Understanding Linear Regression

Understanding Linear Regression

The CNT-90 timer/counter/analyzer employs linear regression techniques for improved measurement resolution. The inclination of the regression line corresponds to the estimated average period time of the input signal (T*), and is calculated as:


xk = the number of cycles in sample k;

yk = the time-stamping value in sample k; and

n = the number of samples in the measurement

The uncertainty (variance) of the inclination T* is:


s(y) = the normal root-mean-square (RMS) resolution, tRES, for an individual time stamp and s(x) = the standard deviation of an approximate rectangular distribution,

(xk = x0 + kN/n i.e.,

s(x) ≈ Σ = N/2(3)0.5

for large values of n, which leads to the relative resolution in period or frequency:

s(T*)/T* = s(f*)/f* = 0.52tRES>/0.5>

TAGS: Contribs
Hide comments


  • Allowed HTML tags: <em> <strong> <blockquote> <br> <p>

Plain text

  • No HTML tags allowed.
  • Web page addresses and e-mail addresses turn into links automatically.
  • Lines and paragraphs break automatically.