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Fundamentals of Real Estate Lecture 13 Spring, 2003 Copyright © Joseph A. Petry www.cba.uiuc.edu/jpetry/Fin_264_sp03

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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

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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

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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

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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

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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.

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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

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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?

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