Problem Set #3

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Problem Set #3 Fallon Sheffield Q3. Analyze the Nike data given in Internet and Computer Exercises 1 of Chapter 15 . The data file and the description of key variables can be downloaded from the Web site for this book. Do the three usage groups differ in terms of awareness, attitude, preference, intention, and loyalty toward Nike when these variables are considered simultaneously?

The user group in Nike’s test pool are divided up into three categorical groups: light users, medium users, and heavy users. The eigenvalue of function one has a higher value, meaning that function 1 is performing much better than function 2 and doing a better job of discriminating the variables. In addition to the eigenvalue, the second function only explains 3.3% of variance while function 1 explains 96.7% of variance. Under the “Wilks’ Lambda” table, function 1 shows as significant, with a p-value of less than 0.001, meaning that this is a reliable analysis and a Wilks’ Lambda of 0.135. Therefore, the function we should use for this analysis would be function 1. Looking at the “Standardized Canonical discriminant Function Coefficients” table, both attitude (0.588) and awareness (0.547) stick out as significant coefficients in our discriminant analysis. Both of these are relatively high and positive, suggesting that attitude and awareness both have strong positive impacts on discriminating between user groups. This holds true in the structure matrix as well, as awareness is represented by 0.708 and attitude 0.672. In addition to this, the canonical discriminant function coefficients table also shows attitude and awareness as significant variables. Because of this, we can assume that intention, loyalty, and preference do not differ greatly between the three groups. When looking at the classification Results table, we see that 87.5% of “original grouped cases correctly satisfied” and “80% of cross-validated grouped cases correctly classified.” This would show us that the analysis did a pretty good job of classifying different variables into the correct groups. Q4. Analyze the outdoor lifestyle data given in Internet and Computer Exercises 2 of Chapter 15 . The data file and the description of key variables can be downloaded from the Web site for this book. Do the three groups based on location of residence differ on the importance attached to enjoying nature, relating to the weather, living in harmony with the environment, exercising regularly, and meeting other people ( V 2 to V 6 ) when these variables are considered simultaneously? The groups in this analysis are divided up into three categories: mid/downtown, suburbs, and countryside, all based off of residence for a poll on outdoor lifestyle. For this analysis we will use function 1, as it is more reliable. This can be known because of the higher eigenvalue shown in the “eigenvalues” chart. Function 1 has an eigenvalue of 2.257 versus function 2’s 0.174. We can also see that there is a much higher percentage of variance of about 93% in function 1, compared to 7% in function 2. In addition to this, the Wilks’ Lambda for Function 1 is valued at 0.262 and has a reliable p-value of less than 0.001. Function is the better and more reliable function to use in this data set. When we look at the “Standardized Canonical discriminant Function Coefficients” table, we can see that preference (-0.767), nature (0.817), and meeting people (0.798) have the largest standardized coefficients that have a significant impact on the discriminant functions.

“Preference” has a negative coefficient, which suggests that this variable decreases, but is associated with higher values on the discriminant function. “Nature” and “Meeting People” both have positive values, meaning there is an increase of these variables. The structure matrix also shows that all of these variables are, in fact, significant. “Preference” (0.738) and “nature” (0.407) both have positive correlations with function 1, however “meeting people” (-0.044) has a weak negative correlation with function 1. The canonical discriminant function coefficients shows that nature has the highest positive coefficient (0.63), indicating its strong contribution to the function. Preference has a negative coefficient again in function 1 and meeting peopl has a positive coefficient for function 1. Higher values with “nature” and “meeting people” are associated with one group, while lower values are associated with another group. Preference also plays a role in discriminants, but has a negative association with one of the groups, meaning that as “preference” decreases, it is linked to that particular group. The other variables, “weather,” “harmony,” and “exercising” seem to have weaker associations with the discriminant functions, deeming them as insignificant.

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