ECON 3300: Applied Statistical and Optimization Models 3 Credit Hours
Prerequisite: (ECON 2300 or STAT 1401 ) and 60 credit hours with a minimum GPA of 2.00 and (Admission to the Coles College Undergraduate Professional Program or student in a Coles College Partner Program that includes this course).
This course conveys a working knowledge of several of the most commonly employed quantitative models to support data analysis and improved decision-making within a business environment. Students learn to identify and apply the appropriate modeling techniques as well as how solve the resultant models via spreadsheet tools and applications. In addition, the course promotes and develops problem-solving and critical thinking skills through the evaluation of problem scenarios and short case-studies.
Course Learning Outcomes
Linear Programming (LP):
1. Describe the features common to the Standard and Integer LP models.
2. Develop the associated LP model for given a verbal description of an objective and constraints.
3. For an LP problem understand graphically the optimal solution(s) and the optimal value of the objective function as well as key definitions such as slack, surplus, feasibly region/solution, binding and non-binding constraints.
4. Use Excel’s SOLVER tool to obtain an optimal solution, the optimal value for the objective function, and a sensitivity analysis report for an LP problem.
5. Analyze the impact on the optimal solution and the impact on the optimal value of the objective function of each of the following single changes:
a. Increasing or decreasing the right-hand side (RHS) of a constraint by a specified amount.
b. Increasing or decreasing the objective function coefficient (OFC) of a decision variable by a specified amount.
Linear Regression Analysis:
1. With respect to the (classical normal) linear regression model, express (symbolically) the model and distinguish between the population regression equation and sample regression equation.
2. Formulate the corresponding regression model and indicate (where possible) the signs of the model coefficients based upon the relationship between a dependent variable and a set of independent variables.
3. Generate scatter plots (Excel) to assess linearity of the relationship between dependent and independent variables (and note the sign of the relationship)
4. For a particular regression model specification and relevant sample data:
a. use Excel to perform an ordinary least squares regression analysis and develop the estimated regression equation.
b. analyze which model assumptions appear to be met based upon the residual plots and normal probability plots (in the Excel)
c. identify in the Excel output and interpret in the context of the problem R-squared.
d. test for the significance of the overall model, and test for the significance of each individual coefficients
e. interpret a point estimate for the mean value of the dependent variable across all entities having specified values for the independent variables.
f. evaluate the point estimate for the value of the dependent variable given specified values for the independent variables.
g. interpret the estimated regression coefficients in the context of the problem as well as specified confidence intervals.
Decision Analysis
1. Apply each of the following criteria to select an alternative action for given alternative actions and their payoffs for states of nature with unknown probabilities and determine the preferred decision alternative for every approach (a)-(e).
a. Optimistic approach/criterion
b. Pessimistic (Conservative) approach/criterion
c. the Hurwicz criterion (for a given coefficient of optimism)
d. the equal likelihood (LaPlace) criterion
e. minimax Regret criterion.
2. Given alternative actions and their payoffs for states of nature with known probabilities:
a. select an action using the expected value criterion.
b. calculate and interpret the expected value of perfect information (EVPI).
3. Given a sequence of decisions (with each decision requiring one to choose among alternative actions), states of nature with known probabilities, and a payoff for each relevant sequence of alternative actions and states of natures, apply decision trees to:
a. apply the expected value criterion to arrive at a decision strategy, and
b. analyze that decision strategy.
Forecasting
1. Forecast (by hand and using Excel) a future value of a time series using:
a. a moving average
b. a weighted moving average
c. exponential smoothing
d. adjusted exponential smoothing.
e. a linear trend equation (derived from Excel)
2. Analyze the impact of:
a. increasing the number of time periods over which a moving average is calculated.
b. increasing the smoothing constant in exponential smoothing.
3. Develop using Excel and manually the following measures of forecast error and analyze which forecasting method is the best for the given data and also evaluate forecast bias.
a. MAD (mean absolute deviation)
b. MAPD (mean absolute percentage deviation)
c. average error
d. average cumulative error.
4. Calculate and apply seasonal adjustment using a seasonality factor.
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