Introduction

This presentation aims to study a data set from R : mtcars. We will model the miles per gallon mpg according to the weight wt.

It’s cover :

only short data exploration (due to the limitation of 5 slides) ;
simple linear regression : building model and rending plot

This work could be completed (of more slides are allowed) by :

fitting model responding to the question that try to explain the relationship between miles per gallon consmption and weight for each car.
discussions

Data exploratory

knitr::opts_chunk$set(echo = FALSE)
library(ggplot2)
library(dplyr)
library(plotly)
library(radiant.data)

data(mtcars)
str(object = mtcars)

## 'data.frame':    32 obs. of  11 variables:
##  $ mpg : num  21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
##  $ cyl : num  6 6 4 6 8 6 8 4 4 6 ...
##  $ disp: num  160 160 108 258 360 ...
##  $ hp  : num  110 110 93 110 175 105 245 62 95 123 ...
##  $ drat: num  3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
##  $ wt  : num  2.62 2.88 2.32 3.21 3.44 ...
##  $ qsec: num  16.5 17 18.6 19.4 17 ...
##  $ vs  : num  0 0 1 1 0 1 0 1 1 1 ...
##  $ am  : num  1 1 1 0 0 0 0 0 0 0 ...
##  $ gear: num  4 4 4 3 3 3 3 4 4 4 ...
##  $ carb: num  4 4 1 1 2 1 4 2 2 4 ...

Modelisaation : Simple Linear Regression (SLM) - building model

Please scroll

library(tidymodels)
my_mtcars <- mtcars
my_mtcars[which(my_mtcars$am==0),"am"] <- "auto"
my_mtcars[which(my_mtcars$am==1),"am"] <- "manual"

my_fit <- my_mtcars %>% lm(formula = mpg~wt)
summary(my_fit)

## 
## Call:
## lm(formula = mpg ~ wt, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5432 -2.3647 -0.1252  1.4096  6.8727 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  37.2851     1.8776  19.858  < 2e-16 ***
## wt           -5.3445     0.5591  -9.559 1.29e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.046 on 30 degrees of freedom
## Multiple R-squared:  0.7528, Adjusted R-squared:  0.7446 
## F-statistic: 91.38 on 1 and 30 DF,  p-value: 1.294e-10

Comparaison between predictions and observaions

mpg_pred <- predict(object = my_fit,newdata=data.frame(wt=my_mtcars$wt))
# Buildong prediction data frame
predDF <- data.frame(wt=my_mtcars$wt,mpg=mpg_pred)
data.frame(wt=my_mtcars$wt,mpg_predicted=mpg_pred,mpg_observ=my_mtcars$mpg,residuals=my_fit$residuals)

##       wt mpg_predicted mpg_observ  residuals
## 1  2.620     23.282611       21.0 -2.2826106
## 2  2.875     21.919770       21.0 -0.9197704
## 3  2.320     24.885952       22.8 -2.0859521
## 4  3.215     20.102650       21.4  1.2973499
## 5  3.440     18.900144       18.7 -0.2001440
## 6  3.460     18.793255       18.1 -0.6932545
## 7  3.570     18.205363       14.3 -3.9053627
## 8  3.190     20.236262       24.4  4.1637381
## 9  3.150     20.450041       22.8  2.3499593
## 10 3.440     18.900144       19.2  0.2998560
## 11 3.440     18.900144       17.8 -1.1001440
## 12 4.070     15.533127       16.4  0.8668731
## 13 3.730     17.350247       17.3 -0.0502472
## 14 3.780     17.083024       15.2 -1.8830236
## 15 5.250      9.226650       10.4  1.1733496
## 16 5.424      8.296712       10.4  2.1032876
## 17 5.345      8.718926       14.7  5.9810744
## 18 2.200     25.527289       32.4  6.8727113
## 19 1.615     28.653805       30.4  1.7461954
## 20 1.835     27.478021       33.9  6.4219792
## 21 2.465     24.111004       21.5 -2.6110037
## 22 3.520     18.472586       15.5 -2.9725862
## 23 3.435     18.926866       15.2 -3.7268663
## 24 3.840     16.762355       13.3 -3.4623553
## 25 3.845     16.735633       19.2  2.4643670
## 26 1.935     26.943574       27.3  0.3564263
## 27 2.140     25.847957       26.0  0.1520430
## 28 1.513     29.198941       30.4  1.2010593
## 29 3.170     20.343151       15.8 -4.5431513
## 30 2.770     22.480940       19.7 -2.7809399
## 31 3.570     18.205363       15.0 -3.2053627
## 32 2.780     22.427495       21.4 -1.0274952

Modelisaation : (SLM) - plot

my_l <- list(
  itle=list(text='<b> Legend : </b>'),
  orientation = 'v',
  y = 0.05,
  x = 0.05,
  font = list(
    family = "sans-serif",
    size = 18,
    color = "#000"),
  bgcolor = "#E2E2E2",
  bordercolor = "#FFFFFF",
  borderwidth = 4)

mpt <- my_mtcars %>% rownames_to_column('car') %>%
    plot_ly() %>%
    add_trace(type = "scatter",
              x = ~wt, 
              y = ~mpg,
              text = ~car,
              legendgroup = 'group1',
              symbol = ~paste0("Transmission type : ", am),
              symbols = c('circle','x'),
              mode = 'markers',
              marker = list(color = "grey", size = 25)) %>%
    add_trace(type = "scatter",
              x = ~wt, 
              y = ~mpg,
              text = ~car,
              legendgroup = 'group2',
              color = ~paste0("N° of cyl : ", cyl),
              mode = 'markers',
              marker = list(size = 19)) %>%
  add_trace(data = predDF, x = ~wt, y = ~mpg, name = 'Regression Fit', mode = 'lines', alpha = 1) %>%
 layout(legend = my_l)

mpt

Reproducible pitch