Evaluation of Regression Equitation
The primary goal of the first part is to conduct the sufficient regression analysis to determine the interdependence and relationship between the variables. In this instance, the data for testing was collected for ten days, day by day, as it was the most appropriate approach to calculating the results. Figure 1 presents the order of the data, which was collected. It displays information about time, time in minutes, day, and frequency. In this instance, the total number of observations is 10. Consequently, N = 10. Additionally, another set of data displays the order of the sets including from one to ten, as this aspect will be used as an independent variable. Furthermore, the table provides information about the frequency of measures.
Figure 1. Data for ten days
The next step is to run the regression analysis by using the original set of data (dependent variable, y) and time series (independent variable, x). In this instance, the primary goal of regression analysis is to determine the slope coefficient and determine the interrelation between the variables by using the linear function (Allen 21). In this instance, the regression equitation is y = 58 ā 0.4545x. In turn, the coefficient of co-relation is -0.414, and coefficient of determination is 0.0017. In the instance, the regression coefficients will contribute to the data interpretation (Freund, Wilson and Sa 81). In this instance, the coefficient of co-relation is closer to -1, which signifies that when the values of x increase the values of y decrease. In turn, the coefficient of determination depicts the strong relationship between y and x.
ANOVA testing
The next step is to calculate ANOVA and evaluate the results, which will be determined at the end of the analysis. In this instance, the original set of data will be split into two categories. Nonetheless, the primary goal of ANOVA is to test the original hypothesis and determine whether the significant differences between two data sets have a tendency to exist (Mann and Larke 544). In this instance, the mean for the first five days is (110+15+45+90+30)/5=58. In turn, the standard deviation is ā((110-58)2+(15-58)2+(45-58)2+(90-58)2+(30-58)2)/5=2704+1849+169+1024+784=36.12. For the second five days, the mean is (20+75+35+45+90)/5=53. The standard deviation is ā ((20-53)2+(75-53)2+(35-53)2+(45-53)2+(90-53)2)/5=57.4. In this case, the test reveals that Group 1 vs Group 2: Diff=-5.0000, 95%CI=-74.9402 to 64.9402, p=0.8729.
Nonetheless, the interpretation of ANOVA results is essential, as it contributes to the understanding of the differences between the groups, which are chosen for comparison (Zikmund et al. 603). In this instance, it remains evident that the differences between the variables have a tendency to exist. It could be said that the primary reason for the significant differences between the variables lays in the complexity of the prepared meals, as it remains evident that it took me longer to prepare dishes during some days. In the end, it remains evident that the complexity of the dishes and my desire to cook them defines the time, which is required for the preparation of the dishes in general. Lastly, it is clear that the external factors such as the availability of the cooking facilities and ingredients, and desire to cook complex dishes contribute to the definition of time, which is required to cook the particular dish successfully.
Conclusion
In the end, the statistical data is an important element, which contributes to the better understanding of the data sets (Manly 95). In turn, the statistics remain an important part in different spheres including business (Black 56). Nonetheless, different analyses contribute to the understanding of the dependence between the variables in the context of the presented example while measuring the time, which is required for the food preparation. In this instance, the primary finding is the fact that the differences have a tendency to exist. It could be said that they are dependent on the
Firstly, the regression analysis was conducted to determine the relationship between the variables. The regression depicted that the dependence between the variables has a tendency to exist. Secondly, ANOVA testing was another approach to compare two data sets to determine whether the differences have a tendency to exist. Additionally, the numerical portrayal of information by using different analytical tools contributed to acquiring a clear image of the different variables. In the end, these two analyses revealed that the primary reason for the differences between two data sets is the dependency of time on the complexity of the food. In this instance, it remains evident that sometimes it took longer to cook dishes due to the external factors.
References
Allen, Michael. Understanding Regression Analysis, New York: Plenum Press, 2007. Print.
Black, Ken. Business Statistics for Contemporary Decision Making: Statistics, New York: John Wiley & Sons, Inc., 2009. Print.
Freund, Rudolf, William Wilson and Ping Sa. Regression Analysis, Burlington: Elsevier, Inc., 2006. Print.
Manly, Bryan. Statistics for Environmental Science and Management, London: CRC Press, 2008. Print.
Mann, Prem and Christopher Larke. Introductory Statistics, New York: John Wiley & Sons, Inc., 2010. Print.
Zikmund, William, Barry Babin, Jon Carr and Mitch Griffin. Business Research Methods, Mason: South-Western Cengage Learning, 2012. Print.