YouTube “Multiple Regression” videos

Route Delivery Schedule is as followed:

rds <- data.frame(miles=c(89,66,78,111,44,77,80,66,109,76),
                  numDelivers=c(4,1,3,6,1,3,3,2,5,3),
                  gasPrice=c(3.84,3.19,3.78,3.89,3.57,3.57,3.03,3.51,3.54,3.25),
                  travelTime=c(7,5.4,6.6,7.4,4.8,6.4,7,5.6,7.3,6.4))
rds  
##    miles numDelivers gasPrice travelTime
## 1     89           4     3.84        7.0
## 2     66           1     3.19        5.4
## 3     78           3     3.78        6.6
## 4    111           6     3.89        7.4
## 5     44           1     3.57        4.8
## 6     77           3     3.57        6.4
## 7     80           3     3.03        7.0
## 8     66           2     3.51        5.6
## 9    109           5     3.54        7.3
## 10    76           3     3.25        6.4

Calculate all linear models with 2 or 3 dependent variables

fit.m <- lm(travelTime ~ miles, data=rds)
fit.d <- lm(travelTime ~ numDelivers, data=rds)
fit.g <- lm(travelTime ~ gasPrice, data=rds)
fit.md <- lm(travelTime ~ miles + numDelivers, data=rds)
fit.mg <- lm(travelTime ~ miles + gasPrice, data=rds)
fit.dg <- lm(travelTime ~ numDelivers + gasPrice, data=rds)
fit.mdg <- lm(travelTime ~ miles + numDelivers + gasPrice, data=rds)

Show all linear models

data <- sapply(list(fit.m, fit.d, fit.g, fit.md, fit.mg, fit.dg, fit.mdg), function(f) {
  s <- summary(f)
  formula_name <- gsub("travelTime ~ ", "", deparse(f$call$formula))
  p_value <- pf(s$fstat[1], s$fstat[2], s$fstat[3], lower.tail=F)
  
  list(name=formula_name,
       fstat=s$fstatistic[1],      
       pvalue=p_value,
       sigma=s$sigma,
       adj.rsq=s$adj.r.squared)
})
t(data)
##      name                             fstat     pvalue       sigma    
## [1,] "miles"                          49.76813  0.0001066757 0.3423088
## [2,] "numDelivers"                    41.95894  0.0001926088 0.3680914
## [3,] "gasPrice"                       0.6151381 0.4554534    0.8864028
## [4,] "miles + numDelivers"            23.71607  0.0007626921 0.3526424
## [5,] "miles + gasPrice"               22.63189  0.0008793061 0.3598834
## [6,] "numDelivers + gasPrice"         27.63499  0.0004762859 0.329703 
## [7,] "miles + numDelivers + gasPrice" 16.99052  0.002452078  0.3446936
##      adj.rsq    
## [1,] 0.8442047  
## [2,] 0.8198521  
## [3,] -0.04467275
## [4,] 0.8346565  
## [5,] 0.8277966  
## [6,] 0.8554681  
## [7,] 0.8420264