Data from the High School and Beyond (HS&B) longitudinal study, a nationally representative survey of U.S. high school students conducted by the National Center for Education Statistics (NCES). This full sample of 350 students includes academic achievement scores, socioeconomic status, and school program information. Used in regression teaching to illustrate model diagnostics, multicollinearity among correlated achievement measures, and multiple regression with both continuous and categorical predictors.
Format
A tibble with 350 rows and 16 columns:
- id
Student identifier. Type: numeric. Range: (1, 599).
- gender
Student gender. Type: numeric. Values: 1 = male, 2 = female.
- race
Student race/ethnicity. Type: numeric. Values: 1 = Hispanic, 2 = Asian, 3 = African American, 4 = White.
- ses
Socioeconomic status. Type: numeric. Values: 1 = low, 2 = middle, 3 = high.
- sch
School type. Type: numeric. Values: 1 = public, 2 = private.
- prog
Academic program. Type: numeric. Values: 1 = general, 2 = academic, 3 = vocational.
- locus
Locus of control composite score. Type: numeric. Range: (-2.23, 1.36). Higher values indicate more internal locus of control.
- concept
Self-concept composite score. Type: numeric. Range: (-2.62, 1.19). Higher values indicate more positive self-concept.
- mot
Motivation. Type: numeric. Range: (0, 1). Proportion-based measure of academic motivation.
- career
Career choice code. Type: numeric. Range: (1, 17). Categorical code for intended career.
- read
Reading achievement test score (standardized). Type: numeric. Range: (28.3, 73.3). Mean approximately 52.
- write
Writing achievement test score (standardized). Type: numeric. Range: (28.1, 67.1). Mean approximately 52.
- math
Mathematics achievement test score (standardized). Type: numeric. Range: (31.8, 75.5). Mean approximately 51.
- sci
Science achievement test score (standardized). Type: numeric. Range: (26.0, 74.2). Mean approximately 52.
- ss
Social studies achievement test score (standardized). Type: numeric. Range: (25.7, 70.5). Mean approximately 52.
- sample
Sample weight indicator. Type: numeric. Constant value of 1 for all observations in this subsample.
Source
National Center for Education Statistics (NCES). High School and
Beyond (HS&B) Longitudinal Study. U.S. Department of Education.
Original data file: hsbs1.dta
Details
This dataset is used in Chapter 8 (Model Diagnostics) to illustrate regression diagnostic techniques including residual analysis, leverage and influence measures, and detection of outliers. It also serves as a demonstration dataset for model building with multiple correlated predictors (the five achievement test scores) and for examining the effects of categorical predictors such as program type and SES on academic outcomes. Key analyses include: multiple regression of writing scores on reading and math, residual plots, Cook's distance, leverage diagnostics, and VIF assessment for multicollinearity.
Examples
data(hsbs1)
head(hsbs1)
#> # A tibble: 6 × 16
#> id gender race ses sch prog locus concept mot career read write
#> <int> <int> <int> <int> <int> <int> <dbl> <dbl> <dbl> <int> <dbl> <dbl>
#> 1 303 2 4 1 1 1 -0.840 -0.240 1 4 54.8 64.5
#> 2 404 2 4 2 1 1 -0.380 -0.470 0.670 4 62.7 43.7
#> 3 225 1 4 2 1 2 0.890 0.590 0.670 6 60.6 56.7
#> 4 553 1 4 2 2 2 0.710 0.280 0.670 16 62.7 56.7
#> 5 433 2 4 2 1 3 -0.640 0.0300 1 4 41.6 46.3
#> 6 189 2 4 3 1 2 1.11 0.900 0.330 6 62.7 64.5
#> # ℹ 4 more variables: math <dbl>, sci <dbl>, ss <dbl>, sample <int>
# Multiple regression of writing on reading and math
fit <- lm(write ~ read + math, data = hsbs1)
summary(fit)
#>
#> Call:
#> lm(formula = write ~ read + math, data = hsbs1)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -18.1588 -4.8532 0.1208 4.9720 17.4686
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 13.87143 2.29829 6.036 4.07e-09 ***
#> read 0.35117 0.05323 6.597 1.57e-10 ***
#> math 0.39387 0.05852 6.730 7.01e-11 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 7.205 on 347 degrees of freedom
#> Multiple R-squared: 0.4539, Adjusted R-squared: 0.4507
#> F-statistic: 144.2 on 2 and 347 DF, p-value: < 2.2e-16
#>