managerial decision analysis 1

1. Group:For this project you may work in a group of your choosing.Your group may be no larger than four.You may work individually on this project.

1. Data:Each group should select a realistic and interesting data set consisting of at least fifty (50) cases.To facilitate your interpretations of regression results the data should relate to a circumstance you are familiar with.Data can come from a published source, be drawn from your work where appropriate, or be gathered by you in a direct observation or a designed experiment.Your data should include a continuous dependent variable (y), two continuous independent variables (X1 and X2), and one nominal or ordinal independent variable occurring in two levels (X3).One basic example of such a data set might be found in the warehouse of a company which ships small orders to individual consumers who purchase products via the Internet.The principal concern would be shipments which arrive late (beyond a predetermined target date) to customers.A regression model potentially could be developed in an attempt to explain major causes of late arrivals.One data set with variable notations for such a circumstance might be:

Variable	Definition
Dependent (y)	Number of packages shipped on a given day that ultimately arrive to customers late.
Independent 1 (X1)	Number of employees absent on the given date of shipment.
Independent 2 (X2)	Number of packages shipped on the given date.
Independent 3 (X3)	Use of UPS or Fedex as the predominant carrier on a given day.(This variable will be binary.)

Note:You’ll have fewer difficulties in completing your project if cases of your X3 variable are mostly evenly split between its two levels.In the example above a perfect split would mean 25 cases with UPS as the predominant carrier and 25 cases with Fedex as the predominate.Data sets more out of balance than a 35/15 split on the X3 variable are not acceptable.

1. Analysis:Using Minitab, Excel, or any combination conduct a complete multiple regression analysis of the data including model building and residual analysis.Your deliverable will be in a Microsoft Office-compatible format (.doc, .docx, .xls, .xlsx format preferred; no .pdf or .zip files, please). In constructing your deliverable you will include the following:

• A cover page with the names of all persons deserving credit for the work.
• A citation for the source of the data analyzed (if coming from a published source), or a description of the resource used (if self-gathered data) or of the observation or experiment conducted to collect the data.
• A clear description of 1) all variables, including a statement of which is the dependent variable, 2) the case used in your data set, 3) the levels represented in your binary independent variable.

• A complete listing of the data used in your project if less than 100 cases are used.If more, a sample of 100 cases is sufficient.
• Regression analyses of the following model combinations:
• For each of the ten required model combination you will provide 1) a written statement of the regression equation with slope and intercept coefficients, 2) a written statement of the independent variables used in the regression model, and 3) the basic standard output of the regression analysis provided by the software you use.
• Select one of your model combinations which you believe to be your “best fit” model.Please remember that “best fit” may not mean good fit.For that “best fit” model you will provide:

Three simple regression models of the form (y, X1), (y, X2), and (y, X3).

Three multiple regression models using two independent variables of the form (y, X1, X2), (y, X1, X3), and (y, X2, X3).

One full main-effects multiple regression model of the form (y, X1, X2, X3).

One multiple regression model using an interaction term of the form (y, X1, X2, X1X2).

Two simple regression models using squared terms to investigate the presence of non-linear relationships.These models will be of the form (y, X1, X12) and (y, X2, X22).

A detailed statement of your justifications for selecting this model as “best fit”.

An assessment of whether your model violates any of the common regression assumptions for linearity, independence of errors, normality of errors, and equality of error variances (L.I.N.E.).

Written interpretations of the model’s slope and intercept coefficients.

Estimation and prediction intervals resulting from independent variable values you choose.