Tools › Statistics › Regression and Modelling › Regression and Curve Fitting › Example

NIST StRD Longley: ill-conditioned multiple regression of employment on six economic predictors

ToolRegression and Curve Fitting
SourceNational Institute of Standards and Technology (2012). Statistical Reference Datasets: Linear Regression. NIST, Gaithersburg, MD. Longley dataset (higher difficulty), certified values (copy in References/Regression-StRD/Longley.dat).
LevelGraduate

Problem

Longley's 16 annual observations (1947–1962) of total employment against the GNP deflator, GNP, unemployment, armed forces, population and year are to be fitted by multiple linear regression with an intercept. The predictors are nearly collinear, so the problem tests the numerical accuracy of the solver. Report the seven coefficients with their standard deviations, the residual standard deviation, R² and the F statistic.

Inputs to Enter

  • Model: multiple linear regression; data: 16 lines of x1 x2 x3 x4 x5 x6 y (the NIST file lists y first)
  • Confidence 95 %
Open the Regression and Curve Fitting tool

Answers

  • B0 = −3,482,258.63459582 (SD 890,420.383607373), B1 = 15.0618722713733 (SD 84.9149257747669), B2 = −0.0358191792925910 (SD 0.0334910077722432)
  • B3 = −2.02022980381683 (SD 0.488399681651699), B4 = −1.03322686717359 (SD 0.214274163161675), B5 = −0.0511041056535807 (SD 0.226073200069370), B6 = 1,829.15146461355 (SD 455.478499142212)
  • Residual SD = 304.854073561965, R² = 0.995479004577296
  • Regression SS = 184,172,401.944494, F = 330.285339234588

Notes

Choose the multiple-regression model and paste the six predictor columns followed by y. Reproduced to 1e-7 relative or better by Householder QR with column equilibration (test_regression.php).

More Examples for This Tool