pvalues = zero?

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wesleynotwise
wesleynotwise 2017-5-28
编辑： wesleynotwise 2017-8-7
The pvalues of the coefficients and model are equal to zero. Are they too significant to be true?
mdl =
Nonlinear regression model:
Emod ~ [Nonlinear formula with 7 coefficients and 9 predictors]
Estimated Coefficients:
Estimate SE tStat pValue
________ __________ ______ ___________
b1 4.5028 0.05506 81.78 0
b2 0.99989 0.00011413 8761.1 0
b3 4.3701 0.048136 90.786 0
b4 0.99986 3.0081e-05 33239 0
b5 1.0002 0.00125 800.15 0
b6 1.0246 0.004444 230.55 0
b7 4.4177 0.065778 67.16 8.3514e-279
Number of observations: 597, Error degrees of freedom: 591
Root Mean Squared Error: 3.7
R-Squared: 0.348, Adjusted R-Squared 0.342
F-statistic vs. zero model: 7.69e+03, p-value = 0

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Star Strider
Star Strider 2017-5-28
Looking at the t-statistics, the p-values are simply too small to be calculated. Very small p-values are characteristically the result of a very large data set (here 597).
So yes they are all highly statistically significantly different from zero, meaning that they are all required in the regression, and all help to explain the result.
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wesleynotwise
wesleynotwise 2017-5-28
You blew my mind. I wish you work with Matlab and make it more user-friendly.
If t-stat measures the distance from the mean, isn't the greater the t-value, the larger the distance, i.e. not good?
Given that both the p-values are calculated for both the coefficient and model, I assume the former is meant for individual predictor (or variable), and the latter is the overall/global p-value.
Star Strider
Star Strider 2017-5-28
Thank you! I appreciate your compliment!
‘If t-stat measures the distance from the mean, isn't the greater the t-value, the larger the distance, i.e. not good?’
No, because the t-distribution is essentially the normal distribution, so the mean is also the mode, i.e. the most frequently observed values, creating a ‘bell-shaped’ curve. The lowest probabilities (corresponding to the greatest absolute t-values) are at the tails.
‘Given that both the p-values are calculated for both the coefficient and model, I assume the former is meant for individual predictor (or variable), and the latter is the overall/global p-value.’
Correct (1) for the estimated coefficient of the predictor variable, and (2) for the model explaining more than the mean value of the dependent variable.

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