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As we know, after applying a linear regression model to a continuous data set we carry out a significance test to each parameter $\beta_i$ associated with the predictor variable $x_i$ to check whether the latter contributes to the explanation of the dependent variable $y_i$.

$${{\begin{cases}H_0: \beta_i = 0,\\H_1: \beta_i \neq 0.\end{cases}}}$$

Can we apply the same procedure to a linear SVM classifier? and if so how do we apply it in R?

Here is my code:

library(e1071)

edudata <- read.csv("https://stats.idre.ucla.edu/stat/data/binary.csv")
svm_model <- svm(formula = admit ~ gre + gpa + rank, data = edudata, kernel = "linear", scale = F)

summary(svm_model)

Call:
svm(formula = admit ~ gre + gpa + rank, data = edudata, kernel = "linear", 
scale = F)


Parameters:
SVM-Type:  eps-regression 
SVM-Kernel:  linear 
   cost:  1 
  gamma:  0.3333333 
epsilon:  0.1 


Number of Support Vectors:  342

The data:

head(edudata)

A data.frame: 6 × 4     admit   gre gpa rank
<int>   <int>   <dbl>   <int>
1   0   380 3.61    3
2   1   660 3.67    3
3   1   800 4.00    1
4   1   640 3.19    4
5   0   520 2.93    4
6   1   760 3.00    2

Thanks in advance.

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    $\begingroup$ What would be the null and alternative hypotheses for such a test? $\endgroup$
    – Matthew Drury
    Commented Mar 10, 2020 at 21:59
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    $\begingroup$ I really don't know. I just wanted to know whether the statistical procedure we apply to the linear and logistic regression models can be generalized over some supervised learning methods. $\endgroup$
    – Goldman Clarck
    Commented Mar 10, 2020 at 22:04
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    $\begingroup$ There isn't a parameter like that in an SVM, so it will be important for you to say exactly what you want to test, if not in math than at least in English that we can help turn into the necessary mathematics. $\endgroup$
    – Dave
    Commented Feb 22, 2022 at 15:33
  • $\begingroup$ This question is not answerable without a description of what hypothesis is being tested. $\endgroup$
    – Sycorax ♦
    Commented Feb 22, 2022 at 16:00

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