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Examining the influence of demographic characteristics in predicting and relating to a dependent variable is prevalent internationally (Silverstein, Angelelli & Parrott, 2001; Rhodebeck, 1993; Ponza, Duncan, Corcoran & Groskind, 1988). Commonly used demographic characteristics include: age, income, gender, race, education, occupation, demographic location, social class and relationship status. The current research placed most of these independent variables along with their corresponding dummy variables into the Ordinary Least Squares Regression Model for predicting the outcome variable (factor). The criteria for retaining particular independent variables were based upon the Backward Elimination Procedure (Milton and Arnold, 2003, pp. 483-484). This procedure requires the researcher to pick an independent variable and eliminate it from the model.

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The conversion of variables enables nominal characteristics to be compared with a factor and continuous attributes can be split up into subcategories; for example, breaking ages up into groups called generations to allow for the assessment of internal responses relative to the factor; and variables that have been converted into logistic scores, such as income, can be related to the factor. Few or many independent variables can be added into the regression model.

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The elimination of the independent variable changes the mean square error (MSE)87 and Multiple R value88 for the model. The researcher continues eliminating variables until there is a balance between a small mean square error (MSE) and a reasonably large Multiple Rvalue. However, a large Multiple Reventually produces a large mean square error (MSE) and this is why a balance between these two statistics is necessary. Therefore, independent variables are eliminated until any further deletion of independent variables results in the regression model being rejected. The removal of other demographic characteristics is an attempt to find the best and simplest regression model. This is so that when an Ordinary Least Squares Regression Analysis is performed a ‘good fit’ is found between the independent variables and dependent variables (Milton and Arnold, 2003, p. 481).

As a consequence of the Backward Elimination procedure, two independent variables were retained for all the Analyses of Variances and the Ordinary Least Squares Regression Analyses. Independent variables play a particular role in the welfare attitudes of New Zealanders. These independent variables that predict welfare attitudes are: age and household income. Arguably, the effects of these two independent variables are a consequence of New Zealand’s particular culture. The other demographic characteristics (gender, ethnicity, social class, education and occupation) were excluded from further Analysis.

Each variable (age and household income) was split into dummy variables. The basic statistics for them are located in Table One. The age distribution of respondents resembles a positive skew with the older population being over represented. This means that for each subsequent age-group (generation), from young to old, the number of participants occupying each birth cohort increases. The ages of respondents are split into groups called generations. There are six generations that are split into five dummy

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The mean square error is the mean measure of variability for the model. A small mean square error indicates that the confidence intervals for βn are narrow and the estimates for βn are accurate.

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The R2 value explains the amount of variance in the outcome that is accounted for by the predictors, independent variables, in the model. Meanwhile, the Multiple R value is the sample correlation coefficient that shows how much age and household income play a role in the overall predictor of the dependent variable. In other words, the Multiple R correlation refers to a statistic that is a predictor constant for the overall model.

variables with one generation (those aged 18-21) taking the reference position for the Regression Analysis. The Analysis calculates a Beta score for each generation. These scores are representations of each generation’s effect on the factor score for the factor in the population. Therefore, generations have no effect on the Beta scores of other generations.

The Beta score is not influenced by the distribution of ages and the numbers of participants included in each generational category. This is because the generational categories used in this research satisfy the assumption that the number of participants in each subsidiary sample fulfils the minimum sample size requirements of thirty with no overlap between them (statistical partitioning). In principle, the larger the sample of respondents in each category, the greater the ability of the Regression Analysis to detect the effect of the relationship between the dummy variable and the dependent variable. Consequently, the point estimate of the summed responses from a dummy variable with a larger number of participants makes it easier to detect its position on the factor score compared with a dummy variable that has a smaller number of participants.

Table 1: Dummy Categories for Independent Variables in Regression Analysis

Generation N = 512 % 18-21 21 4.1 22-31 64 12.5 32-41 82 16 42-51 103 20.1 52-61 103 20.1 62+ 139 27.2 Income N = 487 % $0 - $15,000 27 5.5 $15,001-$25,000 62 12.7 $25,001-$40,000 71 14.6 $40,001-$50,001 50 10.3 $50,001-$70,000 86 17.7 $70,001 plus 191 39.3

The demographic characteristic for household income entails five dummy variables with one reference position. This position is the lowest household income. The distribution of household income among those participating resembles a negative geometric distribution.

This means that participants with high household incomes are over represented, while participants with low to medium household incomes are under represented in the survey. The distribution of household income categories does not influence the Beta scores of other categories, but does play a role in the interpretation process.