Null deviance logistic regression

The result 5. This provides. More importantly, the scaled deviance can be used for performing hypotheses tests on sets of coefficients of a generalized linear model. In other words, assume M1 is nested within M2. Then we can test the null hypothesis that the extra coefficients of M2 are simultaneously zero. This can be done by means of the statistic Hopefully, this dependence is removed by employing 5.

View all posts by Zach. Prev How to Fix in R: not defined because of singularities. Next What Are i. Random Variables? Leave a Reply Cancel reply Your email address will not be published. Since your model includes some predictors, we would expect it to fit the data better than the reference model i.

The size of the difference between the deviance of your model and that of the reference reflects how important the independent variables are in your model. You can also compare the deviance of your model with that of another one that includes, for example, 1 additional independent variable. The lower the deviance of the larger model is compared to the smaller model , the more important this variable is.

In fact the model with the lowest deviance will certainly represent the sample data better than any other model. Multiple logistic regression uses the following null and alternative hypotheses:. The null hypothesis states that all coefficients in the model are equal to zero.

In other words, none of the predictor variables have a statistically significant relationship with the response variable, y. The alternative hypothesis states that not every coefficient is simultaneously equal to zero. The following examples show how to decide to reject or fail to reject the null hypothesis in both simple logistic regression and multiple logistic regression models. Suppose a professor would like to use the number of hours studied to predict the exam score that students will receive in his class.

He collects data for 20 students and fits a simple logistic regression model. We can use the following code in R to fit a simple logistic regression model:.