Researchers interested in the relationship between absenteeism from school and c

Question

Researchers interested in the relationship between absenteeism from school and certain demographic characteristics of children collected data from 135 randomly sampled students in rural New South Wales, Australia, in a particular school year. 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). The variance of the residuals is 241.57 and the variance of the number of absent days for all students in the dataset is 265.44.

Estimate Std. Errort value Prt) (Intercept) 17 2.527.770 eth sex Irn 9.822.683.11 0 3.39 2.64 2.59 1.89 0.2092 2.55 0.41 0.404 (a) Write the equation of the regression line Xeth + ×sex + xlrn (b) For each of the following sentences, fill in the blanks. (Hint: enter either LOWER or HIGHER where appropriate, or a number otherwise) The estimated absence days of students who are not aboriginal is days than the aboriginal students The estimated absence days of male students is days than females The estimated absence days of students who are slow learners is days than students who are average learners (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) Calculate the R2 value (e) Calculate the adjusted R value

Explanation / Answer

(a) Estimated regreesion line

y^ = 17 - 9.82 * eth + 3.39 * sex + 2.64 * lrn

(b)

The estimated absence days of students who are aboriginal is 9.82 days lower than aboriginal students

The estimated absence days of male students is 3.39 days higher than female students.

The estimated absence days of students who are slow learners is 2.64 days higher than students who are average learners.

(c) Here aboriginal = 0

Male = 1

Slow learner = 0

y^ = 17 -9.82 * 0 + 3.39 * 1 + 2.64 * 1 = 23.03

Residual = y(original) - y(predicted) = 2 - 23.03 = -21.03

(d) R2 = 1 - SSE/SST = 1 - 241.57/265.44 = 0.0899

(e) Adjusted R2 = 1 - [(1-R2)(n-1)/(n-k-1)]

=1 - [(1 - 0.0899) * (135 -1)/ (135 - 3-1)]

= 0.0691

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