1 BA 555 Practical Business Analysis Midterm Examination #1 Conjoint Analysis Linear Programming (LP) Introduction LINDO and Excel-Solver Agenda

2 Residual Analysis (pp.33 – 34) The three conditions required for the validity of the regression analysis are: the error variable is normally distributed with mean = 0. the error variance is constant for all values of x. the errors are independent of each other. How can we identify any violation?

3 Residual Analysis (pp. 33 – 34) Examining the residuals (or standardized residuals), help detect violations of the required conditions. Residual = actual Y – estimated Y We do not have  (random error), but we can calculate residuals from the sample.

4 Residuals, Standardized Residuals, and Studentized Residuals (p.33)

5 The random error  is normally distributed with mean = 0 (p.34)

6 The error variance   is constant for all values of X and estimated Y (p.34) Constant spread !

7 Constant Variance When the requirement of a constant variance is violated we have a condition of heteroscedasticity. Diagnose heteroscedasticity by plotting the residual against the predicted y, actual y, and each independent variable X The spread increases with y ^ y ^ Residual

8 The errors are independent of each other (p.34) Do NOT want to see any pattern.

Time Residual Time Note the runs of positive residuals, replaced by runs of negative residuals Note the oscillating behavior of the residuals around zero. 00 Non Independence of Error Variables

10 Residual Plots with FACTA (p.34) Which factory is more efficient?

11 Dummy/Indicator Variables (p.36) Qualitative variables are handled in a regression analysis by the use of 0-1 variables. This kind of qualitative variables are also referred to as “dummy” variables. They indicate which category the corresponding observation belongs to. Use k–1 dummy variable for a qualitative variable with k categories. Gender = “M” or “F” → Needs one dummy variable. Training Level = “A”, “B”, or “C” → Needs 2 dummy variables.

12 Dummy Variables (pp. 36 – 38) A Parallel Lines Model: Cost =  0 +  1 Units +  2 FactA +  Least squares line: Estimated Cost = Units – FactA Two lines? Base level?

13 Dummy Variables (pp. 36 – 38) An Interaction Model : Cost =  0 +  1 Units +  2 FactA +  3 Units_FactA +  Least squares line: Estimated Cost = Units – FactA Units_FactA

14 Conjoint Analysis (pp. 55 – 56)

15 Data Preparation Variable: Location Variable: Salary Y

16 Regression Coefficients Estimated Utility = Constant X1_Seattle – 8.33 X2_NY – 5.33 X3_Denver –1.67 X4_LA X5_PDX + 3 X6_100K X7_90K

17 Location is more important than Salary (Customer A13)

18 Location is more important than Salary (Customer B20)

19 Salary is more important than Location (Customer A2)

20 Salary is a bit more important than Location (Customer B19)

21 Location is most important, but … (Customer B24)

22 An Irrational Customer? (I made this one up.)

23 Market Segmentation

24 Decision-making under Uncertainty Decision-making under uncertainty entails the selection of a course of action when we do not know with certainty the results that each alternative action will yield. This type of decision problems can be solved by statistical techniques along with good judgment and experience. Example: buying stocks/mutual funds.

25 Decision-making under Certainty Decision-making under certainty entails the selection of a course of action when we know the results that each alternative action will yield. This type of decision problems can be solved by linear/integer programming technique. Example: A company produces two different auto parts A and B. Part A (B) requires 2 (2) hours of grinding and 2 (4) hours of finishing. The company has two grinders and three finishers, each of which works 40 hours per week. Each Part A (B) brings a profit of $3 ($4). How many items of each part should be manufactured per week?

26 Steps in Quantifying and Solving a Decision Problem Under Certainty Formulate a mathematical model: Define decision variables, State an objective, State the constraints. Input the model to a LP/ILP solver, e.g., LINDO or EXCEL Solver. Obtain computer printouts and perform sensitivity analysis. Report optimal strategy.

27 What to prepare for our next topic? Install LINDO or EXCEL Solver (do at least one.) LINDO: Go to DOWNLOAD HOMEPAGE. On the left-hand-side, chose LINDO FOR WINDOWS (not LINDO API, not LINGO.) Its syntax is given on pp. 78 – 80 of the class packet. EXCEL Solver: Under Tools / Add-Ins. Check the SOLVER ADD-INS box. Click OK. It is supported by the textbook (Chapter 4, pp. 209 – 281)