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Assignment_4_solution

Assignment_4_solution - Stat 231 Assignment 4 Solutions 1...

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Stat 231 Assignment 4 Solutions 1. Methylcyclopentadienyl Manganese Tricarbonyl (MMT) has been added to unleaded gasoline in Canada to help reduce engine knock. The automobile manufacturers claim that the addition of MMT to gasoline increases the amount of carbon monoxide (CO) emitted, measured in gm/km. Consider the target population of all cars in Canada at the current time. a) Using the language of the course, what do we mean by the statement “Adding MMT to gasoline increases the amount of CO emitted.” We mean that adding MMT to gasoline causes an increase in mean CO emission level. That is, if we were to calculate the mean CO emission level of all cars in Canada and, while holding all other explanatory variables fixed , increase the concentration of MMT in the gasoline in all cars, we would see an increase in mean CO emission level. Since all other explanatory variates remained unchanged, we could say that the change in mean CO was caused by the change in MMT. In an investigation to examine this issue, 100 cars were haphazardly selected at Drive Clean centers throughout Ontario over the course of one summer. For each selected car, the required emissions test determined the amount of CO emitted. The researchers determined the concentration of MMT (mg/l) in the car’s fuel tank and also recorded the distance the car had driven to the nearest thousand kilometers, as measured by the odometer. You can find the data with the R code source(‘http://uwangel.uwaterloo.ca/AngelUploadsuwangel/Content/MRG-041122- 144725-_admin/_assoc/sourceAss4q1.txt ’) The variate names are: MMT: concentration of MMT in mg/l CO: CO emissions (gm/km) distance: thousands of kilometers driven b) Is this Plan observational or experimental? Explain. This is an observational Plan, since the investigators did not have control over or manipulate the value of the focal variate (MMT) for each car in the sample. c) Construct a scatterplot showing the relationship between CO levels and MMT concentrations. Is the graph consistent with the statement that adding MMT to the gasoline increases the amount of CO emitted? Yes, the graph is consistent with this statement. There appears to be a positive (linear) relationship between CO emission and MMT - CO emission increases as MMT increases.
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d) Fit the model ( ) , 1,...,100, j j j Y x x R j α β = + + = to the data and add the fitted line to the scatterplot. Estimate the rate of increase in average emitted CO for an increase in MMT concentration of 1 mg/l.
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