MTcars
Daniel Jeffry
3/1/2021
Description
This report describe characteristics affect the quality of cars based on variables. We can create data visualizations based on existing variables using ggplot2.
The dataset can be downloaded -> https://www.kaggle.com/lavanya321/mtcars
Report Outline :
1. Data Extraction
2. Exploratory Data Analysis
3. Data Processing
4. Modelling
5. Summary
1. Data Extraction
The Dataset is downlaoded from kaggle and saved in the data folder or we can the dataframe in Rstudio and we put in mtcars_df.
mtcars## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
## Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
## Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
## Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
## Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
## Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
## Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
## Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
## Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
## Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
## Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
## Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
## Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
## Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
## Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
## Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
## Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
## AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
## Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
## Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
## Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
## Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
## Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
## Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
## Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
## Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
## Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2mtcars_df <- mtcarsTo see the number of rows and column, we used dim fuction. The dataset has 32 rows and 33 columns
dim(mtcars_df)## [1] 32 112. Exploratory Data Analysis
To find out the column names and types, we used **str() function
str(mtcars_df)## '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 ...copy data type from numeric to factor
mtcars_df$am <- factor(mtcars_df$am, levels = c(0,1),
labels = c("Automatic", "Manual"))
mtcars_df$vs <- factor(mtcars_df$vs, levels = c(0,1),
labels = c("V-Engine", "Straight Engine"))
mtcars_df$cyl <- factor(mtcars_df$cyl)2.1 Multivariate Data Analysis
There are three types of measurements: horse power (hp), miles per galoon (mpg), cylinder (cyl). Each measurement has 32 variables so the total is 96 variables. We want to compute and visualize correlation coefficient of each measurement.
Visualize cars Automobile data by Engine type.
library(ggplot2)
ggplot(data = mtcars_df, aes(x=hp, y=mpg,
shape = cyl, color=cyl)) +
geom_point(size = 3) +
facet_grid(am~vs) +
labs (title = "Automobile data by Engine type",
x = "horsepower", y = "Miles Per Gallon")
3.1 Training and Test Division
Use set.seed() for reproducible result. Ratio train:test = 80:20.
m = nrow(mtcars_df)
set.seed(3101)
train_idx <- sample(m, 0.8 * m)
train_df <- mtcars_df[train_idx, ]
test_df <- mtcars_df[-train_idx, ]
sort(train_idx)## [1] 1 3 4 6 7 8 9 11 12 13 14 15 16 17 19 20 21 22 23 26 27 28 29 30 314. Modelling
We compute to model using simple linear, polynomial linear regression, multiple linear, and MLR with interaction.
4.1 Simple Linear
fit.linreg <- lm(formula = hp ~ mpg, data = train_df)
summary(fit.linreg)##
## Call:
## lm(formula = hp ~ mpg, data = train_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.63 -29.06 -16.25 25.52 143.95
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 323.737 32.755 9.884 9.53e-10 ***
## mpg -8.846 1.574 -5.621 1.01e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 47.77 on 23 degrees of freedom
## Multiple R-squared: 0.5787, Adjusted R-squared: 0.5604
## F-statistic: 31.59 on 1 and 23 DF, p-value: 1.014e-05fit.linreg <- lm(formula = mpg ~ hp, data = train_df)4.2 Polynomial Linear Regression
fit.polyreg <- lm(formula = hp ~ mpg + I(mpg^1), data = train_df)
summary(fit.polyreg)##
## Call:
## lm(formula = hp ~ mpg + I(mpg^1), data = train_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.63 -29.06 -16.25 25.52 143.95
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 323.737 32.755 9.884 9.53e-10 ***
## mpg -8.846 1.574 -5.621 1.01e-05 ***
## I(mpg^1) NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 47.77 on 23 degrees of freedom
## Multiple R-squared: 0.5787, Adjusted R-squared: 0.5604
## F-statistic: 31.59 on 1 and 23 DF, p-value: 1.014e-054.3 Multiple Linear
fit.multireg <- lm(formula = hp ~ mpg + disp + hp +wt,
data = train_df)## Warning in model.matrix.default(mt, mf, contrasts): the response appeared on the
## right-hand side and was dropped## Warning in model.matrix.default(mt, mf, contrasts): problem with term 3 in
## model.matrix: no columns are assignedsummary(fit.multireg)##
## Call:
## lm(formula = hp ~ mpg + disp + hp + wt, data = train_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -57.807 -20.653 -9.296 23.892 135.026
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 296.2875 115.6947 2.561 0.0182 *
## mpg -6.3025 3.3094 -1.904 0.0706 .
## disp 0.5166 0.1909 2.705 0.0133 *
## wt -44.0510 21.4164 -2.057 0.0523 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 42.83 on 21 degrees of freedom
## Multiple R-squared: 0.6909, Adjusted R-squared: 0.6467
## F-statistic: 15.64 on 3 and 21 DF, p-value: 1.421e-054.4 MLR with Interaction
fit.inmultireg <- lm(formula = mpg ~ cyl + disp + hp + wt, data = train_df)
summary(fit.inmultireg)##
## Call:
## lm(formula = mpg ~ cyl + disp + hp + wt, data = train_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.2619 -0.9078 -0.4087 1.2333 5.8860
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 34.099382 2.268082 15.034 5.29e-12 ***
## cyl6 -3.915288 1.606717 -2.437 0.0248 *
## cyl8 -4.842958 2.790837 -1.735 0.0989 .
## disp -0.001558 0.014443 -0.108 0.9152
## hp -0.012854 0.012793 -1.005 0.3276
## wt -2.800616 1.188623 -2.356 0.0294 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.39 on 19 degrees of freedom
## Multiple R-squared: 0.8822, Adjusted R-squared: 0.8512
## F-statistic: 28.46 on 5 and 19 DF, p-value: 3.354e-08