Hello I'm working on the interpretation of logistic regression. I am not sure whether I understand it fully. Can you help me with it? Really appreciate it.

This is my sample data. I want to study factors impacting the college attendance. The dependent variable is the dummy variable, whether to attend college, the independent variables are family income, a continuous variable, and whether live in a city, a dummy variable.

```
# Set seed for reproducibility
set.seed(42)
# Number of observations
n <- 20
# Simulate data
attend_college <- rbinom(n, 1, 0.5) # 50% chance of attending college
family_income <- rnorm(n, mean = 50000, sd = 15000) # Family income with mean = $50,000, sd = $15,000
live_in_city <- rbinom(n, 1, 0.6) # 60% chance of living in a city
# Create a dataframe
simulated_df <- data.frame(AttendCollege = attend_college, FamilyIncome = family_income, LiveInCity = live_in_city)
# Display the first few rows of the dataframe
head(simulated_df)
```

```
# Perform logistic regression
model <- glm(AttendCollege ~ FamilyIncome + LiveInCity, family = binomial(link = "logit"), data = simulated_df)
# Display the summary of the logistic regression model
summary(model)
```

This is the output.

```
Call:
glm(formula = AttendCollege ~ FamilyIncome + LiveInCity, family = binomial(link = "logit"),
data = simulated_df)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.397e-01 1.285e+00 0.264 0.792
FamilyIncome 1.421e-05 2.506e-05 0.567 0.571
LiveInCity -5.751e-01 1.058e+00 -0.544 0.587
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 25.898 on 19 degrees of freedom
Residual deviance: 25.367 on 17 degrees of freedom
AIC: 31.367
Number of Fisher Scoring iterations: 4
```

Can I interpret the relationship between the family income and whether to attend college in this way: each additional dollar of family income increases the odds of attending college by approximately (1.421e-05) *100 = 0.001421%, all else being equal. For example, if family income increases by 1000 dollars, the likelihood of attending college increases by around 0.001421% * 1000 = 1.421 %. Or do I need to calculate the exp(0.001421)? Appreciate your help.