Lecture 27 Chapter 20.3: Nominal Variables HW6 due by 5 p.m. Wednesday Office hour today after class. Extra office hour Wednesday from Final Exam: May 1 st, 4-6 p.m., SHDH 351 Practice Exam will be posted tomorrow.

20.3 Nominal Independent Variables In many real-life situations one or more independent variables are nominal. Including nominal variables in a regression analysis model is done via indicator (or dummy) variables. An indicator variable (I) can assume one out of two values, “zero” or “one”. I= 1 if data were collected before if data were collected after if the temperature was below 50 o 0 if the temperature was 50 o or more 1 if a degree earned is in Finance 0 if a degree earned is not in Finance

Nominal Independent Variables; Example: Auction Car Price (II) Example revised (Xm18-02a)Xm18-02a –Recall: A car dealer wants to predict the auction price of a car. –The dealer believes now that odometer reading and the car color are variables that affect a car’s price. –Three color categories are considered: White Silver Other colors Note: Color is a nominal variable.

Example revised (Xm18-02b)Xm18-02b 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 The category “Other colors” is defined by: I 1 = 0; I 2 = 0 Nominal Independent Variables; Example: Auction Car Price (II)

Note: To represent the situation of three possible colors we need only two indicator variables. Conclusion: To represent a nominal variable with m possible categories, we must create m-1 indicator variables. How Many 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 Nominal Independent Variables; Example: Auction Car Price

Odometer Price Price = (Odometer) (0) (1) Price = (Odometer) (1) (0) Price = (Odometer) (0) (0) (Odometer) (Odometer) (Odometer) The equation for an “other color” car. The equation for a white color car. The equation for a silver color car. From JMP (Xm18-02b) we get the regression equationXm18-02b PRICE = (Odometer)+90.48(I-1) (I-2) Example: Auction Car Price The Regression Equation

From JMP we get the regression equation PRICE = (Odometer)+90.48(I-1) (I-2) A white car sells, on the average, for $90.48 more than a car of the “Other color” category A silver color car sells, on the average, for $ more than a car of the “Other color” category. For one additional mile the auction price decreases by 5.55 cents. Example: Auction Car Price The Regression Equation

Comprehension Question From JMP we get the regression equation PRICE = (Odometer)+90.48(I-1) (I-2) Consider two cars, one white and one silver, with the same number of miles. How much more on average does the silver car sell for than the white car?

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. Xm18-02b Example: Auction Car Price The Regression Equation

Recall: The Dean wanted to evaluate applications for the MBA program by predicting future performance of the applicants. The following three predictors were suggested: –Undergraduate GPA –GMAT score –Years of work experience It is now believed that the type of undergraduate degree should be included in the model. Nominal Independent Variables; Example: MBA Program Admission (MBA II)MBA II Note: The undergraduate degree is nominal data.

Nominal Independent Variables; Example: MBA Program Admission (II) I 1 = 1 if B.A. 0 otherwise I 2 = 1 if B.B.A 0 otherwise The category “Other group” is defined by: I 1 = 0; I 2 = 0; I 3 = 0 I 3 = 1 if B.Sc. or B.Eng. 0 otherwise

MBA Program Admission (II)

Practice Problems 20.6, 20.8, 20.22,20.24