Just a short of how fitting and output of linear models looks like in R, Python and Stata. Will be expanded to more complex models (GLM, GAM) in hte future.
For the illustration purposes dataset mtcars will be used. It comes from the 1981 paper in Biometriks where it was one used to contrast manual vs automatic variable selection in multiple linear regression.
Henderson and Velleman (1981), Building multiple regression models interactively. Biometrics, 37, 391–411.
Here is how it looks in R:
> 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 2
> fit <- lm(mpg ~ hp + disp + gear + as.factor(cyl), data = mtcars)
> summary(fit)
Call:
lm(formula = mpg ~ hp + disp + gear + as.factor(cyl), data = mtcars)
Residuals:
Min 1Q Median 3Q Max
-3.6204 -2.0939 -0.3684 1.6364 6.0358
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 23.91102 4.38958 5.447 1.04e-05 ***
hp -0.04484 0.01902 -2.357 0.0262 *
disp -0.01745 0.01111 -1.571 0.1283
gear 2.02711 1.13371 1.788 0.0854 .
as.factor(cyl)6 -3.30466 1.67687 -1.971 0.0595 .
as.factor(cyl)8 0.07182 3.41572 0.021 0.9834
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.777 on 26 degrees of freedom
Multiple R-squared: 0.822, Adjusted R-squared: 0.7877
F-statistic: 24.01 on 5 and 26 DF, p-value: 5.566e-09
In Python mtcars dataset has to imported from ggplot library:
In [1]: from ggplot import mtcars
In [2]: from sklearn import linear_model
In [3]: reg = linear_model.LinearRegression()
TODO: fit the model and get the summary
In Stata the auto.dta dataset is rather different (1978 models, rather than 1974):
. sysuse auto.dta
(1978 Automobile Data)
TODO: import 1974 models and fit the regression model