STAT210/410-Assessment 3 Model Building, Variable Screening and Residual Analysis Solved

Question 1                                                                                                                                                       

At the start of a second wave of the corona virus in a particular country, epidemiologists attempted to predict when the numbers of new cases would begin to decline due to lockdown procedures. The data is in file virus.txt. Data was available for the number of covid-19 cases (cases) recorded per week (week) in 5 cities.

(a)    Plot cases against week. What does the plot suggest?          

(b)   Determine the order of the polynomial model required to fit the data. With reference torelevant outputs, justify each step in the process.

(c)    For the final model in (b), check the model assumptions, and also identify any potentialoutliers or influential points.        

(d)   Plot the fitted values on a scatter plot of the data. Include a plot of the 95% confidencebands on your graph     

Question 2                                                                                                                                                       

A gas turbine is a combustion engine that can convert natural gas or other liquid fuels to mechanical energy which is then turned into electrical energy. Gas turbines are often used to power aircraft, trains, ships, electrical generators, pumps etc. Several measurements are used to analyse gas turbines performance including

•    heat rate (HEATRATE) which indicates the amount of fuel required to generate one unit of electricity. Heat rate is measured in kilojoules per kilowatt per hour, and generally a lower heat rate is ideal.

•    exhaust gas temperature (EXH) which generally stays between 400 - 700 0C

•    inlet temperature (INLET) which can go up to 16000C

•    air mass flow rate (AIRFLOW) which is a volumetric flow at standard conditions translates to a specific mass flow rate, in kilograms per second

A researcher collected these data on 67 gas turbines (GASTURBINE.txt) and tried to model HEATRATE as a function of three predictors EXH, INLET and AIRFLOW.

1

 

(a)    Produce and interpret a pairs plot. What does the plot suggest as an appropriate model? Explain your response.    

(b)   Fit a main effects model. Produce relevant outputs that will allow you to check the four indicators of multicollinearity. Summarise your findings.

(c)    Run forward stepwise model selection with the “upper” model containing all possible interactions. Include all relevant outputs and the summary table for the final model.

 

Write a concise (one to two paragraphs), informative conclusion based on your analysisand results.