Question: Housing Prices; Inflation in Canada; 2.140 Aspirin and Heart Attacks

Question 1: Housing Prices [50 marks]

In this question you will be working with the provided data on housing prices; ”house-price-data”. This dataset contains two quantitative variables: value (Value of the house) and ls (Lot-Size). We will try to analyze the relationship between the value of a house and its lot size.

a) Provide a graphical summary of the distribution of both variables. Explain what the graphs tell us about the variables, and whether any issues are present that could affect fur-ther statistical analysis. Explain how we can fix a key issue with these variables. [10 marks]

b) Based on your comments in a), create new variables that implement your solution. Pro-vide graphical summaries of the new variables you created, and conclude whether the issues have been fixed. [5 marks]

c) Using the Stata command qnorm, create a normal quantile plot for these two variables and provide a conclusion based on the quantile plots. [5 marks]

d) Hypothesize about the relationship between these two variables. Do you think one of these variables has an effect on the other? Which do you think is the independent variable? [5 marks]

e) Based on your answers in d), provide both graphical and numerical summaries of the relationship between these two variables. Is the numerical summary appropriate for these two variables? Comment on the form, direction, and strength of the relationship. [5 marks]

f) Estimate a linear regression model to describe the relationship between these variables. Write down the estimated linear regression equation. Provide the correct interpretation of both coeficients. Are these interpretations valid for this data? [5 marks]

g) What is the predicted price of a house if the lot size is 4000 sq-ft? What is the residual? [5 marks]

h) Create a residual plot. Describe what an ideal residual plot would look like. Does your residual plot indicate any issues with the linear regression model? [10 marks]

Question 2: Inflation in Canada [20 marks]

In this question you will be analyzing how inflation in Canada, as measured by CPI growth, has changed over time. You will be working with the dataset named ”canada-inflation-cpi.csv”.

a. Create a timeplot for the inflation data. Summarize the changes in the inflation measure in Canada over time. Do some background research to provide context for particularly high or low inflation years. [10 marks]

b. Provide the 5 number summary for the inflation data. Are any of the particularly high or low years statistical outliers? [5 marks]

c. Create a boxplot. Comment on the graph. [5 marks]

Question 3: 2.140 Aspirin and Heart Attacks [30 marks]

Does taking aspirin regularly help prevent heart attacks? “Nearly five decades of research now link aspirin to the prevention of stroke and heart attacks,” according to the Bayer As-pirin website (bayeraspirin.com). The most important evidence for this claim comes from the Physicians’ Health Study. The subjects in this study were 22,071 healthy male doctors at least 40 years old. Half the subjects, chosen at random, took aspirin every other day. The other half took a placebo, a dummy pill that looked and tasted like aspirin. The results are shown in the following table. (The row for “None of these” is left out of the two-way table.)

Aspirin GroupPlacebo Group

Fatal heart attacks           10                    26 Other heart attacks          129                  213

Strokes                   119 98

Total                  11,037 11,034

a) Hypothesize about the association between taking aspirin and having a heart attack or stroke. [10 marks]

b) Provide numerical and graphical evidence to support your hypothesis. What can you conclude? [10 marks]

c) Does this provide evidence that aspirin has a cause and effect on the risk of heart at-tacks and strokes? Why do we have to be careful with this conclusion? [10 marks]