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Purpose

Question:

Background One of the biggest challenges in the higher education sector has been the recent growth of online universities. The Online Education Database is an independent organisation whose mission is to build a comprehensive list of accredited online colleges. The Excel spreadsheet (OnlineEdu.xlsx) contains data on the retention rate (%) and the graduation rate (%) for 29 online colleges in the United States.

(a) Provide a descriptive analysis of the two variables (e.g., mean, standard deviation, minimum and maximum).

(b) Develop a scatter diagram with retention rate as the independent variable. What does the scatter diagram indicate about the relationship between the two variables?

(c) Develop and estimate a regression equation that can be used to predict the graduation rate (%) given the retention rate (%).

(d) State the estimated regression equation and interpret the meaning of the slope coefficient.

(e) Is there a statistically significant association between graduation rate (%) and retention rate (%). What is your conclusion?

(f) Did the regression equation provide a good fit? Explain.

(g) Suppose you were the president of South University. After reviewing the results, would you have any concerns about the performance of your university compared to other online universities?

(h) Suppose you were the president of the University of Phoenix. After reviewing the results, would you have any concerns about the performance of your university compared to other online universities?

Your report needs to be structured as follows:

(1) Purpose

(2) Background

(3) Method

(4) Results

(5) Discussion

(6) Recommendations

Is Graduation rate (%) is related to Retention rate (%)?

Purpose

Main aim of this study is to find the relation between the two variables; retention rate (%) and graduation rate (%).  Through this study we would also like to explore the association between these two variables.

Background

Retention rate means the number of students converted to the percentage who persist to the next year of the college in which they enrol for the course. Eg: if a student enrols to first year of Bachelors degree in a college, he again joins the same college for the next year as well. Graduation rate means the number of students converted to percentage that completed and earned the bachelor degree within time limit. Generally 150% of the issued time limit is considered acceptable. Eg: 4 years bachelor’s degree completed by passing within 6 years of enrolment is counted and included in graduation rate.

Recently much attention has been gained by Retention rates and Graduation rates. Many institutes providing higher education are recently focusing on improving their retention and graduation rates. They identified the key points which can improve retention rates and graduation rates at an institute (Hanover Research). 

The study published on IPEDS data found a not significant correlation between institute retention plans and graduation rate (Ronald Anthony Milon, 2006).

Many of the studies were published which tried to find relation of retention rates and graduation rates with other environmental and social factors. None of the study tried to examine relation between retention rate and graduation rate.

Background

In this study we try to inspect relation between these two variables; retention rate and graduation rate.  

Method

This study includes the data of 29 online education institutes of USA. The number of observations for this study is 29 and includes two variables. The two variables in the study, retention rates and graduation rates are continuous variables. These were described as mean and standard deviation. In addition, minimum and maximum were also calculated. To find the association between the variables correlation technique was used. Pearson correlation coefficient was calculated. To visually inspect the relation between the variables under the study scatter plot was plotted.

To find the relation between the independent variable, retention rate (%) and dependent variable, graduation rate (%) regression analysis was carried out. Goodness of fit, Analysis of Variance and hypothesis testing for slope was also carried out.

Value of Pearson correlation coefficient would lie between 0 to 1. Pearson correlation coefficient value close to 0 indicate no correlation and close to 1 indicates strong correlation. Value of goodness of fit (R-squared) will also lie between 0 to 1. Goodness of fit value close to 0 indicates poor fit and close to 1 indicates good fit.

All the comparisons and hypothesis testing will be carried out at 5 % level of significance.

Hypothesis for Analysis of Variance –

Ho: Regression model is not significant

Ha: Regression model is significant 

Hypothesis for slope –

Ho: Slope is not different from zero

Ha: Slope is different from zero

The analysis was performed on MS Excel. Additionally, Excel Data Analysis Toolpak was used to perform correlation and regression.

Results

Data of retention rates and graduation rates were collected for 29 online colleges of USA. Analysis was performed on this data for the two variables, retention rate and graduation rate. Descriptive statistics for the variables retention rate and graduation rate is presented below.

