# Understanding the Slope Coefficient and its Implications

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Assignment1.Purpose:The main purpose of this study is to examine the relationship between graduation rateand retention rate. This paper presents a linear regression analysis and providesrecommendation to improve graduation rate. 2.BackgroundIn the last decade, there is rapid growth of online education compared to conventionalways of learning. Ease of accessibility is one of the main reasons in the rapid growthof online education. Most of the past researches suggests that financial downturn hasexpanded interest for online courses. This study is planned to focus on specific twovariables: graduation rate and retention rate. Graduation rate is the percentage of firstyear undergraduate students, who complete their programme within 150% of thepublished time for the program. Retention rate is the percentage of first time, first-year undergraduate students who continue study at that university for next year.3.MethodsThis study presents simple linear regression analysis by using data of 29 onlineuniversities. Graduation rate is taken as the dependent variable and retention rate istaken as the independent variable. Regression model used in this study is given asGR=β0+β1(RR)+εWhere, GR is the Graduation rate and RR is retention rate. β0is the intercept andβ1istheslopecoefficient.εis the stochastic error, which is normally distributed withzero mean and 1 variance.4.Resultsa)Provide a descriptive analysis of the two variables (e.g., mean standarddeviation, minimum and maximum). (2 marks).Descriptive Analysis of Graduation rate (%) and Retention rate(%) is shown in thetable 1.Table 1GR (%)RR(%)Mean41.7586257.41379Median39.0000060.00000Maximum61.00000100.0000Minimum25.000004.000000Std. Dev.9.86572423.24023Skewness0.167108-0.293654Kurtosis2.0625663.185897
Jarque-Bera1.1968320.458549Probability0.5496820.795110Sum1211.0001665.000Sum Sq. Dev.2725.31015123.03Observations2929b)Develop a scatter diagram with retention rate as the independent variable. What does the scatter diagram indicate about the relationship between the two variables? (3marks)Figure 1 shows a scatter plot between Graduation rate(%) and retention rate(%).020406080100120010203040506070GR(%) Vs RR(%)Retention Rate(%)GraduationRate(%)It can be easily observed that there is linear relationship between Graduation rate(%) and retention rate(%).c)Estimate a regression equation that can be used to predict the graduation rate (%) given the retention rate (%) (2 marks).Regression estimates are shown in the table 2. Graduation rate is the dependent variable and retention rate is the independent variable.Dependent Variable: GRMethod: Least SquaresDate: 02/11/19 Time: 07:15Sample: 1 29Included observations: 29VariableCoefficientStd. Errort-StatisticProb.

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