chisq.test vs manual calculation - why are different results produced?

Hello,

I am trying to fit gamma, negative exponential and inverse power  
functions
to a dataset, and then test whether the fit of each curve is good.  
To do
this I have been advised to calculate predicted values for bins of  
data (I
have grouped a continuous range of distances into 1km bins), and  
then apply
a chi-squared test. Example:

data <- data.frame(distance=c(1,2,3,4,5,6,7),  
observed=c(43,13,10,6,2,1),

predicted=c(28, 18, 10, 5 ,3, 1, 1))

chisq.test(data$observed, data$predicted)

Which gives:

       Pearson's Chi-squared test

data:  data$observed and data$predicted
X-squared = 35, df = 25, p-value = 0.0882

Warning message:
In chisq.test(data$observed, data$predicted) :
 Chi-squared approximation may be incorrect

I understand this is due to having observed/predicted values of less  
than
five, however I am interested to know firstly why R uses such a large
number of degrees of freedom (when by my understanding there should  
only be
4 df), and secondly whether using the following manual calculation is
therefore inappropriate -

X2 <- sum(((data$observed - data$predicted)^2)/data$predicted)
1-pchisq(X2,4)

[1] 0.04114223

If chi-squared is unsuitable, what other test can I use to determine
whether my observed and predicted data come from the same  
distribution? The
frequently recommended fisher's test doesn't seem to be any more
appropriate as it requires values of greater than 5 for contingency  
tables
larger than 2 x 2.

Thanks for your help.

Louise

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