# STAD29 / STA 1007 assignment 1

(f) (2 marks) Which of your two confidence intervals is longer? Explain briefly why that is not surprising. 3. Work through, or at least read, chapter 16 of PASIAS. 4. Coronary heart disease affects many people. Is there an association between a person having significant evidence of coronary heart disease and the person’s age? 100 subjects were selected to participate in a study. For each person these four things were recorded: • an ID for that person (which we ignore) • the person’s actual age, to the nearest year • the “age group” in which the person falls • whether the person has “significant evidence of coronary heart disease” (“Yes”) or not (“No”). The data are at http://www.utsc.utoronto.ca/~butler/d29/chdage.csv as a CSV file. (a) (2 marks) Read in and display (at least some of) the data. To make the next part easier, call your data frame heart. (b) (2 marks) I wanted to have you plot the proportion of people in each age group that have significant symptoms against age group. This turns out to be a bit fiddly, but this code does it. Replace the initial data frame with whatever name you gave to the data frame you read in from the file (if you called it something different): heart %>% group_by(agegrp, chd) %>% summarize(n=n()) %>% spread(chd,n) %>% mutate(proportion=Yes/(Yes+No)) %>% ggplot(aes(x=agegrp, y=proportion))+geom_col() Run this code (by typing it or copy-pasting it). What does your graph tell you about how the likelihood of having symptoms depends on age? Explain briefly. (c) (2 marks) Fit a logistic regression predicting presence or absence of coronary heart disease from the (actual) age. Use the data frame you read in from the file, and display the results. (d) (3 marks) Is there a significant association between age and presence of significant symptoms of coronary heart disease? If there is, what kind of relationship is it? Explain briefly but carefully, using the output from this part only. (e) (3 marks) An alternative format for the same data is in http://www.utsc.utoronto.ca/~butler/ d29/chdage2.csv. Read the data

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