Question

A cancer researcher wonders if there is a relationship between rates of death from skin cancer and latitude of residence. She collects data from each of the contiguous U.S. states: the state’s approximate latitude (measured at the center of the state) and the number of deaths from skin cancer out of every 1 million people in the state. Here is a summary of her findings: Latitude: AVG = 39.5 degrees, SD = 4.6 degrees Deaths per million: AVG = 15.3 people, SD = 3.3 people r = -0.82 A scatterplot of the two variables was football shaped.

(a) Predict the number of deaths per million people in each of the following states. Oregon (latitude = 44 degrees): predicted deaths = _____________ per million Florida (latitude = 28 degrees): predicted deaths = _____________ per million Utah (latitude = 39.5 degrees): predicted deaths = _____________ per million

(b) Each of the above predictions is subject to error. The typical size of these errors is about _____________ per million.

(c) Suppose one of the states is at the 80th percentile of both latitude and number of cancer deaths. Relative to what would be predicted by regression, this state’s number of cancer deaths is (circle one) lower than predicted about what is predicted higher than predicted Explain your reasoning. You might want to draw a picture.

(d) Fill in the blank: To make a conclusion based on this study about an individual’s risk of skin cancer based on their latitude would be an example of the _________________ fallacy.

Answer 1

a)

Step 1 : Find the regression equation

Predicted values

Oregon (latitude = 44 degrees): predicted deaths = _____________ per million

Florida (latitude = 28 degrees): predicted deaths = _____________ per million

Utah (latitude = 39.5 degrees): predicted deaths = _____________ per million

For the remaining questions, we need additional data.