8.4 Absenteeism, Part I. Researchers interested in the relationship between abse

Question

8.4 Absenteeism, Part I. Researchers interested in the relationship between absenteeism from school and certain demographic characteristics of children collected data from 146 randomly sam- pled students in rural New South Wales, Australia, in a particular school year. Below are three observations from this data set eth sex days 146 1 0037 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 (1rn: 0- average learner, 1 slow learner).18 Estimate Std. Error t value Prt 18.93 9.11 3.10 2.15 2.57 2.60 -3.5 0.0000 2.64 2.65 Intercept 7.37 0.0000 eth sex rn 1.18 0.2411 0.81 0.4177 (a) Write the equation of the regression line (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

Explanation / Answer

From the given data, we find....

a) Equation of the Regression Line is,

nr days=18.93-9.11*ethnicity+3.1*sex+2.15*learner status

c) Residual for the first Observation in the data set is,

eth=0
sex=lrn=1
days=2
the fitted value is
days=18.93-9.11*ethnicity+3.1*sex+2.15*learner status=
=18.93+3.1+2.15=24.18
The residual is observed value-fitted value=2-24.18=-22.18

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