Monday, February 4, 2013

NLS (nonlinear least square)

summary()->output

Formula: val ~ exp(-k * time)

Parameters:
   Estimate Std. Error t value Pr(>|t|)    
k 4.456e-03  3.398e-05   131.2 9.77e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.003644 on 3 degrees of freedom

Number of iterations to convergence: 4 
Achieved convergence tolerance: 3.743e-06 



Using T-Tables
We have learned the following things about a t-test:
  • The t-test produces a single value, t, which grows larger as the difference between the means of two samples grows larger;
  • t does not cover a fixed range such as 0 to 1 like probabilities do;
  • You can convert a t-value into a probability, called a p-value;
  • The p-value is always between 0 and 1 and it tells you the probability of the difference in your data being due to sampling error;
  • The p-value should be lower than a chosen significance level (0.05 for example) before you can reject your null hypothesis.