Negative Value on Represents Decrease †Free Samples to Students

Question: Discuss about the Negative Value on Represents Decrease. Answer: Introduction: According to surveys, ozone layers are thickening drastically. It is due to the effect of global rise in pollution levels that has invited this devastating effect in ozone levels. Given are the data about conditions of ozone layers in different year according to an authentic survey. The data are tested and smoothened and a model has been predicted here for future forecast of ozone layers. The process and the required calculations are discussed below. Given is data set of yearly changes in the thickness of Ozone layer from 1927 to 2016 in Dobson units. Negative value on the dataset represents decrease in thickness and a positive value indicates increase in thickness. The dataset is tested for stocasticity. It is being plotted in line diagram and tested for any data trend. The line diagram is: It can be clearly seen from the graph that the dataset has a downward trend. Dataset Management is then calculated at lag 1 and plotted again in the line diagram. The second plot is given below: It can be seen from the diagram that the dataset is smooth and linear without any trend (Draper and Smith 2014). Therefore, lag 1 value can be taken for the prediction model. A single equation prediction model can be considered here. Fitted model will be: yt = + yt-1 . In testing whether the model is a good fit, the test hypothesis will be: H0 = Not a good fit vs. H1: = Good fit. Table for the fit of data values and lag 1 values is given below: Table 1: Single equation or regression fit table. SUMMARY OUTPUT Regression Statistics Multiple R 0.088801092 R Square 0.007885634 Adjusted R Square -0.003517979 Standard Error 3.505851158 Observations 89 ANOVA df SS MS F Significance F Regression 1 8.499259289 8.499259289 0.691503099 0.407930174 Residual 87 1069.316334 12.29099234 Total 88 1077.815593 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -3.284496953 0.373493063 -8.793997202 1.18626E-13 -4.026854844 -2.54214 -4.02685 -2.54214 X Variable 1 -0.046675512 0.05612961 -0.831566653 0.407930174 -0.158239188 0.064888 -0.15824 0.064888 It can be said from the table that required prediction model is yt = (-0.046)yt-1, where yt are the given data values and yt-1 are the values at lag 1. F statistic for ANOVA test is 0.691 and tabulated F at 5% level of significance is 0.407. F statistic Tabulated F. Therefore, the null hypothesis will be rejected here at 5% level of significance and the model is a good fit (Bennell and Canter 2017). Again, P-value of the intercept is 1.18626E-13 which is less than 0.05 and therefore intercept term can be rejected. P value of Variable 1 is 0.4079 and hence, variable 1 can be accepted. Conclusion: Data for different years are being calculated and smoothened and tabulated. The data shows a downward trend initially which is smoothened. A regression line is being fitted here which is a good fit for the dataset according to the test results Management. Therefore, future value of the ozone levels can be calculated through this fit. References: Bennell, C. and Canter, D.V., 2017. Linking Commercial Burglaries by Modus Operandi: Tests Using Regression and ROC Analysis?.Science and Justice. Draper, N.R. and Smith, H., 2014.Applied regression analysis(Vol. 326). John Wiley Sons.