Table 1: Descriptive Statistics

 

Retention Rate (%)

Graduation Rate (%)

Mean

57.41

41.76

SD

23.24

9.87

Min

4

25

Max

100

61

 Average retention rate (%) of the 29 online colleges of USA is 57.41 % and graduation rate (%) of these 29 online colleges of USA is 41.76 %. Standard deviation for the retention rate is 23.24 % and Graduation rate is 9.87 %. Dispersion from mean is less observed in Graduation Rate than Retention Rate. Minimum Retention Rate of 4 % is for University of Phoenix and maximum Retention Rate of 100 % is for National University and Florida National College. Minimum Graduation Rate of 25 % was observed for South University and Western International University and maximum Graduation Rate of 61 % was observed for Florida National College.

Association between the variables is visually inspected using the scatter plot presented below. The plot was plotted with retention rate as independent variable plotted on x axis and graduation rate as dependent variable plotted on y axis. 

Figure 1: Scatter plot with Retention rate as independent variable 

From the above plot we can observe a minor linear positive relationship. Thus, visually a linear relationship can be observed between the two variables. The line if drawn will not be inclined to an angle of 45° but neither it would be parallel to x axis. With increase in retention rate graduation rate also increases gradually.

Method

Correlation was carried out using Excel Data Analysis Toolpak. Pearson correlation coefficient of 0.67 was obtained. This implies that there is moderately positive linear relationship between the two variables which supports the visual results of scatter plot. Positive because correlation coefficient is positive value which implies increase in retention rate is correlated with increase in graduation rate and vice-versa. Moderate because the value is around 0.5.

Regression analysis was carried out using Excel Data Analysis Toolpak. Regression analysis was carried out with retention rate as independent variable and graduation rate as dependent variable.

Table 2: Linear Regression Results

SUMMARY OUTPUT

           
             

Regression Statistics

         

Multiple R

0.670245

         

R Square

0.449228

         

Adjusted R Square

0.428829

         

Standard Error

7.456105

         

Observations

29

         
           

ANOVA

           

 

df

SS

MS

F

Significance F

 

Regression

1

1224.286

1224.286

22.02211

6.95E-05

 

Residual

27

1501.024

55.5935

     

Total

28

2725.31

 
             

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

25.4229

3.746284

6.786166

2.74E-07

17.73616

33.10964

RR(%)

0.284526

0.060631

4.692772

6.95E-05

0.160122

0.40893

 The R-square value of 0.4492 was obtained for the model. The R-square value implies the goodness of fit. Thus, it can be said that this model is moderately good fit which is in agreement with the correlation results. Goodness of fit is moderate because the value is around 0.5. This further implies that 44.92 % of variance in graduation rate is accounted for by the retention rate. This also implies that approximately 65 % of variance is not accounted by the model. Analysis of Variance was carried out to calculate the significance of the model. The p-value of

Regression equation obtained from the regression result is –

Graduation Rate = 0.28*Retention Rate + 25.42

Value of the slope obtained from regression is 0.28 which indicates positive relation between the two variables. The value of slope implies that with unit increase in Retention rate 0.28 unit increases in graduation rate was observed. t-test was performed to explore the significance of slope. The slope was found highly significant with p-value of

Thus, the results imply that there exist significant linear relationship between retention rate and graduation rate with moderate goodness fit of the model. 

Discussion

In this study data of retention rates and graduation rates from 29 online colleges of USA were included and analysed with the aim to find relation between these two variables. Along with inspecting the relation, this study we also tried to find association between the two variables. Relation and association between these two continuous variables were visualised by plotting Scatter Plot.

Average Retention Rate for the 29 online colleges was found greater than average Graduation Rate. It means number of students being retained or attend the college next year is greater than number of students completing their graduation.

Average retention rate and average graduation rate in this study were found to be less than as reported by National Center for Education Statistics. National Center for Education Statistics also reported that higher graduation rate for females than males. Most selective institutions have higher retention rates compared to least selective institutions.

Fernald (2011) reported retention rate of 89% and graduation rate of 78% for UC Santa Cruz which is quiet high from most of the colleges included in the study. Susan Wang (2011) reported that retention rate of Oregan State University for the Fall term 2009-2010 is 83.1% and graduation rate from 2004 to 2010 is 60.4%.

