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Multiple linear model p value f test t test

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Hi! I am a bit confused by the matlab documentation: Linear regression model: y ~ 1 + x1 + x2 + x3
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!!!!

Accepted Answer

Shashank Prasanna
Shashank Prasanna on 21 Jul 2014
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:
Shashank Prasanna
Shashank Prasanna on 22 Jul 2014
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 on 22 Jul 2014
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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