Generalized Linear Models w/ Examples in R, Solution to Problem 2.14

Question 2.14
Numerous studies have shown an association between seasonal ambient temperature (in ◦C) and blood pressure (in mm Hg). A study of 574 rural Ghanaian men aged between 18 and 65 studied this relationship [9] (and also included a number of extraneous variables) using a linear regression model, producing the results in Table 2.8.
Table 2.8 The parameter estimates and the standard errors in the linear regression model for estimating the systolic blood pressure (in mm Hg) in Ghanaian men aged between 18 and 65 (Problem 2.14)
Explanatory variable β^j se( β^j )
Constant 100.812 13.096
Age(in years 0.332 0.062
Waist circumference (in cm) 0.411 0.090
Alcohol (yes:1; no:0) -3.003 1.758
Smoking (yes:1; no:0) -0.362 2.732
Ambient temperature (in ◦C) -0.521 0.262
Compute the P-values for each term in the model, and comment.
After adjusting for age, waist circumference, alcohol consumption and smoking habits, describe the relationship between ambient temperature and systolic blood pressure.
Plot the line describing the relationship between ambient temperature and systolic blood pressure for 30-year-old men who do not smoke, do drink alcohol and have a waist circumference of 100 cm. The authors state that
Daily mean temperatures range between an average minimum of 20◦C in the rainy season and an average maximum of 40◦C in the dry season. In the dry season, early mornings are usually cool and the afternoons commonly hot with daily maximum temperatures going as high as 45◦C (p. 17).
Use this information to guide your choice of temperature values for your plot.
Compute a 95% confidence interval for the regression parameter for ambient temperature.
Interpret the relationship between ambient temperature and all the variables in the regression equation.
Predict the mean systolic blood pressure for 35 year-old Ghanaian men (who do not smoke, do drink alcohol and have a waist circumference of 100 cm) when the ambient temperature is 30◦C.
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