Proj-6 - Proj-6 PDF

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MT230

MINITAB PROJECT SHEET 6 A business analysis consultancy carried out a survey of the 16 leading companies producing a particular item. They looked at the delivery times, price, manufacturer’s image as estimated by a subcontractor, service standards, product quality and, market share Y which is the response variable. The data are in the file Data for Project 3 on Moodle. Save this to your files. (a) Determine whether there is multicollinearity among the explanatory variables. (b) Carry out the regression of market share against variables Price, Image and Service. Determine whether there are unusual observations in the data. (c) Determine the extent of influence by removing unusual observations from the data and refitting the model. Suggested procedures: (a) Regress each of the five explanatory variables on all other X-s. If there is certain linear dependency among the explanatory variables, then at least one of these regressions will fit well (have a large R2 and thus, be very well predicted by other explanatory variables). As a rough guide, if R2 > 90%, the corresponding variable may be treated as redundant and removed from the model. (b) Minitab labels observations with extreme leverage or residual values (outliers) in the table of unusual observations. An R denotes an observation with a large standardised residual (|e′i | is greater than 2). An X denotes an observation with a large leverage hii > 3(K + 1)/n (an influential observation). An observation can be labeled with both an R and an X, indicating that it is a leverage point and an outlier. (c) To determine the extent of influence, you can fit the model with and without the unusual observation and compare the coefficients, p-values, R2 , and other model parameters. To delete observations, use DATA/SUBSET WORKSHEET and in dialog boxes choose the following: Use row numbers; Exclude rows; Row number between; and enter the required row numbers. (In practice, if the model changes significantly then you may need to determine the accuracy of the observation. You may also need to examine the model further to determine if you have omitted an important term or variable, or have incorrectly specified the model.) Observations should not be removed from the data set unless there is a serious doubt about their accuracy. A lot of marks are given in problems of this kind for the quality of the discussion and the analysis, so you should get used to commenting on the results as much as deriving them....