Answer :
The number of possible regression models using the best-subset method is given as follows:
31.
How to obtain the number of regression models?
There are five variables in this problem being considered to build the regression model, hence the possible options for which variables to consider are given as follows:
- One variable from a set of five.
- Two variables from a set of five.
- Three variables from a set of five.
- Four variables from a set of five.
- Five variables from a set of five.
These are all combinations, which are given by the combination formula, presented as follows:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Which gives the number of combinations of x elements from a set of n elements.
Thus the total number of regression models in this problem using the best-subset method is given as follows:
[tex]N = C_{5,1} + C_{5,2} + C_{5,3} + C_{5,4} + C_{5,5}[/tex]
N = 5 + 10 + 10 + 5 + 1.
N = 31.
More can be learned about the combination formula at https://brainly.com/question/11732255
#SPJ1
