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For the activity data related to a small project, as shown, draw the PERT chart and find

a. the critical path and its expected time

b. the slack in all other paths

c. the standard deviation associated with the project end date

For the activity data related to a small project, as shown, draw the PERT chart and find a. the...

Design a cost monitoring report that expands the data provided in Table 4.1.

You are at the 18-month point of a 24-month project with a $400,000 budget. The schedule variance has been estimated as $30,000 and the cost variance as $20,000. The BCWS is $300,000.

a. ACWP

b. BCWP

c. ECAC

d. ETAC

Compare these results with those in the EVA example in the text. Why are they different?

In general, for a project:

a. If BCWP > BCWS, is the project early or late? Explain.

b. If ACWP > BCWP, is the project over or under cost? Explain.

c. If ACWP

 
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The data file co2data.csv contains monthly mean atmospheric CO2 concentrations measured at Mauna Loa, Hawaii, from January 1959 to December 2003. Atmospheric CO2 concentrations show a distinct seasonal pattern, reflecting the annual cycle of plant activities. The data set has four columns: CO2 (monthly CO2 concentrations in ppm), mon (calendar month), year, and months (months since January 1959). The data plot (Figure 6.30) showed an unmistakable increasing temporal trend in CO2 concentrations. In this question you are asked to quantify the magnitude of this increase. A frequently used statistical method for estimating temporal trend is to fit a linear regression model of the CO2 concentration against a time variable (e.g., number of months since a starting point). In this case, the column months in the data set is such a time variable.

(a) Fit a simple regression model using CO2 as the response variable and months as the predictor variable. Quantify the temporal trend (monthly or annual rate of increase in CO2 concentration) and discuss the potential problems of the model. (Hint: plot the residuals against months.)

(b) Refit the model by using mon as a second (factor) predictor and explain the temporal trend in CO2 concentrations.

In both models, the residuals versus fitted plot shows a systematic pattern. What may be the cause of such pattern?

 
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Increased nitrogen loading to rivers due to human activities was blamed for the rise in abundance of algae in coastal waters. For example, the Neuse River Estuary fishkills in the 1990s were attributed to the increased algae due to increased nitrogen loading from the Neuse River basin, especially from concentrated animal farming in Eastern North Carolina. Conclusions like this are often made from analyzing crosssectional or metadata. Cole et al. [1993] assembled a data set including many large river systems in the world to study the effect of human activities on nitrogen loadings to rivers (data file nitrogen.csv). They included nine variables in the data set: (1) discharge (DISCHARGE), the estimated annual average discharge of the river into ocean (in m3/sec); (2) runoff (RUNOFF), the estimated annual average runoff from watershed (in liters/(sec×m2 )); (3) precipitation (in cm/yr) (PREC); (4) area of watershed (in km2 ) (AREA); (5) population density (in people/km2 ) (DENSITY); (6) nitrate concentration (in µ mol/L) (NO3); (7) nitrate export (EXPORT), the product of runoff and nitrate concentration; (8) deposition (DEP), nitrate loading from precipitation – product of precipitation and precipitation nitrate concentration; and (9) nitrate precipitation (NPREC), the concentration of nitrate in wet precipitation at sites located near the watersheds (in µ mol/(sec×km2 )). In the paper, the authors used nitrate concentration (NO3) and nitrate export (EXPORT) as measures of human impact on rivers. The authors looked at these two response variables separately to determine whether the impact of human activities in river nitrogen level is a result of direct pollutant discharge input to the river or discharged indirectly through atmospheric pollution. They suggested that population density in the watershed can be used as a measure of direct discharge and nitrate precipitation can be served as a measure of indirect discharge.

Fit a regression model for each of the two response variables and discuss whether anthropogenic impact of river nitrogen is more through direct discharge or through indirect atmospheric deposition. Note that the two factors are correlated and their effects are unlikely to be additive.

 
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Schoener [1968] collected information on the distribution of two Anolis lizard species (A. opalinus and A. grahamii) to see if their ecological niches were different in terms of where and when they perched to prey on insects. Data are in file lizards.txt. Perches were classified by twig diameter, their height in the bush, whether the perch was in sun or shade when the lizard was counted, and the time of day at which they were foraging. The response variable is a count of the number of times a lizard of each species was seen under each of the contingencies. GLM was not yet available when the study was published. Obviously, a Poisson regression can be appropriate for analyzing the data. Develop a model using the general principles of Section 5.4 to predict the expected number of times a lizard would be seen. Interpret the model result in terms of habitat niches of each of the two species. Note that all predictors are categorical. Consider developing one model using species as a factor predictor.

 
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