1. Regression through the origin
Procedures for when you know the regression function must pass through the origin (0,0)

2. Examples Circumference of circle = π×diameter
Man hours = β1×number of items processed
Distance traveled = β1×speed
Blood alcohol content = β1×number drinks

3. No intercept model where: β1 is unknown slope parameter
Xi are known constants
i are unknown, independent normally distributed error terms with mean 0 and variance σ2

4. Example: Circumference = β1×diameter
Diam Circum

5. No intercept model in Minitab
Stat >> Regression >> Regression …
Specify response and predictor.
Under Options…, remove the default check mark from the “Fit the intercept” box.
Note: Stat >> Regression >> Fitted line plot does not handle regression through origin.

6. Diam Circum DxC D_sq The regression equation is Circum = 3.11 Diam
Predictor Coef SE Coef T P
Noconstant
Diam
S =
Diam Circum DxC D_sq

7. S =
Diam Circum RESI1 RESI1_sq
is unbiased estimator of σ2.

8. Summary of key points
Residuals don’t necessarily sum to 0 for regression through the origin.
Error degrees of freedom is n-1, not n-2, since estimating only one parameter.
Formulas are different for no-intercept model.

9. Analysis of Variance Source DF SS MS F P
Regression
Error
Total
Diam Circum RESI1 RESI1_sq Circ_sq FITS FITS_sq

10. Summary of key points
n total degrees of freedom, n-1 error degrees of freedom
Total sum of squares is “uncorrected for the mean.” It is just sum of squared observed responses.
Regression sum of squares also uncorrected for the mean. Just sum of squared fitted responses.
SSTOU = SSRU + SSE

11. The regression equation is Circum = 3.11 Diam
Predictor Coef SE Coef T P
Noconstant
Diam
S = ????
Many software packages, Minitab included, do not display an R2 value for regression through the origin. This is because it is possible that it is negative when you force the regression line through the origin, and therefore has no meaningful interpretation here.

12. Predicted Values for New Observations
Diam Fit SE Fit % CI % PI
(21.449,22.115) (20.581,22.983)