Bivariate Regreesion revision

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Bivariate Statistic with Minitab
Introduction
Bivariate analysis determines an association between two continuous variables (Lesik). The project utilized a student’s survey dataset comprised of 50 observations from a simple random selection. A bivariate regression test was completed to establish whether class absence has an association with the student score. Sores were at a scale of 100, while absenteeism at 40. Therefore, the students’ number of class absenteeism was the predictor, whereas the learner’s score was an outcome variable. Both the variables were captured in a continuous scale. The experiment’s assumptions were to test for a linear or a nonlinear relationship (slope direction, either positive or negative). Statistical significance, and the strength of the relationship (strong or weak) between the variables. For this experiment, (r) and (p), values, confidence, and prediction intervals are obtained. For p-value, significance level is 0.05 while for C.I and P.I, a 95 and 99%, a confidence level was applied respectively. Therefore, a linear and a two-tailed tests were performed to obtain the values.
Data description
Scatter plot also referred to as XY plot was utilized to describe the data in a visual way. The plot offers the best bivariate relationship presentation (Everitt &Hothorn 39). Based on the Figure 1 below, there are two typical features of the study’s data. First, there is a slight relationship between the level of class absenteeism and the student’s Score.

Secondly, the value-point’s cluster alongside a straight line a straight line, which suggests that there is a linear relationship between the variables. Nonetheless, some outliers were noticed in the dataset.

Figure1: A scatter plot of Student’s Score vs. Absence
Analyses
Spearman’s correlation Rho (ρ), linear regression, 95% C.1 usefulness, and 99% confidence and prediction interval for the predictor variable. The results were noted below.
Spearman Rho: StuAbsence, Score:
Spearman rho -0.670
P-value 0.000
Spearman’s rho (ρ) was completed to examine the association between learner’s class absence and Score, n=51. The results indicated a moderate negative association between student’s class absence and Score, which was statistically significant, rs = -0.670, p < .0005. A linear regression found that class absence predicted the student’s Score and was statistically significant. From the F-test, F (1, 49) = 49.38, p < .0005. Nevertheless, class absence accounted for 50.71% of the clarified variability in the student’s score. Furthermore, the regression equation that was established in the analysis was such that: predicted Score= 73.06 – 1.207 x (Student Absence) with a slight Lack-of-Fit: (1, 38) =2.72, p=0.047.
The slope of the model, b1 = -1.207, indicates that for each instance of class absence (unit decreases in Score), there is a related decrease in Score of -1.207. From the study, hence, it is evident that the mean score lies between 55.2 and 61.9 at 95% CI, as illustrated in Figure 2 of the appendix section (Test for usefulness). That said, the confidence intervals widen as the value of (x) moves significantly far from the mean. Despite that the relationship lies outside the range of (x), it is valid to argue that the confidence intervals are extremely wide, which reduces the usefulness of the predicted value is as suggested by Helsel.
With a 99% CI, we are 99% certain that with a 12.5 unit of class absence, the test’s score will range between 28.01 and 87.91. Also, with a 99% PI of 12.5 unit of class absenteeism, we can 99% confidently predict that the mean score will range between 53.56 and 62.36. According to (Mathews 290-94), such a prediction interval is too wide to create any usefulness.
Conclusion
The overall results of the bivariate regression test indicate a reasonable negative relationship between the number of class absence and learner’s attained scores, with a statistically significant. The outcome implies that, if absence decreases, the student’s score increases and Visa-verse. Therefore, the number of class absence effectively predicts or explains the student’s score. The study utilized survey data from a simple random selection technique. The study challenge was that, the school was not willing to disclose the students’ data due to privacy policy. In addition, there is a possibility that sampled students provided wrong information. The incorrect information was evident from the observed outliers in the dataset. Surprisingly, the confidence level of 95% and the 99% prediction interval generated too wide interval to be useful, which decreased the precision. The results of this study would be different if a larger sample sizes were employed. In case the project is repeated, I would apply the use of larger sample sizes. A larger sample sizes not only reduce the margin of errors but also obtain a reasonable narrow interval, which increases interval precision. The possibility that the interval consists the mean response would be higher. Works Cited
Helsel, Dennis R. “Confidence Intervals for the Proportion.” Statistics for Censored Environmental Data Using Minitab and R. New Jersey: Wiley, 2012. 39. Print.
Lesik, Sally. “Simple Linear Regression.” Applied Statistical Inference with MINITAB®. Connecticut: CRC Press, 2009. 115. Print.
Everitt, Brian, and Torsten Hothorn. An Introduction to Applied Multivariate Analysis with R [recurso Electrónico]. Estados Unidos: Springer New York, 2011.
Mathews, Paul G. “Prediction Limits for the Observed Values.” Design of Experiments with MINITAB. Milwaukee: ASQ Quality press, 2005. 290-294. Print.

Appendix
Dataset (Double Click the icon below to open the dataset utilized for this test)
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Plots

Data Description

Figure2: Test for Usefulness