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Kyphosis a factor telling whether a postoperative deformity (kyphosis) is ”present” or ”absent” Age the age of the child in months

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

Complete the exercises and answer the questions outlined below. Submit your solutions in an R Notebook or Markdown file. Your code must run successfully and you must answer the questions to get credit.

1. Download the “stack.df.csv” file, and load the data into R. This file contains stack loss data from the operation of a plant for the oxidation of ammonia to nitric acid, measured on 21 consecutive days. The data include

Variable Description

 stack loss percent of ammonia lost (times 10) Air Flow air flow to the plant

Water Temp cooling water inlet temperature

Acid Conc acid concentration as a percentage (coded by subtracting 50 and then multiplying by 10)

(a) Display a summary of the data. Interpret the output and describe the data.

(b) Plot a pairwise scatterplot. What are your observations regarding the relationships.

(c) Use the lm function to fit a regression model with stack loss as the dependent vari- able and the other three as explanatory variables. Display a summary of the modeling results and interpret the findings.

(d) Plot the diagnostic plots and interpret.

(e) Revise your model to remove any terms that are not significant and display the summary of your model.

(f) Compare the original and revised models and discuss what you find.

[50 points]

2. Download the “kyphosis.csv” file, and load the data into R. The file contains 81 observa- tions representing data on 81 children who have had corrective spinal surgery. The outcome Kyphosis is a binary variable, the other three variables are numeric.

 

Variable Description

 Kyphosis a factor telling whether a postoperative deformity (kyphosis) is ”present” or ”absent” Age the age of the child in months

Number the number of vertebrae involved in the operation

Start the beginning of the range of vertebrae involved in the operation

(a) Make sure Kyphosis is a factor. If not, convert it from character to factor. Display the summary statistics for the data.

 (b) Set up your plot for one row of three plots (par(mfrow = c(1,3))). Then make three boxplots side by side one for each variable against Kyphosis.

(c) Interpret your plots. What can you say about the distributions when kyphosis is present or absent?

(d) Fit a logistic regression model that relates the probability of developing Kyphosis to the three predictor variables, Age, Number, and Start. Fit the model using glm.

(e) Display the summary statistics for your model. Interpret the coefficients to describe how the variables influence the probability of Kyphosis.

(f) Call anova(<model name>, test = "Chi") and identify any insignificant vari- ables. Revise your model based on this.

 

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