To model the relationship between p$($X$)=$ PrY $=1|$ X$)$ and X$,$ logistie regression takes the form

p$$X$=$

$1+\mathrm{.}00+$Brx$|$

which always returns a value between $0$ and $1.$

Consider the 'ISLR$2$::Default' dataset.

$>$ str $($ISR$2$:: Default $)$

'data, frame': $10000$ obs. of $4$ variables:

$$ default: Factor W$/2$ levels $"$No RYe $1111212144$

$$ student: Factor w$/2$ levels $"$No$"$ "Yes": $1211121211$

$

balance: num $7308171074529786...$

$ income : num $4436212106317673570438463...$

A logistic regression model of 'default' on 'balance' is fitted, and a summary of the coefficient estimates is shown below.

$>$ summary $($gim $($default $-$ balance, data $=$ Default, family $=$ "binomial" $))$Scoef

Estimate

Std$.$ Error

$($Intercept$)-10\mathrm{.}6513306140\mathrm{.}3611573721$

balance

$0\mathrm{.}0054989170\mathrm{.}0002203702$

z value

Pr $(>|$z$|)$

$($Intercept $)$

$-29\mathrm{.}492213\mathrm{.}623124$e$-191$

balance

$24\mathrm{.}953091\mathrm{.}976602$e$-137$