Calculate the residual, R squared and adjusted R squared from the summary table.

Question

Calculate the residual, R squared and adjusted R squared from the summary table.

5 points) Researchers interested in the relationship between absenteeism from school and certain demographic characteristics of children collected data from 148 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 (n: 0 average leaner, 1- slow learner). The variance of the residuals is 240.51 and the variance of the number of absent days for all students in the dataset is 265.29. Estimate Std (Intercept) 17.92 251 7.37 0 eth 9.21 2.55 -3.93 0 sex 3.04 2.58 192 0.215 Im269 2.68 0.13 0,412 a) Write the equation of the regression line 17.92 +-9.21 xeth3.04 xser 2.69 (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 9.21 The estimated absence days of male students is 3.04 The estimated absence days of students who are slow learners is 2.69 (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 R2 value days lower than the aboriginal students. days higher than females days higher than students who are average leamers.

Explanation / Answer

(c) Here Multiple regeession equation

y^ = 17.92 - 9.21 * eth + 3.4 * sex + 2.69 * lrn

Here the students is aborignial so ; aboriginal = 0

Male; so sex = 1

Learn = slow ; so lrn = 1

y^ = 17.92 - 9.21 * eth + 3.4 * sex + 2.69 * lrn = 17.92 - 9.21 * 0 + 3.4 * 1 + 2.69 * 1 = 24.01

so residual = y(original) - y(predicted) = 24 - 2 = 22

(d) R2 = 1 - SSE/SST = 1 - 240.51/265.29 = 0.0934

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

= 1 - [(1 - 0.0934) * (148 - 1) / (148 - 3 - 1)]

= 1 - 0.9255

= 0.0745

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