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This report presents the results and analysis of an investigation on the relationship between the length of tenure and divorce status of top executives of a certain corporation. Data was collected about the length of tenure of these and whether the executives have has a divorce. The information obtained from this study and analysis would be useful to the human resource department of the corporation in making decision related to hiring of staff.
The data collected concerning the top executives is in the table below:
The most suitable procedure for evaluation of the relationship between divorce and tenure is performing a correlation and regression analysis. The regression analysis would involve hypothesizing a model of the relationship as well as using estimates of the values of the tenure and divorce parameters to develop an approximated regression equation.
In additions, a z-test would be performed to establish whether the regression model is agreeable (Archdeacon¸1994). Subsequently, if the model is considered to be satisfactory, the approximated regression equation is utilized to predict whether a top executive has been divorced given the length of his or her tenure.
The nominal scale variable divorce was coded so that a numeric value of one (1) represented a ‘No’ response while a numeric value of two (2) represented a ‘yes’ response.
The correlation analysis of the variables tenure and divorce using Excel software gave a correlation coefficient (r) of 0.75. This coefficient correlation implies that the relationship between tenure and divorce is strong and positive. Correlation is useful in showing how good a relationship (correlation) of two variables is and whether it is negative or positive (Weinberg & Abramowitz, 2008). However, it is only suitable for relationships that are characterized by a straight line. In addition, “correlation does not mean causation” (Archdeacon¸1994; Weinberg & Abramowitz, 2008).
Coefficient of Determination
Further analysis of the variables gives yields a coefficient of determination, which is given by R-square (R2), of 0.5625. This means that only 56.25% of whether executives have been divorced can be accounted for by their length of tenure. Similarly, only 56.25% of tenure can be explained by whether there has been a divorce.
Lengthy Causing Tenure Divorce
Since the correlation between length of tenure and divorce is positive, it means that divorce is likely to exist as the length of tenure increases, and vice versa. The results of the regression analysis show that divorce is related to tenure by the following linear equation: divorce = -3.5625 + 0.5 tenure. The p-value (shown as significance F in Excel) of approximately 0.0321 for the regression is less than the alpha of 0.05 (based on the 0.05 significant level).
This means that the null hypothesis that the regression model is not important (β=0) is rejected in favour of the alternative hypothesis that the regression model is important (β≠0). Therefore, the model denotes theoretically that for every increase in length of tenure, the likelihood of a divorce increases by 0.5 units.
Divorce Causing Lengthy Tenure
Since the correlation between length of tenure and divorce is positive, it means that the length of tenure is likely to increase when there is divorce, and vice versa. The results of the regression analysis show that divorce is related to tenure by the following linear equation: tenure = 8.4374 + 1.125 divorce.
The p-value (shown as significance F in Excel) of approximately 0.032 for the regression is less than the alpha of 0.05 (based on the 0.05 significant level). This means that the null hypothesis that the regression model is not important (β=0) is rejected in favour of the alternative hypothesis that the regression model is important (β≠0). Therefore, the model denotes that length of tenure increases by 1.25 units for every divorce.
Archdeacon¸T. J. (1994). Correlation and regression analysis: A historian’s guide. Madison, Wisconsin: University of Wisconsin Press.
Weinberg, S. L. & Abramowitz, S. K. (2008). Statistics using SPSS: An integrative approach. Cambridge: Cambridge University Press.