# 统计代写|回归分析作业代写Regression Analysis代考|AH7722

## 统计代写|回归分析作业代写Regression Analysis代考|Using Indicator Variables to Represent an Ordinal X Variable

Ordinal variables are discrete variables, typically with only a few levels, where the levels have numerical meaning. A perfect example is the $1,2,3,4$, or 5 response you give to a survey item, such as “Rate your satisfaction with our customer service.” Another example occurs in the Charity data set: The variable DEPS (number of claimed dependents) takes the values $0,1,2, \ldots, 6$. An example where a discrete variable with few numerical levels is not an ordinal variable is the MAJOR variable of the GPA data set, which has levels 2, 66, 70, 114, 115, 118, and 203: Since these levels refer to distinct majors, they have no numeric meaning. In other words, 2 is not less than 66 when these numbers refer to MAJOR categories. (MS Accounting is not “less than” MS Finance.) Instead, MAJOR is a nominal variable, not an ordinal variable, despite having numerical values in the data set.
Linearity is nearly always wrong, as discussed in Chapter 1 . When an $X$ variable is ordinal, the cause of the nonlinearity is often due to spacing between the ordinal levels. For example, the difference between people with 0 versus 1 dependent might be much greater than the difference between people with 1 versus 2 dependents. Similarly, a survey taker might view the difference between a ” 1 ” versus ” 2 ” response as being much greater than the difference between a ” 2 ” versus ” 3 ” response.

Fortunately, with ordinal $X$ data, there are few levels of the variable, which in turn generally implies much data per level (roughly $\mathrm{m} / \mathrm{g}$ data values per level, assuming $g$ levels). Thus, it is easy to construct accurate estimates of the within-level mean values without having to rely on the linearity assumption. You can do this using indicator variables.
Consider the analysis of the charitable contribution data, and model the mean charitable contributions (CHARITY) as a function of number dependents (DEPS). Clearly, Income will be a better explanatory variable, but number of dependents is also interesting, so let’s expand the model to include income and number of dependents. Both INCOME and CHARITY are expressed in terms of natural logarithms of the actual dollar amounts in the code below.

## 统计代写|回归分析作业代写Regression Analysis代考|Repeated Measures, Fixed Effects, and Unobserved Confounding Variables

No matter whether the indicator variable model or the linear model was used, the charitable contributions example given above was strange, in that it predicts greater charitable contributions for people with more dependents, even when they have identical income. A possible explanation for this contradiction is that there are unobserved confounding variables. As noted in Chapter 6, confounding variables make causal claims dubious.

One possible unobserved confounding variable is Religiosity: Recall the two sets of potentially observable people identified above: (i) Those reporting 50,000 income and 3 dependents, and (ii) Those with 50,000 income and 4 dependents. It may be the case that in the group of people with 4 dependents you find a greater percentage of religious people, and that such a difference is even more pronounced when comparing the DEPS $=6$ and DEPS $=0$ groups. In general, one might surmise that, among the larger families, there is a greater percentage of religious people, or at least that the degree of religiosity among larger families is generally higher. If this is so, then the increasing effect of DEPS on CHARITY is not caused by DEPS at all; instead, it is caused by the fact that people with more DEPS tend to donate more money to their religious organizations. These donations are lumped into “Charitable contributions” on their tax returns.

Or it could be that people with more children simply tend to be more charitable because people with children tend to be more humanitarian. Thus, Humanitarianism is another possible unobserved confounding variable. There can be myriad other unobserved confounding variables as well.

## 统计代写|回归分析作业代写Regression Analysis代考|Repeated Measures, Fixed Effects, and Unobserved Confounding Variables

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