#help(mtcars)
summary(mtcars)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000head(mtcars)## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1Logistic am ~ qsec
am_qsec_glm <- glm(am ~ qsec, data = mtcars, family = binomial)
summary(am_qsec_glm)##
## Call:
## glm(formula = am ~ qsec, family = binomial, data = mtcars)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.7389 4.0452 1.171 0.241
## qsec -0.2882 0.2279 -1.265 0.206
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 43.230 on 31 degrees of freedom
## Residual deviance: 41.465 on 30 degrees of freedom
## AIC: 45.465
##
## Number of Fisher Scoring iterations: 4explanation: I created a logistic regression to predict the transmission type(am), using “1/4 mile time”(qsec) as the predictor.
The coefficients for qsec is -0.2882. It means that as qsec increase (car takes longer to finish 1/4 mile), the probability of being manual decrease. In another word, the longer a car takes to finish 1/4 mile, the higher probability being a automatic
p-value = 0.206, which is grearer than 0.05 significant level, the predictor is not a statistically significant.
scatter plot
# calculate odds
prob <- predict(am_qsec_glm, type = "response")
odds <- prob / ( 1 - prob)
plot(mtcars$qsec, odds, col = "darkorange",
xlab = "1/4 mile time",
ylab = "Calculated odds of manual transmission",
main = "1/4 mile time vs odds")
explanation: the scatter plot of odds vs 1/4 mile shows a clear negative downward trend: cars with faster acceleration (lower qsec) have higher odds of being manual.
regression line
plot(mtcars$qsec, odds, col = "darkblue",
xlab = "1/4 mile time",
ylab = "Calculated odds of manual transmission",
main = "1/4 mile time vs odds")
abline(am_qsec_glm, col = "red", lwd = 2)