Data 621 Blog 4
Bryan Persaud
11/13/2020
Beta Regression
For my fourth blog I will be going over beta regression. Beta regression is mostly used when you have a dependent variable that fall in the (0,1) interval.
Load Dataset
To demonstrate beta regression I will be using the betareg package. Within the package also has the gasoline yield dataset.
library(betareg)data("GasolineYield")
head(GasolineYield, 32)## yield gravity pressure temp10 temp batch
## 1 0.122 50.8 8.6 190 205 1
## 2 0.223 50.8 8.6 190 275 1
## 3 0.347 50.8 8.6 190 345 1
## 4 0.457 50.8 8.6 190 407 1
## 5 0.080 40.8 3.5 210 218 2
## 6 0.131 40.8 3.5 210 273 2
## 7 0.266 40.8 3.5 210 347 2
## 8 0.074 40.0 6.1 217 212 3
## 9 0.182 40.0 6.1 217 272 3
## 10 0.304 40.0 6.1 217 340 3
## 11 0.069 38.4 6.1 220 235 4
## 12 0.152 38.4 6.1 220 300 4
## 13 0.260 38.4 6.1 220 365 4
## 14 0.336 38.4 6.1 220 410 4
## 15 0.144 40.3 4.8 231 307 5
## 16 0.268 40.3 4.8 231 367 5
## 17 0.349 40.3 4.8 231 395 5
## 18 0.100 32.2 5.2 236 267 6
## 19 0.248 32.2 5.2 236 360 6
## 20 0.317 32.2 5.2 236 402 6
## 21 0.028 41.3 1.8 267 235 7
## 22 0.064 41.3 1.8 267 275 7
## 23 0.161 41.3 1.8 267 358 7
## 24 0.278 41.3 1.8 267 416 7
## 25 0.050 38.1 1.2 274 285 8
## 26 0.176 38.1 1.2 274 365 8
## 27 0.321 38.1 1.2 274 444 8
## 28 0.140 32.2 2.4 284 351 9
## 29 0.232 32.2 2.4 284 424 9
## 30 0.085 31.8 0.2 316 365 10
## 31 0.147 31.8 0.2 316 379 10
## 32 0.180 31.8 0.2 316 428 10Model
To create the model we will be using the betareg function. The variable we will be looking at is yield with two explanatory variables, temp and pressure.
model <- betareg(yield ~ temp + pressure, data = GasolineYield)
summary(model)##
## Call:
## betareg(formula = yield ~ temp + pressure, data = GasolineYield)
##
## Standardized weighted residuals 2:
## Min 1Q Median 3Q Max
## -1.7109 -0.8289 -0.1883 0.9519 2.3047
##
## Coefficients (mean model with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.4993819 0.2717802 -20.23 <2e-16 ***
## temp 0.0097150 0.0006717 14.46 <2e-16 ***
## pressure 0.1745610 0.0160964 10.85 <2e-16 ***
##
## Phi coefficients (precision model with identity link):
## Estimate Std. Error z value Pr(>|z|)
## (phi) 131.06 32.72 4.005 6.19e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 65.43 on 4 Df
## Pseudo R-squared: 0.8921
## Number of iterations: 28 (BFGS) + 5 (Fisher scoring)Here we see the information of the model created with the variable yield with temp and pressure. We see that there is a precision model in the data and a pseudo R-squared of 0.8921.
Let’s plot the model
plot(model)
When you plot the model you get different graphs, including a graph on Cook’s distance and graphs on the residuals and leverage and predicted values.