The name is absent



26


Stata Technical Bulletin


STB-57


. regress mpg sp*,noconst robust

Regression with robust standard errors


Number of obs = 74
F( 7, 67) = 618.91
Prob > F = 0.0000
R-squared = 0.9792
Root MSE = 3.3469

I                 Robust

≡pg I

Coef.

Std. Err.

t

p>t

[957. Conf.

Interval]

spi I

29.21133

1.761704

16.581

0.000

25.69495

32.72771

sp2 I

25.89924

1.073405

24.128

0.000

23.75671

28.04177

sp3 I

20.98226

.7479685

28.052

0.000

19.4893

22.47521

sp4 I

19.4749

.610094

31.921

0.000

18.25715

20.69266

sp5 I

15.97982

.5560974

28.736

0.000

14.86985

17.0898

sp6 I

16.74691

1.934879

8.655

0.000

12.88487

20.60894

sp7 I

10.60747

1.585487

6.690

0.000

7.442828

13.77212

Finally, for technical people, we can fit the same model yet again, using bspline instead of frencurv. Here, the splines
are В-splines rather than reference splines. The variable labels show the range of positive values of each В-spline, delimited
by knots, including the extra knots calculated by bspline. The parameters are expressed in miles per gallon but are not easy
for nonmathematicians to interpret.

. bspline,xvar(weight) knots(1760(770)4840) gen(bs) power(3) labf(%4.0f)
. describe bs*

27. bsl

float

7.8.4f

B-spline

on [-550,2530)

28. b≡2

float

7.8.4f

B-spline

on [220,3300)

29. b≡3

float

7.8.4f

B-spline

on [990,4070)

30. b≡4

float

7.8.4f

B-spline

on [1760,4840)

31. bs5

float

7.8.4f

B-spline

on [2530,5610)

32. bs6

float

7.8.4f

B-spline

on [3300,6380)

33. b≡7

float

7.8.4f

B-spline

on [4070,7150)

. regress

mpg bs*,noconst robust

Regression with robust

standard errors

Number of obs

=      74

F( 7,     67)

= 618.91

Prob > F

= 0.0000

R-squared

= 0.9792

Root MSE

= 3.3469

I

I

Robust

≡pg I

I        Coef.

Std. Err.

t

p>t

[957. Conf.

Interval]

bsl I

I 8.530818

24.5484

0.348

0.729

-40.468

57.52964

bs2 I

I 36.83022

5.330421

6.909

0.000

26.19066

47.46979

bs3 I

I 19.41627

2.252816

8.619

0.000

14.91963

23.91291

bs4 I

I 21.45246

1.708278

12.558

0.000

18.04272

24.8622

bs5 I

I 11.62333

2.241923

5.185

0.000

7.148434

16.09823

bs6 I

I 25.14979

7.910832

3.179

0.002

9.359707

40.93988

bs7 I

I -48.57765

34.29427

-1.416

0.161

-117.0293

19.87399

Technical note

There are other programs in Stata to generate splines. mkspline (see [R] mkspline) generates a basis of linear splines to
be used in a design matrix, as does frencurv, power (1), but the basis is slightly different because the fitted parameters for
frencurv are reference values, whereas the fitted parameters for mkspline are the local slopes of the spline in the inter-knot
intervals. spline and spbase (Sasieni 1994) are used for fitting a natural cubic spline, which is constrained to be linear outside
the completeness region and parameterized using the truncated power basis. The splines fitted using bspline or frencurv,
on the other hand, are unconstrained (hence the extra degrees of freedom corresponding to the external reference points) and
parameterized using the В-spline or reference spline basis, respectively. frencurv and bspline are therefore complementary
to the existing programs and do not supersede them.



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