Linear Regression and log-log Transformation, R

Linear Regression and log-log Transformation

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#R version 3.3.2 
# Let's see the variables

head(cars) 
#Let's see descriptive statistics 
summary(cars)
#Let's see standard deviation as well
print(apply(cars,2,sd))
#do te same thing for log transformation of variables
lncars <- log(cars)
summary(lncars)
print(apply(lncars,2,sd))
#plot variables 
scatter.smooth(x=cars$speed, y=cars$dist, main="Dist ~ Speed")

#run a regressio using original data 
original <- lm(dist ~ speed, data=cars)
summary(original)
#get predicted y 
cars$predicted <- predict(original)
#Plot actual vs predicted

library(ggplot2)
ggplot(cars, aes(x = speed, y = dist)) +
geom_smooth(method = "lm", se = FALSE, color = "lightgrey") +  # Plot regression slope
  geom_segment(aes(xend = speed, yend = predicted), alpha = .2) +  # alpha to fade lines
  geom_point() +
  geom_point(aes(y = predicted), shape = 1) +
  theme_bw() 
#run a regressio using log transformation of  data 
scatter.smooth(x=lncars$speed, y=lncars$dist, main="lnDist ~ lnSpeed")
loglog <- lm(dist ~ speed, data=lncars)
summary(loglog)
#get predicted y 
lncars$predicted <- predict(loglog)

#Plot actual vs predicted 
ggplot(lncars, aes(x = speed, y = dist)) +
  geom_smooth(method = "lm", se = FALSE, color = "lightgrey") +  # Plot regression slope
  geom_segment(aes(xend = speed, yend = predicted), alpha = .2) +  # alpha to fade lines
  geom_point() +
  geom_point(aes(y = predicted), shape = 1) +
  theme_bw()

[ + ] Show input
Absolute running time: 1.61 sec, cpu time: 1.38 sec, memory peak: 49 Mb, absolute service time: 1,63 sec

speed dist 1 4 2 2 4 10 3 7 4 4 7 22 5 8 16 6 9 10 speed dist Min. : 4.0 Min. : 2.00 1st Qu.:12.0 1st Qu.: 26.00 Median :15.0 Median : 36.00 Mean :15.4 Mean : 42.98 3rd Qu.:19.0 3rd Qu.: 56.00 Max. :25.0 Max. :120.00 speed dist 5.287644 25.769377 speed dist Min. :1.386 Min. :0.6931 1st Qu.:2.485 1st Qu.:3.2581 Median :2.708 Median :3.5835 Mean :2.662 Mean :3.5359 3rd Qu.:2.944 3rd Qu.:4.0254 Max. :3.219 Max. :4.7875 speed dist 0.4149081 0.7764719 Call: lm(formula = dist ~ speed, data = cars) Residuals: Min 1Q Median 3Q Max -29.069 -9.525 -2.272 9.215 43.201 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -17.5791 6.7584 -2.601 0.0123 * speed 3.9324 0.4155 9.464 1.49e-12 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 15.38 on 48 degrees of freedom Multiple R-squared: 0.6511, Adjusted R-squared: 0.6438 F-statistic: 89.57 on 1 and 48 DF, p-value: 1.49e-12 Call: lm(formula = dist ~ speed, data = lncars) Residuals: Min 1Q Median 3Q Max -1.00215 -0.24578 -0.02898 0.20717 0.88289 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.7297 0.3758 -1.941 0.0581 . speed 1.6024 0.1395 11.484 2.26e-15 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.4053 on 48 degrees of freedom Multiple R-squared: 0.7331, Adjusted R-squared: 0.7276 F-statistic: 131.9 on 1 and 48 DF, p-value: 2.259e-15