How do I compute a partial F-test for multiple linear regression?

How can I compute a partial F-test for multiple linear regression in MATLAB?

I see built-in functions to compute an F-test, but not to compute a partial F-test.

Answer 1

[MathWorks Support Team]

You can use the function "coefTest" to find both the overall F-test and a partial F-test. Here's an example of the general process:

>> % Setting up the data and example
>> load hald
>> f = fitlm(ingredients,heat)

This returns a table with the overall p-values and t-statistics for individual coefficients and overall statistics for the intercept. However, you can also use "coefTest" to compute other partial F statistics by declaring a matrix M so that M*b (b is the vector of coefficient estimates) specifies the constraints that you want to set to zero. Here is examples using this method to compute the overall F statistic, a single t statistic, and a partial F statistic for testing two coefficients.

Notice the overall F and p values from above - here is how they are computed:

>> M = [0 1 0 0 0; 0 0 1 0 0; 0 0 0 1 0; 0 0 0 0 1];
>> [p,F] = coefTest(f,M)

Notice the t and p values for x1 - here is how they are computed:

>> M = [0 1 0 0 0];
>> [p,F] = coefTest(f,M)
>> sqrt(F)

To compute a partial F-test for just coefficients x3 and x4:

>> M = [0 0 0 1 0; 0 0 0 0 1];
>> [p,F] = coefTest(f,M)

Alternatively, you could use the function "stepwiselm" to perform the partial F-test. See the following documentation page for more information about "stepwiselm":

https://www.mathworks.com/help/stats/stepwiselm.html

"stepwiselm" starts with a model, and incrementally adds or removes features to find the best model according to the specified criterion. One of the criteria is SSE (sum of squared errors). You can see the F-statistic for each model during the adding/removing of the features while the training is done.