# generate some data:
at=5;bt=3.5;ct=2
er=rnorm(50,0,0.5)
x=rep(1:10,each=5)
y=rep(2:6,times=10)
z=runif(50,3,13)
f=a+bt*x+ct*y+bt*ct*z+er

x y        z         f
       1 2  4.41772  43.13881
       1 3  3.27877  37.86786
       1 4 11.72467  98.11645
       1 5 12.89926 108.31700
       1 6 12.70191 109.26653
       2 2  5.56601  53.74264
       2 3  7.51415  69.91123
       2 4  3.29666  43.43002
       2 5 10.48299  95.09565
       2 6 12.97598 113.94662
       3 2 11.01474  96.14735
       3 3  6.45463  66.72930
       3 4  7.29405  73.81140
       3 5  4.66598  59.69668
       3 6 10.73396 102.12973
       4 2  4.75961  56.11710
       4 3  5.25630  61.94787
       4 4  5.31457  64.68823
       4 5  9.02318  92.40222
       4 6  5.85377  72.45057
       5 2  5.19293  62.11454
       5 3  5.85723  69.51613
       5 4  4.48740  62.66245
       5 5 11.15931 110.75395
       5 6  7.90122  90.20729
       6 2  7.48214  82.41067
       6 3  5.11017  68.06972
       6 4 11.08377 111.01008
       6 5  7.91120  91.51254
       6 6 11.57816 119.30712
       7 2  9.69650 102.06396
       7 3 11.13549 113.36050
       7 4 11.41179 117.03492
       7 5 12.72066 127.97719
       7 6  8.66705 102.38321
       8 2  6.50427  82.27634
       8 3  5.92371  79.93017
       8 4  9.89270 110.24138
       8 5  9.12479 107.29101
       8 6 12.87875 134.94524
       9 2  9.41497 106.09548
       9 3  8.71814 103.16074
       9 4  8.89625 106.66582
       9 5  3.51514  71.61044
       9 6 10.43254 121.21656
      10 2  7.32917  94.60507
      10 3 10.70345 121.05722
      10 4  4.34320  78.78394
      10 5 10.92676 126.43769
      10 6  9.90614 121.39587

lm(f~x+y+z)

(Intercept)            x            y            z
      4.930        3.529        2.162        6.903

nlsfit = nls(f~a+b*x+c*y+b*c*z,start=list(a=4.9,b=3.5,c=2.1))

Formula: f ~ a + b * x + c * y + b * c * z

Parameters:
  Estimate Std. Error t value Pr(>|t|)
a  5.37481    0.23287   23.08   <2e-16 ***
b  3.50528    0.02278  153.89   <2e-16 ***
c  1.98310    0.01408  140.82   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.4798 on 47 degrees of freedom

Number of iterations to convergence: 3
Achieved convergence tolerance: 6.281e-07