26134 Business Statistics Mahrita.Harahap@uts.edu.au Week 6 Tutorial Additional Issues in Regression (Chapter 19) Introduction: Key concepts in this tutorial are listed below 1. Dummy variables (Page 837-840 of prescribed textbook) 2. Prediction 3. Multicollinearity

THRESHOLD ASSESSMENT WEEK 5 WEEK 9 WEEK 11 MARKS QUIZ 1 QUIZ 2 “MAKE-UP QUIZ FINAL EXAM TH 1 10 marks 10 marks TH 2 TH 3 10 marks 10 marks TH 4 TH 5 This objective of threshold assessment and demonstration of “faultless” understanding translates to obtaining either a full score (e.g. 10/10) or zero score if student lags in either theoretical understanding or analytical abilities. TH1-TH4 : Each of these threshold will be tested as one question with 1 to max 2 subparts; student can obtain either 10/10 OR 0/10. No part marks. TH5-TH6: Each of these threshold will be tested as one question with 1 to max 5 subparts; student can obtain part marks for sub-parts that are correctly answered. Part-marking is allowed since there is no second opportunity for TH5 and TH6. 20 marks TH 6 20 marks Assignment 20 marks = alternate opportunity to achieve marks for TH1 and TH2 100 marks = alternate opportunity to achieve marks for TH3 and TH4

Student Resources UPASS - is a voluntary “study session” where you will be studying the subject with other students in a group. It is led by a student who has previously achieved a distinction or high distinction in that subject, and who has a good WAM. You can sign up for U:PASS sessions in My Student Admin https://onestopadmin.uts.edu.au/. Note that sign up is not open until week 1, as it’s voluntary and only students who want to go should sign up To Sign Up to these groups go to this website: helps-booking.uts.edu.au Maths Study Center @ CB04.03.331 Free drop-in one on one consultation tutoring on math/stats related questions 11am to 5pm on weekdays Online resources such as youtube or www.khanacademy.org Discussion Board on UTS Online Videos about variability https://www.youtube.com/watch?v=ipYaHqutMds https://www.youtube.com/watch?v=MRqtXL2WX2M Mon 09:00-10:00 CB02.06.37 10:00-11:00 11:00-12:00 14:00-15:00 16:00-17:00 17:00-18:00 Tue 18:00-19:00 Wed CB05C.01.015 12:00-13:00 15:00-16:00 CB05C.02.054

In statistics we usually want to statistically analyse a population but collecting data for the whole population is usually impractical, expensive and unavailable. That is why we collect samples from the population (sampling) and make inferences about the population parameters using the statistics of the sample (inferencing) with some level of accuracy (confidence level). A population is a collection of all possible individuals, objects, or measurements of interest. A sample is a subset of the population of interest.

Multiple Linear Regression A single metric dependent variable with two or more independent variables. Regression Equation: Interpretation of coefficients: For a one unit increase in Xi, Y increases/decreases by Bi units on average, holding other variables constant. NOTE: The interpretation of the intercept may be nonsensical since it is often not reasonable for the explanatory variable to be zero. As “x” is zero, the response variable is ….. If zero is not in the given sample x range then the intercept cannot be interpreted because 0 is outside of the sample range. Avoid trying to apply a regression line to predict values far from those that were used to create it.

R2 and Adjusted R2 The R2 is a numerical value between 0 and 1 which explains the variation in the dependent variable as explained by all independent variables. R2 always increases with addition of independent variables in the model irrespective of whether these variables contribute to the overall fit of the model. This can be misleading about the model assessment… The adjusted R2 recalculates the R2 based on the number of independent variables in the model and the sample size. In layman terms – this value tells us how useful the model is. Interpretation: …% of the variation in the dependent variable is explained by variation in the independent variables, taking into account the sample size and number of independent variables

Multicollinearity With multiple regression, we are often adding variables that are themselves partially related to each other. This becomes a problem when a combination of variables become close to collinear: The regression of one predictor against the other predictor has an R2 very close to one. WHY IS MULTICOLLINEARITY A PROBLEM: If two (or more) variables are collinear we cannot interpret the parameter as the relationship between one x variable and y holding ALL the other x¡’s constant: *Can get negative relationships when they should be positive. There could be independent variables that have limited impact on the dependent variables as they have a strong association with other independent variables. *Adding highly collinear variables inflates the standard error on the parameter estimates. *This can lead to make individual variables (t-test) look non-significant.