A paper published by Florida State University Student Success Team states that graduation rate at public institute is 52.4%, much higher than average retention rate obtained in this study.

Results

Variation in retention rate is wider than in graduation rate. Minimum retention is 4 % which is very low while maximum retention rate is 100 %. But minimum graduation rate is 25 % and maximum graduation rate is 61 %. So, minimum graduation rate is greater than minimum retention rate while maximum graduation rate is lower than maximum retention rate.

Moderately positive correlation was found between the two variables which is also supported by moderate goodness fit (R-squared) value. 44.92% of variation in graduation rate was accounted for by retention rate. So, approximately 55 % of variations are not explained by this model. Thus, there will be other environmental and social factors which affects graduation rate. Regression model was found to be significant based on Analysis of Variance results with significant slope. This means that these two variables share significant linear relationship and this relationship is not evident only by chance. This is also supported by the trend observed in the scatter plot.

Value of slope obtained from regression equation display that unit increase in retention rate leads to 0.28 units increase in graduation rate.

Thus, this study found moderate association between the two variables, retention rate and graduation rate, considered in the study. This study also found that there exist significant linear relationship between the two variables, retention rate and graduation rate, considered in the study. This study also found that graduation rate can be significantly predicted by retention rate. Graduation rate and retention rate are positively related. This study also found that there exist other factors which may affect graduation rate significantly as the fit of the model obtained in this study is moderately good.

This study can be further extended by including all the colleges of USA and observe the trend. Also, various other factors which affect graduation rate should be studied and included.

Recommendations

As a President of South University I should implement strategies which would increase the graduation rate. South University have fairly good retention rate but graduation rate is poorest among other 27 online institutes included in the study. Measures should be taken to encourage student not only to continue to next year but also study well and complete their bachelor’s degree.

As a President of University of Phoenix I should implement strategies which would increase the retention rate as well as the graduation rate. University of Phoenix have less graduation rate and retention rate is poorest among other 27 online institutes included in the study. And this retention rate is very poor, of only 4 %. If the University has part time faculty or faculty attrition rate is high then measures should be taken to retain teachers and professors as well. Many studies reported that not changing faculty members are also one of the reasons for low student retention rate. Some serious measures to be taken to motivate students to return to next year and also to complete the graduation rate.

References

1)    Institutional Retention and Graduation Rates for Undergraduate Students. National Center for Education Statistics. (Last Updated: May 2014) Available from: https://nces.ed.gov/programs/coe/indicator_cva.asp (Accessed on 07 Jan 2015)

2)    Julian L. Fernald (2011). WHO LEAVES UC SANTA CRUZ AND WHEN? RETENTION AND GRADUATION AMONG FRESHMEN COHORTS. Available from: https://planning.ucsc.edu/irps/Enrollmt/retain/RetentionStudy(Dec2011).pdf (accessed on 07 Jan 2015)

3)    Practical Steps to Improving Retention and Graduation Rates. Florida State University Student Success Team. Available from: www.hawaii.edu/offices/app/hgi/EDI_02-2013/PracticalStepsFinal.pdf (Accessed on 07 Jan 2015)

4)    HANOVER RESEARCH (2011). Improving Student Retention and Graduation Rates. Available from: www.mybrcc.edu/intranet/attachments/article/110/Improving%20Student%20Retention%20and%20Graduation%20Rates.pdf (Accessed on 07 Jan 2015)

5)    Ronald Anthony Milon (2006). The Relationship Between Institutional Retention Plans and Retention Rates. Chapter 4 Data Collection Analysis (Page 75). Available from : https://books.google.co.in/books?id=3lvGweq5jVgC&printsec=frontcover#v=onepage&q&f=false (Accessed on 07 Jan 2015)

6)    Susan Wang (2011). Retention and Graduation Rate Report Cohort Classes: Fall Term 1994 – Fall Term 2009. Oregon State University. Available from: https://oregonstate.edu/ase/firstyear/sites/default/files/pdfs/retention-graduation-summary.pdf.pdf (Accessed on 07 Jan 2011)

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[Accessed 22 February 2024].

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