Answer parts (a)-(c) only.? 8.4 Absenteeism, Part I. Researchers interested in t
ID: 3374919 • Letter: A
Question
Answer parts (a)-(c) only.?
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 Irn days 2 146 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 (1rn: 0 - average learner, 1 - slow learner) 18 Estimate Std. Error t value Pr(>It) 7.37 0.0000 2.60-3.51 0.0000 0.2411 0.810.4177 18.93 9.11 3.10 2.15 (Intercept) 2.57 eth sex rn 1.18 2.64 2.65 (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
Sol:
a) Write the equation of the regression line.
Answer Absenteeism = 18.93 - 9.11 * (ethnic background) + 3.10 * (sex) + 2.15 * (learner status)
b) Interpret each one of the slopes in this context.
Answer Ethnic background: The model predicts a 9.11 (absent) days decrease in non-aboriginal children, all else held constant.
Sex: The model predicts a 3.10 (absent) days increase in males over females, all else held constant.
Learner status: The model predicts a 2.15 (absent) days increase in slow learners over average learners, all else held constant.
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.
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
d) R-squared = 1 - (variance of residuals)/(variance in outcome)
= 1 - (240.57)/(264.17) = 0.0893
R-squared adjusted. 1 - (variance of residuals)/(variance in outcome)*(n-1)/(n-k-1)
= 1 - (240.57/264.17)*((146-1)/(146-3-1)) = 0.0701