Using Multiple Regression to explain Engagement in early Childhood Programs

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Summary:
Yes, this is a qualitative research. I would use surveys in this case.
In terms of the data analysis part, I think multiple regression analysis will do an excellent job. Multiple regression analysis studies how a dependent variable say Y is related to two or more independent variables (say x1, x2, x3, etc).
The goal of any good survey is to get an unbiased sample value. So keep this in mind for the data analysis piece. Choose a good sample size (example, a desired margin of error for a 95 percent confidence interval).

Qualitative Independent variable (predictor variable", "regressor", "controlled variable") will be the early childhood educators who are involved in these programs. Experiences with father involvement in their program;attitudes toward father involvement in their program and belief and knowledge about father involvement in their program are the dependent variables ("explained variable", "outcome variable")

The link below would be very helpful or your research work.
http://ecrp.uiuc.edu/v5n2/green.html

The Basics of Regression Analysis
"Regression analysis is a tool for statistically describing the relationships between a variable of interest—typically referred to as the "dependent variable"—and other variables that provide information about the variable of interest, typically referred to as "independent variables" or "explanatory variables."[13] In general terms, regression analysis seeks to quantify the relationship between variations in the independent variables and variation in the dependent variable." (Thomas, 2013)

Tools:
Multiple regression analysis is, with rare exception, performed using some type of statistical software package. Although the calculations involved are mathematically relatively simple, they are too complex to be carried out by hand. All of the calculations discussed in this chapter are standard features of commercially available statistical software packages.
A variety of software packages exist; some of the commonly used packages include EViews, Gauss, SAS, SPSS, STATA, and SYSTAT. Open-source alternatives to commercial packages include PSPP and R. Microsoft Excel also has some basic statistical functionality((Thomas, 2013)

John Ruskin once wrote that "The work of science is to substitute facts for appearances, and demonstrations for impressions."
"Measurement is at the heart of all the empirical sciences. Without objective measurement, there can be no science" (Weathington et al, 2012).

PURPOSE OF MEASUREMENT
There are two goals of measurement. The first is to replace the ambiguity of words and general concepts with operationally defined constructs. In our day-to-day language, we often say that someone has an "extraverted personality," is a "senior citizen," or is "adept at mathematics." We may also want to know whether rewards and incentives will "increase the prevalence of organizational citizenship behaviors." Although these phrases convey some information, they also present considerable ambiguity. Who, for example, is a senior citizen—someone over 65, 75, or 85? Defining an age in this case clarifies our meaning of senior by offering an operational definition. As Wilkinson (1999) has noted, the value of an operational definition is that it provides a specific method for converting observations to a specified range of potential values. Using operational definitions helps researchers achieve the goal of public verification of observation because other researchers can then use and, if necessary, critique and revise the operational definition for future work.
The second goal of measurement is standardization or consistency in measurement. Consistency of measurement allows us to compare people using a common set of procedures and scales. Standardization also implies that the numbers used in the measure have a constant meaning. For example, a score of 110 on a standardized test of a construct such as intelligence has a meaning that does not change over time, across situations, or across people.

"Although each research study is unique, there is a relatively uniform process to follow when creating a sound measurement approach....
What Questions are You Trying to Answer?
The best way to answer this question is to carefully review your hypothesis. If you have a well-crafted hypothesis, you should be able to use it to clearly define your independent and dependent variables. Identifying the variables is half the battle won when it comes to measurement, as knowing this helps you determine the types of phenomena (e.g., attitudes, behaviors) you might want to assess. The more specifically you ...