probability of interest [closed]

Question

The model that I created in R is:

fit <- lm(hired ~ educ + exper + sex, data=data)

what I am unsure of is how to fit to model to predict probability of interest where p = pr(hiring = 1).

Edit: This is the computer output for what I have computed so far. I am unsure if this is even a step in the right direction to find the answer to this question.

What I am trying to do is, Fit a logistic regression model to predict the probability of being hired using years of education, years of experience and sex of job applicants.

 > test<-glm(hired ~ educ + exper + sex, data=data, family=binomial(link="logit"))
 > summary(test)

 Call:
 glm(formula = hired ~ educ + exper + sex, family = binomial(link = "logit"), 
     data = data)

 Deviance Residuals: 
     Min       1Q   Median       3Q      Max  
 -1.4380  -0.4573  -0.1009   0.1294   2.1804  

 Coefficients:
             Estimate Std. Error z value Pr(>|z|)  
 (Intercept) -14.2483     6.0805  -2.343   0.0191 *
 educ          1.1549     0.6023   1.917   0.0552 .
 exper         0.9098     0.4293   2.119   0.0341 *
 sex           5.6037     2.6028   2.153   0.0313 *
 ---
 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

 (Dispersion parameter for binomial family taken to be 1)

     Null deviance: 35.165  on 27  degrees of freedom
 Residual deviance: 14.735  on 24  degrees of freedom
 AIC: 22.735

 Number of Fisher Scoring iterations: 7

Answer 1

I will assume that the "probability of interest" is the probability you get from the estimated logistic regression model. To use that as a probability of course is assuming that the model is a reasonably good approximation$^\dagger$, and that the person you use it for is from the same population that your data was sampled from. First, the logistic regression model is $$\DeclareMathOperator{\P}{\mathbb{P}} p=\P(\text{Hired} =1 | x)=\frac{e^{\beta_0+\beta_1 x + \dotsm}}{1+e^{\beta_0+\beta_1 x + \dotsm}} $$ so you just need to insert the value of $x$ for the person of interest, and the estimated coefficients, to get the estimated probability for that person. To do that in R you use the predict method for class "glm", that is, predict.glm. To get information on that you type in R

?predict.glm
example(predict.glm)

and study the output. For your data, you will need a new dataframe with the data for the person of interest (or multiple such persons). To make that I will assume that your variables education and experience are measured in years, and that sex is 0/1. Then do

mynewdata <- data.frame(educ=c(12,15,17),exper=c(20,0,5),sex=c(0,0,1)) 
predict(test, type="response", newdata=mynewdata)

and study the output ...

$^\dagger$ For a logistic regression model, assuming that variables like education and experience (with a large range of values) is acting linearly, is a very strong assumption. It could be, for instance, that very high values for experience, correlating with high age, lowers the probability, a non-monotonic effect that cannot be represented linearly. So I would look into representing those via splines, that is, replacing your glm call with something like

library(splines)
> test <- glm(hired ~ ns(educ,df=5) + ns(exper,df=5) + sex, data=data, family=binomial(link="logit"))