106 3 Diagnostics and Transformations for Simple Linear Regression 4. Tryfos (19
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Question
106 3 Diagnostics and Transformations for Simple Linear Regression 4. Tryfos (1998, p. 57) considers a real example involving the management at a Canadian port on the Great Lakes who wish to estimate the relationship between the volume of a ship's cargo and the time required to load and unload this cargo. It is envisaged that this relationship will be used for planning purposes as well as for making comparisons with the productivity of other ports. Records of the tonnage loaded and unloaded as well as the time spent in port by 31 liquid-carrying vessels that used the port over the most recent summer are available. The data are available on the book website in the file glakes.txt. The first model fit to the data was Time-A, + ,Tonnage + e (3.8) On the following pages is some output from fitting model (3.8) as well as some (a) Does the straight line regression model (3.8) seem to fit the data well? If not, (b) Suppose that model (3.8) was used to calculate a prediction interval for plots of Tonnage and Time (Figures 3.42 and 3.43) list any weaknesses apparent in model (3.8) Time when Tonnage 10,000. Would the interval be too short, too long or about right (i.e., valid)? Give a reason to support your answer. The second model fitted to the data was log(Time) BTonnage2e (3.9) 100 0 oo o 0 5000 10000 15000 0 5000 10000 15000 Tonnage Tonnage Normal Q-Q Plot 2 0.6 0.2 0 5000 10000 15000 Tonnage -2 1 012 Theoretical Quantiles Figure 3.42 Output from model (3.8)Explanation / Answer
a. From the graph 3.42 it can be analyse the linear regression is not fit well to given data. After tonnage 10000 there is not a good fitting line . In graph 3.43 Gaussian density estimate is also showing that the model (3.8) is not fit well.
b. The interval is valid to calculate a prediction interval for time in the model (3.8)From the graph it is appearing that there are few data values for tonnage 10000 and after that which are not on the fitted line. So interval upto 10000 will predict the time well in this fitted model.
Model (3.9)
a.) Yes model (3.9) is improvement over model (3.8) for predicting time. Graph (3.44) and(3.45) are showing that model (3.9) is fitted well to given data. The all data points are fitted well to the line. there is no outliers seems.So it will predict time better than model (3.8).
b) The value of R square and adjusted R square is decrease in model (3.9) which could be said a weakness of this model. But there is not a big difference between these values so model (3.9) is better than Model (3.8).
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