# Multiple linear model p value f test t test

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Tania 2014년 7월 21일
댓글: Tania 2014년 7월 22일
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!!!!

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### 채택된 답변

Shashank Prasanna 2014년 7월 21일
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:
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Shashank Prasanna 2014년 7월 22일
The p-value tests the null hypothesis that the coefficient is equal to zero, or has no effect on the response. In the first example p>0.05 means you can't reject the null hypothesis that the coefficients are zero. But since the model is able to explain a lot of the variance (high R-squared) your variables maybe collinear. Which is precisely what is done in the next example, go through the stepwise example next:
Tania, I recommend some background reading on linear regression and statistics, otherwise your models and its interpretations may be dangerous to whoever will use it.
Also, if you have a new question, please close this questions (accept answer) and post your new question separately. That way you will have more eyes looking at it.
Tania 2014년 7월 22일
Okay cool, i think I missunderstood the sentence in the first example. So the null hypothesis is not rejected here, that makes sense.Thank you :)

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