Historically important coronary heart disease study. Following World War II, many northern European countries experienced notable increases in what was then called degenerative heart disease and is now called coronary heart disease. In 1953, an investigator by the name of Ancel Keys reported the data shown in the following table. In this table, the variable FAT represents “% of total dietary calories consumed as fat” in the six western democracies in question and the variable CHD represents “coronary heart disease mortality per 1000 in 50- to 59-year-old males.”

COUNT FAT CHD Japan 8 0.5 Italy 20 1.4 England 33 3.8 Australia 36 5.5 Canada 37 5.7 USA 39 7.1 Data from Keys, A. (1953). Atherosclerosis: a problem in newer public health, Figure 2. Journal of the Mount Sinai Hospital, 20, 118–139. Data file on companion website is KEYS1953.*.

(a) Explore the relationship between FAT and CHD with a scatterplot.

Interpret this plot (form, direction, strength, and potential outliers). Can linear correlation and regression methods be used on these data as is?

(b) Apply a natural logarithmic transformation to the response variable. Call this new variable LN_CHD. Then generate a plot of FAT versus LN_CHD. Can linear correlation and regression now be used?

(c) Use correlation to determine the proportion of the variance of LN_CHD explained by FAT.

(d) As noted many times in this text, “correlation” does not always equate with “causation.” One reason for this nonequivalence is due to the phenomena of confounding, in which the observed relationship between X and Y is explained by their mutual relationship with a third variable Z lurking in the background.

Proffer an explanation as to how the lurking variable “obesity”

could confound the observed association between fat consumption and coronary heart disease.