# [R] What is the correct model formula for the results of piecewise linear function?

From: zhijie zhang <epistat_at_gmail.com>
Date: Mon, 24 Mar 2008 15:36:09 +0800

Dear friends,
I used the B-spline (degree=1) method to fit the piecewise linear function and the results are listed below.

m.glm<-glm(mark~x+poly(elevation,2)+bs(distance,degree=1,knots=c(16.13,24))

```                +bs(y,degree=1,knots=c(-0.4357,-0.3202
```
)),family=binomial(logit),data=point)
summary(m.glm)

Coefficients:

```                                                      Estimate Std. Error z
value Pr(>|z|)
(Intercept)                                             12.104      3.138
3.857 0.000115 ***
x                                                       5.815      1.987
2.926 0.003433 **
poly(elevation, 2)1                                     6.654      4.457
1.493 0.135444
poly(elevation, 2)2                                     -6.755      3.441  -
1.963 0.049645 *
bs(distance, degree = 1, knots = c(16.13, 24))1         -1.291      1.139  -
1.133 0.257220
bs(distance, degree = 1, knots = c(16.13, 24))2         -10.348      2.025
-5.110 3.22e-07 ***
bs(distance, degree = 1, knots = c(16.13, 24))3         -3.530      3.752  -
0.941 0.346850
bs(y, degree = 1, knots = c(-0.4357, -0.3202))1         -6.828      1.836  -
3.719 0.000200 ***
bs(y, degree = 1, knots = c(-0.4357, -0.3202))2         -4.426      1.614  -
2.742 0.006105 **
bs(y, degree = 1, knots = c(-0.4357, -0.3202))3        -11.216      2.861  -
```
3.920 8.86e-05 ***
I think bs(degree=1) has fitted the piecewise linear functions. Now i hope to write the model formua for the above results, but not very sure about how to write the correct results for *distance* and *y,* because they have three parts .
Logitp=12.104 + 5.815*x + 6.654*elevation - 6.755*elevation^2
```           -1.291*distance1 - 10.348*distance2 - 3.53*distance3
-6.828*y1 - 4.426*y2 - 11.216*y3
```
In the above formula, distance1-3 denotes the three linear functions for*distance
*, my problem is how to replace distace1-3 using original variable *distance *? The same question is for *y*.
Could anybody please show me the correct model formula according to the above result?
Thanks a lot.
```--
With Kind Regards,
Zhi Jie

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