Absenteeism, Part I. Researchers interested in the relationship between absenteeism from school and certain demographic characteristics of children collected data from 146 randomly sampled students in rural New South Wales, Australia, in a particular school year. Below are three observations from this data set.
eth sex lrn days
1 0 1 1 2 2 0 1 1 11 … … … … … 146 1 0 0 37
The summary table below shows the results of a linear regression model for predicting the average number of days absent based on ethnic background (eth: 0 – aboriginal, 1 – not aboriginal), sex (sex: 0 – female, 1 – male), and learner status (lrn: 0 – average learner, 1 – slow learner).10
Estimate Std. Error t value Pr(>|t|) (Intercept) 18.93 2.57 7.37 0.0000
eth -9.11 2.60 -3.51 0.0000 sex 3.10 2.64 1.18 0.2411 lrn 2.15 2.65 0.81 0.4177
(a) Write the equation of the regression model.
(b) Interpret each one of the slopes in this context.
(c) Calculate the residual for the first observation in the data set: a student who is aboriginal, male, a slow learner, and missed 2 days of school.
(d) The variance of the residuals is 240.57, and the variance of the number of absent days for all students in the data set is 264.17. Calculate the R2 and the adjusted R2. Note that there are 146 observations in the data set.
Absenteeism, Part II. considers a model that predicts the number of days absent using three predictors: ethnic background (eth), gender (sex), and learner status (lrn). The table below shows the adjusted R-squared for the model as well as adjusted R-squared values for all models we evaluate in the first step of the backwards elimination process.
Model Adjusted R2
1 Full model 0.0701 2 No ethnicity -0.0033 3 No sex 0.0676 4 No learner status 0.0723
Which, if any, variable should be removed from the model first?
Absenteeism, Part III. provides regression output for the full model, including all ex- planatory variables available in the data set, for predicting the number of days absent from school. In this exercise we consider a forward-selection algorithm and add variables to the model one-at-a-time. The table below shows the p-value and adjusted R2 of each model where we include only the corresponding predictor. Based on this table, which variable should be added to the model first?
variable ethnicity sex learner status
p-value 0.0007 0.3142 0.5870 R2 adj 0.0714 0.0001 0