Student achievement data from 65 London secondary schools, containing GCSE (General Certificate of Secondary Education) exam scores taken at age 16 and London Reading Test (LRT) scores at age 11 for 4,059 students. Both scores have been standardized to have mean 0 and standard deviation approximately 10. This is the primary running example throughout the course, used from simple linear regression through interactions and model diagnostics.
Format
A tibble with 4,059 rows and 9 columns:
- school
School identifier. Type: numeric. Values: 1 to 65. 65 unique London secondary schools.
- student
Student identifier within school. Type: numeric. Range: (1, 913). Not unique across schools.
- gcse
GCSE examination score at age 16, standardized. Type: numeric. Range: (-36.66, 36.66). Mean approximately 0, SD approximately 10. This is the primary outcome variable.
- lrt
London Reading Test score at age 11, standardized. Type: numeric. Range: (-29.35, 30.16). Mean approximately 0, SD approximately 10. This is the primary predictor for intake achievement.
- gender
Gender of student. Type: numeric. Binary indicator (0/1) where 1 = female, 0 = male. 60% female.
- pred
Predicted GCSE score from the regression model. Type: numeric. Range: (-1.91, 2.54). Pre-computed predicted values.
- u0
School-level random intercept. Type: numeric. Contains large negative placeholder values (-1e30) for most schools, indicating unestimated or filtered values. Valid range approximately (-0.65, 0.65) for estimated schools.
- u1
School-level random slope for LRT. Type: numeric. Contains large negative placeholder values (-1e30) for most schools. Valid range approximately (-0.35, 0.35) for estimated schools.
- filter__
Filter variable. Type: numeric. Binary indicator (0/1) where 1 = included in a specific analysis subset (2% of observations), 0 = not included.
Source
Goldstein, H., Rasbash, J., et al. London school effectiveness
study data. Original data file: gcse.dta
Details
This dataset is the primary running example used throughout the course. It appears in virtually every chapter:
Chapter 1 (Simple Linear Regression): Regressing GCSE on LRT for individual schools (e.g., Battersea, Chelsea) to introduce the regression model, OLS estimation, R-squared, and inference.
Chapter 2 (ANCOVA): Comparing schools while controlling for LRT intake scores. The unadjusted difference between Chelsea and Battersea is 9.86 points, but the LRT-adjusted difference is 7.51.
Chapter 5 (Interactions): Testing whether the LRT slope differs across schools (school-by-LRT interaction).
Chapter 8 (Model Diagnostics): Residual analysis, outlier detection, and influence diagnostics.
The variables u0, u1, pred, and filter__ are pre-computed model outputs included for pedagogical purposes. For standard regression analyses, the key variables are gcse, lrt, school, and gender.
Examples
data(gcse)
head(gcse)
#> # A tibble: 6 × 6
#> school student gcse lrt gender pred
#> <int> <int> <dbl> <dbl> <int> <dbl>
#> 1 1 143 2.61 6.19 1 0.785
#> 2 1 145 1.34 2.06 1 0.504
#> 3 1 142 -17.2 -13.6 0 -0.567
#> 4 1 141 9.68 2.06 1 0.504
#> 5 1 138 5.44 3.71 1 0.616
#> 6 1 155 17.3 21.9 0 1.86
# Simple linear regression: GCSE on LRT
lm(gcse ~ lrt, data = gcse)
#>
#> Call:
#> lm(formula = gcse ~ lrt, data = gcse)
#>
#> Coefficients:
#> (Intercept) lrt
#> -0.01195 0.59506
#>
# ANCOVA: school differences controlling for LRT
gcse_sub <- gcse[gcse$school %in% c(1, 2), ]
lm(gcse ~ lrt + factor(school), data = gcse_sub)
#>
#> Call:
#> lm(formula = gcse ~ lrt + factor(school), data = gcse_sub)
#>
#> Coefficients:
#> (Intercept) lrt factor(school)2
#> 3.7937 0.7332 1.1402
#>
# Interaction: does LRT slope differ by gender?
lm(gcse ~ lrt * gender, data = gcse)
#>
#> Call:
#> lm(formula = gcse ~ lrt * gender, data = gcse)
#>
#> Coefficients:
#> (Intercept) lrt gender lrt:gender
#> -1.030480 0.592813 1.699015 -0.004031
#>