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**Unformatted text preview: **ECMT1020: Chapter 6 1 ECMT1020 Chapter 6 Multiple Linear Regression Analysis II Extracted from Australasian Business Statistics Modified by Dr Boris Choy for ECMT1020 ECMT1020: Chapter 6 2 Topics covered 1. Indicator/Dummy variables 2. A variable selection method 3. Hypothesis testing for a subset of variables References Black 15.2, 15.3 ECMT1020: Chapter 6 2 Topics covered 1. Indicator/Dummy variables 2. A variable selection method 3. Hypothesis testing for a subset of variables References Black 15.2, 15.3 ECMT1020: Chapter 6 3 Learning Objectives Perform multiple regression analysis with indicator/dummy variables Interpret the results for indicator variables Build a regression model from a subset of important explanatory/predictor variables using KaddStat Perform a hypothesis test for a subset of variables manually ECMT1020: Chapter 6 4 Indicator (or Dummy) Variables ECMT1020: Chapter 6 5 Indicator Variables In many situations, some independent variables are qualitative (or categorical). Example: X = Gender X takes two possible values: Male (coded as 1) and Female (coded as 0) X = A question in Student Feedback Survey X takes five possible values: Strongly disagree (1), Disagree (2), Neutral (3), Agree (4) and Strongly agree (5) An indicator variable (or a dummy variable) is a variable that takes only two possible values, coded as 0 and 1. For dichotomous variables, such as gender, only ONE dummy variable is needed. For polychotomous variables, such as a student feedback survey question with c possible choices, c 1 dummy variables are needed. ECMT1020: Chapter 6 6 Indicator Variables A categorical variable ( X ) that represents the location of a department store or a head office of an insurance company in a capital city. For example, NSW (1), WA (2), SA (3), TAS (4), NT (5), Vic (6), QLD (7), ACT (8) You can either use ONE independent variable X (not recommended) or SEVEN indicator variables (recommended) d 1 , d 2 , ..., d 7 in the regression model. Here d 1 =1 and other d i = 0 NSW d 1 = 2 and other d i = 0 WA ... All d i = 0 ACT ECMT1020: Chapter 6 7 Indicator Variables ECMT1020: Chapter 6 8 Indicator Variables Let y = Sales (response variable) x 1 = a predictor variable x 2 = state (categorical) Model 1: Without indicator variables (Not recommended) Model 2: With indicator variables (Recommended) 2 2 1 1 x x y 7 27 2 22 1 21 1 1 ... d d d x y ECMT1020: Chapter 6 9 Gender Discrimination and Salaries Example Example: (Black p.615617) A random sample of 15 workers is drawn from a pool of employed workers in a particular industry and the workers average monthly salaries are determined, along with their age (X 1 ) and gender (X 2 ) As gender can only be male or female, this variable is a dummy variable requiring 0/1 coding. We arbitrarily denote male as 1, and female as 0 ECMT1020: Chapter 6 10 Gender Discrimination and Salaries Example Table 15.5 from page 616 of text ECMT1020: Chapter 6...

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