logist_walk2.txt



R version 2.11.1 (2010-05-31)

Copyright (C) 2010 The R Foundation for Statistical Computing

ISBN 3-900051-07-0



Fit logistic regression model: walk (0) vs. drive (1) as function of trip distance.

    Fabricated values, for illustration only.



> z1 <- runif(40, 0, 4)         # generate distances walked (miles)

> z2 <- runif(60, 1, 10)        # generate distances driven (miles)

> z12 <- c(z1, z2)              # combine distances into one explanatory variable

> w <- c(rep(0,40), rep(1,60))  # generate binary response variable (walk, drive)



> trip2 <- glm(w ~ z12, family=binomial)

> plot(z12, w)

> summary(trip2)



> # Fit logistic regression model: walk(0) vs. drive(1) as function of trip distance.

> #    Fabricated values, for illustration only.

> 

> z1 <- runif(40, 0, 4)         # generate distances walked (miles)

> z2 <- runif(60, 1, 10)        # generate distances driven (miles)

> z12 <- c(z1, z2)              # combine distances into one explanatory variable

> w <- c(rep(0,40), rep(1,60))  # generate binary response variable (walk, drive)

> 

> plot(z12, w, xlab="Trip distance", ylab="Travel mode")    # Plot data

> trip2 <- glm(w ~ z12, family=binomial)    # fit logistic regression model

> summary(trip2)



Call:

glm(formula = w ~ z12, family = binomial)



Deviance Residuals: 

    Min       1Q   Median       3Q      Max  

-1.4926  -0.7467   0.1190   0.5697   1.9521  



Coefficients:

            Estimate Std. Error z value Pr(>|z|)    

(Intercept)  -2.6775     0.6191  -4.325 1.53e-05 ***

z12           0.8662     0.1835   4.720 2.36e-06 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1



(Dispersion parameter for binomial family taken to be 1)



    Null deviance: 134.602  on 99  degrees of freedom

Residual deviance:  84.307  on 98  degrees of freedom

AIC: 88.307



Number of Fisher Scoring iterations: 6



> # AIC value not relevant if only one model

> 

> dist <- seq(from=0, to=10, length=200)

> w.pred <- exp(-2.8888 + 0.9861*dist) / (1 + exp(-2.8888 + 0.9861*dist))

> lines(dist, w.pred)



> # Calculate log-likelihood R^2:

> logR2 <- 1 - 73.075 / 134.602

> logR2

[1] 0.4571032

> 

> # Predict probability(drive) at distance = 6 miles

> p6 <- exp(-2.8888 + 0.9861*6) / (1 + exp(-2.8888 + 0.9861*6))

> p6

[1] 0.9538144

> # For distance = 6 miles, Probability(drive) = 0.95



# ********************************************************************



# Fit logistic regression model: walk(0) vs. drive(1) as function of trip distance.

#    Fabricated values, for illustration only.



z1 <- runif(40, 0, 4)         # generate distances walked (miles)

z2 <- runif(60, 1, 10)        # generate distances driven (miles)

z12 <- c(z1, z2)              # combine distances into one explanatory variable

w <- c(rep(0,40), rep(1,60))  # generate binary response variable (walk, drive)



plot(z12, w, xlab="Trip distance", ylab="Travel mode")    # Plot data



trip2 <- glm(w ~ z12, family=binomial)    # fit logistic regression model

summary(trip2)

# AIC value not relevant if only one model



dist <- seq(from=0, to=10, length=200)

w.pred <- exp(-2.8888 + 0.9861*dist) / (1 + exp(-2.8888 + 0.9861*dist))

lines(dist, w.pred)



# Calculate log-likelihood R^2:

logR2 <- 1 - 73.075 / 134.602

logR2



# Predict probability(drive) at distance = 6 miles

p6 <- exp(-2.8888 + 0.9861*6) / (1 + exp(-2.8888 + 0.9861*6))

p6