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Question 1 ... .... 60 points A study has been undertaken to explore what gives concrete its strength. The dataset is saved in A3concrete.csv. There are 4 variables in this dataset: • Cement: weight (in kg) contained in a m' mixture • Water: weight (in kg) contained in a m' mixture Course.aggregate: amount of course aggregate (in kg) in 1mº mixture • Strength: compressive strength of concrete, measured in MPa (response variable) (a) (10 points) Using the ggpairs() function to plot the data. Summarise the infor- mation available from the plot. (b) (15 points) Fit a main effects model. Produce relevant outputs that will allow you to check the four indicators of multicollinearity. Summarise your findings. (c) (15 points) Run backward stepwise model selection with the complete second order model as the “upper” model. Include all relevant outputs and the summary table for the fi nal model (d) (10 points) Carry out residual analysis and comment on whether the model as- sumptions have been met. (e) (10 points) Write a concise, informative conclusion based on your analysis and re- sults. a

Question 2 ... .....30 points UNE researchers undertook an experiment which investigated the level of bacterial infec- tion (C. perfringens) in poultry sheds associated with different ventilation systems. Dust sample material was collected from n=50 sheds when chicks were aged 3 weeks old and measured via PCR. The bacterial level results (bacteria) are reported in units of DNA 1 STAT210/410 Assessment 3, Page 2 of 2 2022 T1 copies/g dust. There were three different ventilation systems: (i) natural (natural), and two fan-ventilated systems in (ii) curtain-sided sheds (curtain), and (iii) fully enclosed sheds (enclosed). The data are in the file ventilation.csv. (a) (15 points) Obtain a numerical (mean and variance) and graphical summary for the level of bacteria against ventilation systems. From there, what assumption/s for analysis of variance appear/s violated? (b) (15 points) Use the boxCox function in R to find suitable transformation/s. Ex- plain why the transformation/s you have chosen is/are deemed appropriate but the other standard power transformations that were discussed in lectures are not.