DOE A3 Smit Shah

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University of North Texas *

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5020

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Statistics

Date

Feb 20, 2024

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pdf

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8

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Page 1 of 8 Example 1: Obtain the regression equation and plot including the confidence intervals for actual and future observations. The regression equation is Rating = 14.20 + 10.09 Yards Comment: This fitted line plot graph displays the analysis between rating and yards. Overall, the graph shows that the broader CI and PI line creates uncertainty about the linkages and results. One entry is outside the PI, while many of the entries are outside the CI. Hardly any entries on the line of best fit. Obtain the normal probability plot of the residuals and comment on the plot.
Page 2 of 8 Comment: The results of my research indicates that the bulk of the data points are on a line, and some of them are near the line of best fit, or what are known as outliers, which suggests that the data distribution is above average. Furthermore, the straight symmetry of the line suggests that the data is normal. Obtain the residuals versus the fitted value � ^ and comment on the plot. The plot presented above shows that the residual regression is successful since there are no point clusters and the points are distributed around zero. Obtain the ANOVA Table and comment on the significance of the regression according to the p-value. Remember, for a significance level of .05 the p-value should be smaller than this value. If it is greater, the regression is not significant and should be discarded. Analysis of Variance Source DF SS MS F P Regression 1 1672.47 1672.47 61.41 0.000 Error 30 817.06 27.24 Total 31 2489.52 Obtain the coefficient of determination and discuss if the regression is good or not depending on the value of this descriptor. Model Summary S R-sq R-sq(adj)
Page 3 of 8 5.21874 67.18% 66.09% Comment: 67.18% makes up the R-Sq coefficient of determination. R-sq values are generally considered good when they are 80% or more, but in this instance, the number is lower, as can be seen. Regression is therefore undesirable. Example 2: Obtain the regression equation and plot including the confidence intervals for actual and future observations. The regression equation is Taxes = - 1.584 + 0.2308 Sales Comment: This fitted line plot graph shows the analysis between sales and taxes. Overall, the graph shows that the broader CI and PI line creates uncertainty about the linkages and results. While none of the entries are outside the PI, the bulk are outside the CI. The best fit line is only partially filled in by the entries. Obtain the normal probability plot of the residuals and comment on the plot. Comment: My research indicates that the data distribution is skewed since most of the points are beyond the line of best fit, yet a tiny percentage are. Since this data is not symmetrical, it cannot be referred to as normal.
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Page 4 of 8 Obtain the residuals versus the fitted value � ^ and comment on the plot. Comment: The chart above shows that the data are distributed around zero, but that the residual regression is effective since there are a few clusters of data near the fitted value, ranging from 4 to 6 and from 7 to 9.
Page 5 of 8 Obtain the ANOVA Table and comment on the significance of the regression according to the p-value. Remember, for a significant level of .05 the p-value should be smaller than this value. If it is greater, the regression is not significant and should be discarded. Comment: The data below demonstrates that the regression is significant because the p-value is less than 0.05 and is 0.00. It shows that there is a statistically significant relationship between the predictor and responder variables, and that the predictor variable's coefficient is significant. Analysis of Variance Source DF SS MS F P Regression 1 44.1702 44.1702 72.56 0.000 Error 22 13.3930 0.6088 Total 23 57.5631 Obtain the coefficient of determination and discuss if the regression is good or not depending on the value of this descriptor. Comment: 76.73% is the coefficient of determination (R-Sq). R-sq values should ideally be 80% or higher, but in this case, the value is lower than 80%. Therefore, regression is not desirable. Model Summary S R-sq R-sq(adj) 0.780238 76.73% 75.68% Example 3: Obtain the regression equation and plot including the confidence intervals for actual and future observations. The regression equation is Usage = - 6.336 + 9.208 Temp
Page 6 of 8 Comment: This generated line plot graph shows the analysis between utilization and temperature. The graph typically shows the relations and the conclusions are certain because the CI and PI line is almost on the best fit. Every entry is on the line of best fit and falls inside the CI and PI. This provides the clearest example of a particular relationship between two variables Obtain the normal probability plot of the residuals and comment on the plot. Commet: My study indicates that there is a dispersion in the data distribution because most of the points are off-line and only one is on the line of best fit. Since the bulk of the points in this data set are outliers, we can classify the data as abnormal because it is not symmetrical. Results are anomalous because most of the data vary from the line of best fit.
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Page 7 of 8 Obtain the residuals versus the fitted value � ^ and comment on the plot. Comment: Since there are no clusters or patterns and all of the points are dispersed around zero, the chart below may be the greatest illustration of a residual chart. Obtain the ANOVA Table and comment on the significance of the regression according to the p-value. Remember, for a significant level of .05 the p-value should be smaller than this value. If it is greater, the regression is not significant and should be discarded . Comment: The data below demonstrates that the regression is significant because the p-value is less than 0.05 and is 0.00. It shows that there is a statistically significant relationship between the predictor and responder variables, and that the predictor variable's coefficient is significant. Analysis of Variance Source DF SS MS F P Regression 1 280583 280583 74334.36 0.000 Error 10 38 4 Total 11 280621
Page 8 of 8 Obtain the coefficient of determination and discuss if the regression is good or not depending on the value of this descriptor. Comment: 99.99% is the coefficient of determination (R-Sq). R-sq is often seen as being good when it is 80% or more, however in this case, the number is 99.99%. Regression is therefore the best fit. Model Summary S R-sq R-sq(adj) 1.94284 99.99% 99.99%

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