Part One – Linear Regression: Prediction (Chapter 6)



You have been provided with a sampling of the (Community College Student Experience Questionnaire) CCSEQ’s National Dataset to use for a block entry multiple regression analysis. For this analysis, you are only interested in those students who have indicated that the most important reason they are attending their community college is to prepare for transfer to a four-year college or university, and have indicated that they do plan to transfer to a four year college or university. In order for your sample of students to have had adequate exposure to their college faculty, students, and courses – you also only selected those students who have indicate that the total number of course credits they have taken (including current semester) at their college is greater than 30. That is, you did not want to be selecting entering freshmen.

The dataset contains 6 variables for a sample of 950 students, and as such an alpha level of .01 is used for all analyses. For this analysis, your dependent measure will be the students’ overall perception of gains in growth and development (totgain). You will use two sets of independent variables. The first set of independent variables will serve as a control and are the affect on their school work by the time they spend at a job (job) and the affect on their school work by their family responsibilities (family). The second set of independent variables is the students’ perception of their quality of effort with faculty members (faculty), with other students (student), and in their coursework (Class).

The Results section addresses the following two research questions, 1) “To what degree do students’ job and family responsibilities and perceived quality of effort with faculty, students, and coursework influence their overall perceived gains in growth and development?” and 2) “Does a students’ perception of their quality of effort with faculty, students, and coursework contribute significantly over and above the affect on school work by the amount of time they spend on a job or with family responsibilities to their overall perceived gains in growth and development?” The results section also includes a table with correlations, means, and standard deviations; and a table showing the B’s, Beta weights (β), and t values (indicating significant t’s).

1. First, check for multicollinearity. Conduct the appropriate diagnostic analysis and indicate your findings below. Be sure to include what you found, the criteria in which it was judged against, and indicate whether there is a concern or not. This summary information will assist you in writing your results section.

2. Using the full dataset – run the regression analysis to answer the following two research questions:

“To what degree do students’ job and family responsibilities and perceived quality of effort with faculty, students, and coursework influence their overall perceived gains in growth and development?” and “Does a students’ perception of their quality of effort with faculty, students, and coursework contribute significantly over and above the affect on school work by the amount of time they spend on a job or with family responsibilities to their overall perceived gains in growth and development?”

Then answer the following questions:

2a. What is the total variance of perceived gains in growth and development explained by the entire set of independent variables (RQ 1)? Is this proportion significant?

2b. What is the total variance of perceived gains in growth and development explained by the set of control variables? Is this proportion significant?

2c. What is the total variance of perceived gains in growth and development explained by the set of quality of effort variables (RQ 2)? Is this proportion significant?

3. Of the five independent variables, which ones (if any) have a significant influence on the dependent measure? Indicate how you made your determination.

4. List the independent variables based on their relative importance from greatest to least influence. Indicate how you made your determination. Be careful on the selection.

5. Choose any one of the significant independent variables from the full model (Model 2) and briefly explain its relationship with the dependent measure. Don’t forget – you will want to be looking at its beta coefficient.

6. Write a results section for this analysis. Your result section should be similar to the in-class example (using APA guidelines), including the two tables and the complete narrative. Be sure to use the example as a guide so as to not loose points. Complete Table 1 and Table 2, using two (2) decimal places. Don’t forget to put asterisks where applicable on Table 2 (showing significance).

Results

Ordinary least squares multiple regression was used to determine whether the amount of time community college students’ expend (at a job or with family responsibilities) and their quality of effort (with faculty, other students, and in classes and coursework) were significant influences on students’ overall perception of gains in growth and development. Additionally, the analysis investigated whether a students’ perception of their quality of effort with faculty, students, and in coursework contribute significantly over and above the amount of time they spend on a job or with family responsibilities on their overall perceived gains in growth and development? The first set of independent variables included 1) Job – the affect of a job on school work and 2) Family – the affect of family responsibilities on school work. This first set of variables served as the control variables. The second set of independent variables included 1) Students’ quality of effort with faculty members, 2) Students’ quality of effort with other students, and 3) Students’ quality of effort in classes and/or coursework. The dependent variable was the students’ overall perceived gains in growth and development.

