Getting p-value via nls in r - r

Question

I'm a complete novice in R and I'm trying to do a non-linear least squares fit to some data. The following (SC4 and t are my data columns) seems to work:
fit = nls(SC4 ~ fin+(inc-fin)*exp(-t/T), data=asc4, start=c(fin=0.75,inc=0.55,T=150.0))
The "summary(fit)" command produces an output that doesn't include a p-value, which is ultimately, aside from the fitted parameters, what I'm trying to get. The parameters I get look sensible.
Formula: SC4 ~ fin + (inc - fin) * exp(-t/T)
Parameters:
Estimate Std. Error t value Pr(>|t|)
fin 0.73703 0.02065 35.683 <2e-16 ***
inc 0.55671 0.02206 25.236 <2e-16 ***
T 51.48446 21.25343 2.422 0.0224 *
--- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.04988 on 27 degrees of freedom
Number of iterations to convergence: 8
Achieved convergence tolerance: 4.114e-06
So is there any way to get a p-value? I'd be happy to use another command other than nls if that will do the job. In fact, I'd be happy to use gnuplot for example if there's some way to get a p-value from it (in fact gnuplot is what I normally use for graphics).
PS I'm looking for a p-value for the overall fit, rather than for individual coefficients.

Answer 1

The way to do this in R is you have to use the anova function to compute the fitted values of your current model and then fit your model with less variables, and then use the function anova(new_model,previous_model). The computed F-score will be closer to one if you cannot reject the null that the parameters for the variables you have removed are equal to zero. The summary function when doing the standard linear regression will usually do this for you automatically.
So for example this is how you would do it for the standard linear regression:
> x = rnorm(100)
> y=rnorm(100)
> reg = lm(y~x)
> summary(reg)
Call:
lm(formula = y ~ x)
Residuals:
Min 1Q Median 3Q Max
-2.3869 -0.6815 -0.1137 0.7431 2.5939
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.002802 0.105554 -0.027 0.9789
x -0.182983 0.104260 -1.755 0.0824 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.056 on 98 degrees of freedom
Multiple R-squared: 0.03047, Adjusted R-squared: 0.02058
F-statistic: 3.08 on 1 and 98 DF, p-value: 0.08237
But then if you use anova you should get the same F-score:
> anova(reg)
Analysis of Variance Table
Response: y
Df Sum Sq Mean Sq F value Pr(>F)
x 1 3.432 3.4318 3.0802 0.08237 .
Residuals 98 109.186 1.1141
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1