## Rows: 32 ## Columns: 13 ## $ mpg <dbl> 21.0, 21.0, 22.8, 21.4, 18.7, 18.1, 14.3, 24.4, 22.8, 19.2, 17.8… ## $ cyl <dbl> 6, 6, 4, 6, 8, 6, 8, 4, 4, 6, 6, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 8… ## $ disp <dbl> 160.0, 160.0, 108.0, 258.0, 360.0, 225.0, 360.0, 146.7, 140.8, 1… ## $ hp <dbl> 110, 110, 93, 110, 175, 105, 245, 62, 95, 123, 123, 180, 180, 18… ## $ drat <dbl> 3.90, 3.90, 3.85, 3.08, 3.15, 2.76, 3.21, 3.69, 3.92, 3.92, 3.92… ## $ wt <dbl> 2.620, 2.875, 2.320, 3.215, 3.440, 3.460, 3.570, 3.190, 3.150, 3… ## $ qsec <dbl> 16.46, 17.02, 18.61, 19.44, 17.02, 20.22, 15.84, 20.00, 22.90, 1… ## $ vs <dbl> 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0… ## $ am <dbl> 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0… ## $ gear <dbl> 4, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3… ## $ carb <dbl> 4, 4, 1, 1, 2, 1, 4, 2, 2, 4, 4, 3, 3, 3, 4, 4, 4, 1, 2, 1, 1, 2… ## $ car <chr> "Mazda RX4", "Mazda RX4 Wag", "Datsun 710", "Hornet 4 Drive", "H… ## $ wt_kg <dbl> 1.1884110, 1.3040770, 1.0523334, 1.4582983, 1.5603565, 1.5694283…
2026-06-06
Data Preparation
MPG vs Engine Displacement
## `geom_smooth()` using formula = 'y ~ x'
MPG vs Weight + Residuals
## `geom_smooth()` using formula = 'y ~ x'
3D Plot: Weight, Horsepower, MPG
Image via R
Least Squares Estimation
\[ S(\beta_0, \beta_1) = \sum_{i=1}^n \left( mpg_i - \beta_0 - \beta_1 \cdot disp_i \right)^2 \]
\[ \hat{\beta}_1 = \frac{\sum_{i=1}^n (disp_i - \bar{disp})(mpg_i - \bar{mpg})} {\sum_{i=1}^n (disp_i - \bar{disp})^2} \]
Example R Output
The First plot shows us that Fuel efficiency is in a reciprocal correlation to the engine size of the car. This is probably beacause The amount of fuel used at a given speed is directly proportional to the engine displacement, and so is reciprocally proportional to fuel efficiency.
The Second plot shows that with respect to weight, the gravitational downforce on the vehicle is directly proportional to the weight of the car.
In the 3d plot we see that small engine cars eg 4cly mazda with less about 1000kg weight have the best fuel efficiency.
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summary(cars)
## 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
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Example Plot
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