The sample for this study consisted of students who completed the national Community College Student Experience Questionnaire (CCSEQ) between 1999 and 2003. For this study, only those participants who indicated that the most important reason for attending their community college was to prepare for transfer to a four-year college or university and indicated that they do plan to transfer to a four-year college or university were selected. In order for this sample of students to have had adequate exposure to their institution’s faculty, students, and courses – we also only selected those students who have indicate that the total number of course credits they have taken (including current semester) at their college was greater than 30. That is, we did not want to be selecting entering freshmen.

With a sample size of 950 students, an alpha level of .01 was used for all analyses. Preliminary examination of the results indicated that there was no extreme multicollinearity in the data (all variance inflation factors were less than 2.0). Using Stevens’ (2002) established criteria for determination, exploratory data analyses were conducted to test the assumptions of regression and to determine if there were any outliers and/or potentially influential data points for which, none were found for this set of data. The means, standard deviations, and correlations among all of the variables are given in Table 1.

To investigate the first research question (To what degree do students’ job and family responsibilities and perceived quality of effort with faculty, students, and coursework influence their overall perceived gains in growth and development?) we found that the entire set of variables (affect of job and family, and quality of effort with faculty, students, and coursework) accounted for approximately 26% [R2 = .26, F(5, 944) = 66.77, p < .001] of the total variance in students’ overall perception of gains in growth and development. Based on the results from this sample of students, the set of five predictor variables appear to provide a significant degree of influence on students’ perceived gains in growth and development.

To investigate the second research question (Does a students’ perception of their quality of effort with faculty, students, and coursework contribute significantly over and above the affect on school work by the amount of time they spend on a job or with family responsibilities to their overall perceived gains in growth and development?), the first set of independent variables (affect of job and family) were entered into the analysis as the first block and served as the control variables – then the second set of independent variables (quality of effort with faculty, students, and coursework) were entered into the analysis as the second block to investigate any significant influence over and above the control variables. The set of quality of effort measures did predict significantly over and above the control variables, R2 ( = .26, F Change(3, 944) = 110.14, p < .001. Based on the results from this sample of students, the three measures of students’ quality of effort appear to offer significant additional predictive power beyond that contributed by the students’ time measures.

The set of control variables accounted for approximately .3% [R2 = .003, F(2, 947) = 1.28, p = .280] of the total variance in students’ overall perceptions of gains in growth and development. Of the two sets of variables used in this study, only the quality of effort variables were significant (important) contributors to the explanation of the students’ overall perceived gains in growth and development – all were significant at the .001 alpha level (see Table 2). Of the three quality of effort measures (in order of importance), the students’ quality of effort in classes or coursework (( = .27) had the strongest influence. This was followed by the students’ quality of effort with faculty members (( = .18) then the students’ quality of effort with other students (( = .16). As can be seen, these measures were all positive, indicating that the greater the students’ quality of effort (in these particular areas) – the greater the students’ overall perception of gains in growth and development.

Table 1

Means, Standard Deviations, and Correlations for Regression of Perceived Gains in Growth and Development (N = ______)

| |1 |2 |3 |4 |5 |6 |

|1. Total Gain |– – | | | | | |

|2. Affect of Job | |– – | | | | |

|3. Affect of Family | | |– – | | | |

|4. Faculty Quality of Effort | | | |– – | | |

|5. Student Quality of Effort | | | | |– – | |

|6. Course Quality of Effort | | | | | |– – |

| | | | | | | |

|Means | | | | | | |

|Standard Deviations | | | | | | |

Table 2

Results of Regression of Total Perceived Gains in Growth and Development on Time Variables and Quality of Effort Variables

|Independent Variables |B |( |t |

|Model 1 | | | |

| Affect of Job | | | |

| Affect of Family | | | |

| | | | |

|Model 2 | | | |

| Affect of Job | | | |

| Affect of Family | | | |

| Faculty Quality of Effort | | | |

| Student Quality of Effort | | | |

| Course Quality of Effort | | | |

Note. R2 = ______ for Model 1 (p ______); R2( = ______ for Model 2 (p ______) – Total R2 = ______ (p ______).

***p < .001

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