Greenwood press
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book-20600
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- LOGISTIC FUNCTIONS
LOGARITHMS
57 Modeling exponential decay using logarithms (finding half-life) Further examples on logarithms ▲ ▼ ▲ LOGISTIC FUNCTIONS Logistic functions predict proportions or probabilities. They are used to deter- mine proportions of successes in “yes–no” situations from underlying factors. They can be used to predict the proportions of students admitted to a university from different SAT-score intervals; the probability of getting an item right on a test depending on underlying knowledge; the probability that a patient with cer- tain symptoms will die or live; the proportions of nerves in the brain that will fire in the presence of different concentrations of stimulating chemicals; the spread of rumors; and the proportion of consumers that will switch brands or stay with their current one when presented with different saturations of advertising. A logistic function takes the form y = 1 1 m +b 0 b x 1 , where m is the maximum value of the dependent variable (in most cases, this will be 1.00). The values b 0 and b 1 are very similar to the numbers used in exponential growth models. The illustration below shows the shape of a logistic function. The scatterplot in it shows the percent of applications for admission to a large state university that resulted in acceptances of the candidates. The groupings of students on the x-axis are by SAT verbal score. The dot at 700 indicates that 95 percent of the appli- cants who had SAT verbal scores at 700 (that is, in the range of 680–720) were accepted. However, only 9 percent of the students at 400 (in the range of 380– 420) were accepted. The equation for the logistic curve that models the data is A = 1 1+9128(0.983) SAT , where A is the proportion accepted at an SAT score level. Download 1.81 Mb. Do'stlaringiz bilan baham: |
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