Multilinear Regression, test for Dependence?

[WWGD]

Hi All,
Say we conduct a standard linear regression test of Y (dep) versus X (independent)

Then there are tests to be made on whether there is a linear relationship between Y and X

(with $H_o$ being that m=0; m is the regression line slope versus $H_A :m \neq 0$)

Is there a similar test for multilinear regression, to determine linear dependence

of Y versus $X_1, X_2,..,X_n$ ?

Thanks.

 

[fresh_42]

I'm no expert on linear optimization but perhaps you find something here:
https://scholar.google.de/scholar?q...ved=0ahUKEwjHzNLZkdXKAhUI0A4KHeh-CEkQgQMIGjAA

 

[WWGD]

Danke.

 

[FactChecker]

Yes. There is a lot available for multiple linear regression. You can test if Y is statistically the entire set of independent variables. You can also use a "stepwise" linear regression algorithm that will only end up with a set / subset of independent variables that are statistically needed for the regression. The statistical software package R is free and has good regression algorithms. ( See stepAIC in http://www.statmethods.net/stats/regression.html ). The algorithm will give you p-values that tell you the statistical significance of the model and the individual variables.

 

[WWGD]

Yes. There is a lot available for multiple linear regression. You can test if Y is statistically the entire set of independent variables. You can also use a "stepwise" linear regression algorithm that will only end up with a set / subset of independent variables that are statistically needed for the regression. The statistical software package R is free and has good regression algorithms. ( See stepAIC in http://www.statmethods.net/stats/regression.html ). The algorithm will give you p-values that tell you the statistical significance of the model and the individual variables.

Thanks, do you think PCA would be in order here, to determine which of the $X_i$ have more weight in determining the value of $Y$?

 

[FactChecker]

Thanks, do you think PCA would be in order here, to determine which of the $X_i$ have more weight in determining the value of $Y$?

No. PCA has a different use. It tries to represent the spread of data the best using fewer dimensions. But it does not single out one variable, Y, to explain, estimate, or predict. In fact, it might give you a linear combination that is very bad at estimating Y. If you want to find the best model for estimating Y = f(X), f linear, then you should use linear regression.

 

[WWGD]

Yes. There is a lot available for multiple linear regression. You can test if Y is statistically the entire set of independent variables. You can also use a "stepwise" linear regression algorithm that will only end up with a set / subset of independent variables that are statistically needed for the regression. The statistical software package R is free and has good regression algorithms. ( See stepAIC in http://www.statmethods.net/stats/regression.html ). The algorithm will give you p-values that tell you the statistical significance of the model and the individual variables.

Sorry to bother, but I can't find the step AIC. Would you please help?

 

[FactChecker]

Sorry to bother, but I can't find the step AIC. Would you please help?

I have actually never used the R version. I assume it is available. Here is a link that makes me believe that: https://stat.ethz.ch/R-manual/R-devel/library/MASS/html/stepAIC.html . I might be wrong. You can Google "stepwise linear regression" for other sources that may be available to you (MATLAB, SAS, SPSS, EXCEL add-in, etc).