Notice that since we have a p-value of 0.000 for this chi-square test, we therefore reject the null hypothesis that all of the slopes are equal to 0. For males, the odds of ever having driven after drinking is 1.85 times the odds for females, assuming DaysBeer is held constant.įinally, the results for testing with respect to the multiple logistic regression model are as follows: the log of the odds ratio for each observation we will use a form of nonlinear regression called logistic regression to estimate the below model: 01 01 1 1 i i i i X E Y G X e EE S E E and in so doing obtain the desired estimates b 0 of and b 1 of. For Gender, the odds ratio is 1.85 (calculated as e 0.6172).For DaysBeer, the odds ratio is still estimated to equal 1.21 to two decimal places (calculated as e 0.18693).This is evidence that both x-variables are useful for predicting the probability of ever having driven after drinking. The p-values are less than 0.05 for both DaysBeer and Gender.Some things to note from the results are: Under Gender, the row for male corresponds to an indicator variable with a value of 1 if the student is male and a value of 0 if the student is female. We now include Gender (male or female) as an x-variable (along with DaysBeer). Notice also, that the results give a 95% confidence interval estimate of the odd ratio (1.14 to 1.28). (Another method is to just do the calculation using the predicted probability at X = 5, as we did above for X = 4.) To find the odds when X = 5, one method would be to multiply the odds at X = 4 by the sample odds ratio. Thus when X = 4, the predicted odds of ever driving after drinking is 0.312/(1 − 0.312) = 0.453. The data is in event/trial format, which has to be taken into account by the statistical software used to conduct the analysis. We can use statistical software to calculate the observed probabilities as the number of observed deaths out of 250 for each dose level.Ī binary logistic regression model is used to describe the connection between the observed probabilities of death as a function of dose level. The data originate from the textbook, Applied Linear Statistical Models by Kutner, Nachtsheim, Neter, & Li.Īt each of six dose levels, 250 insects are exposed to the substance and the number of insects that die is counted ( toxicity.txt). An experiment is done to test the effect of a toxic substance on insects.
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