Public perceptions of health risks
In the Journal of Experimental Psychology: Learning, Memory, and Cognition (July 2005), University of Basel (Switzerland) psychologists tested the ability of people to judge risk of an infectious disease. The researchers asked German college students to estimate the number of people who are infected with a certain disease in a typical year. The median estimates as well as the actual incidence rate for each in a sample of 24 infections are provided in the table. Consider the quadratic model, E(y) = β0 + β1x + β2x2, where y = actual incidence rate and x = estimated rate.
(a) Fit the quadratic model to the data, then conduct a test to determine if incidence rate is curvilinearly related to estimated rate. (Use α = .05.)
(b) Construct a scatterplot for the data. Locate the data point for Botulism on the graph. What do you observe?
(c) Repeat part a, but omit the data point for Botulism from the analysis. Has the fit of the model improved? Explain.