An article by Burch related cigarette smoking to lung cancer. The article presen

Question

An article by Burch related cigarette smoking to lung cancer. The article presents data relating mortality from lung cancer to average cigarette consumption for females in England and Wales over a 40-year period.

Below are summary statistics for cigarette consumption (explanatory/independent) and mortality (outcome/dependent)

We obtain the following results from linear regression for cigarette consumption (explanatory/independent) on mortality (outcome/dependent):

Note that lung-cancer mortality is reported on a log10 scale over 5 years and cigarette consumption is reported on a log10 scale in lb/person.

a. Based on the above results, what is the correlation between cigarette consumption and mortality?

b. Based on the above results, what is the predicted 5-year log10 lung-cancer mortality rate for someone with a log10 annual cigarette consumption of 2 lb/person?

Explanation / Answer

a) Correlation between cigarette consumption and mortality

   Correlation = Slope * Sx / Sy        , Where in your result given Sx = 0.2933 , Sy = 0.2627

                                                              Slope = Coefficient of Cigarette Cosumption = 0.8328

So, Correlation (r) = (0.8328 * 0.2933) / 0.2627 = 0.9298

So, Correlation between cigarette consumption and mortality is 0.9298

b ) From the above result your regression equation is

Mortality (y) = -2.1915 + (0.8328 * Cigarette )

The predicted 5-year log10 lung-cancer mortality rate for someone with a log10 annual cigarette consumption of 2 lb/person

Mortality (y) = -2.1915 + (0.8328 * 2)

                    = - 0.5259

So, the predicted 5-year log10 lung-cancer mortality rate for someone with a log10 annual cigarette consumption of 2 lb/person is - 0.5259

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