is a one-bedroom. 2. How about an efficiency? Two-bedroom? Three-bedroom?Four-bedroom? 3. Assume the same characteristics from above, except it is a two-bedroom, with 400 square feet per bedroom, in a poor neighborhood, and is 4.0 miles from downtown?