MATLAB: Multiple linear model p value f test t test

ftestmultiple linear regressionpvalueStatistics and Machine Learning Toolboxttest

Hi! I am a bit confused by the matlab documentation: Linear regression model: y ~ 1 + x1 + x2 + x3
            *pValue*    
Intercept    4.8957e-21
x1           9.8742e-08
x2           0.08078
x3           0.95236
Number of observations: 93, Error degrees of freedom: 89
Root Mean Squared Error: 4.09
R-squared: 0.752,  Adjusted R-Squared 0.744
F-statistic vs. constant model: 90, *p-value = 7.38e-27*
There are two different p values one can see, ones the individual ones and ones a p-value for all of them together? What is the difference between a f test and f statistic?also why dont we calculate the p-value for a t test?what the difference between f and t test?
According to the documentation the first p value is: p-value for the F statistic of the hypotheses test that the corresponding coefficient is equal to zero or not. For example, the p-value of the F-statistic for x2 is greater than 0.05, so this term is not significant at the 5% significance level given the other terms in the model.]
And the second p-value: p-value for the F-test on the model. For example, the model is significant with a p-value of 7.3816e-27.
Thanks so much!!!!

Best Answer

These phrases have standard meaning in Statistics which is consistent with most literature you may find on Linear Regression. In short the t-statistic is useful for making inferences about the regression coefficients. This is the one right next to your coefficients, x1 x2 in the output. F-statistic is the test statistic for testing the statistical significance of the model.
Here is some explanation that might help, however I'd urge you to go through other textbook/material on this topic:
http://www.mathworks.com/help/stats/f-statistic-and-t-statistic.html
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