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 and then conduct a test to determine if incidence rate is curvilinearly related to estimated rate. (Use α = .05.)
b. Construct a scatter plot 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.

Infection Incidence Rate Estimate 300 1,000 691 200 Polio Diphtheria Trachoma Rabbit fever Cholera Leprosy Tetanus Hemorrhagic fever Trichinosis Undulant fever Well's disease 0.25 1.75 17.5 0.8 1,000 150 326.5 1465 370 400 225 200 200 400 1,500 1000 6,000 5,000 1,500 10 as gangrene Parrot fever Typhoid O fever Malaria Syphilis Dysentery Gonorrhea Meningitis Tuberculosis Hepatitis Gastroenteritis Botulism 39 98 119 152 179 936 1,514 1.627 2.926 4.019 12,619 14.889 203,864 15 10,000 37000 37500