What exactly does tStat of fitlm function refer to?

I am a little confused with the documentation of the fitlm function https://ch.mathworks.com/help/stats/fitlm.html#description. How is tStat calculated?

Is there a link that provides the mathematical background?

Thanks in advance.

Answer 1

[dpb]

Well, it's the basic linear model hypothesis test statistic that each coefficient in the model is significantly different from the null hypothesis that the coefficient is zero. It's simply the value of the coefficient divided by the overall model standard error. That's what the doc says:

• tStat — t-statistic for each coefficient to test the null hypothesis that the corresponding coefficient is zero against the alternative that it is different from zero, given the other predictors in the model. Note that tStat = Estimate/SE. For example, the t-statistic for the intercept is 47.977/3.8785 = 12.37.
• pValue — p-value for the t-statistic of the hypothesis test that the corresponding coefficient is equal to zero or not. For example, the p-value of the t-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.

https://dss.princeton.edu/online_help/analysis/interpreting_regression.htm is one set of class notes; it's covered in any text on regression analysis. I'm long in the tooth; my reference was always Draper and Smith, Applied Regression Analysis for introductory text; I'm sure the edition I have is long out of print...

[Kristen Whitney]

Does the fitlm perform the Student's t-test or the Welch's t-test to obtain tStat?

[dpb]

Student's. Welch's is two-sample for unequal variance and can be obtained from

ttest2(data1, data2, 'Vartype', 'unequal')

AFAIK (but again, remember, I'm "quite long in the tooth") all regression packages assume the standard linear regression assumptions of normality, independence and equal variances. These are explicitly stated in the background section on "What is a Linear Regression Model?" in the MATLAB documentation from which the above conclusions are inferred.

You can take a set of data and confirm this by comparison with the output from ttest

[Kristen Whitney]

Thank you so much for the information and suggestions. Very helpful!