# Variables Binarias en Regresiones Semi-logaritmicas (p. 51-52).
# ln(Y) = Bo + B1X1 + B2X2 + ... + BkXk + u
# En este caso, si "X1" es una variable continua, b1 se interpreta como el cambio porcentual en "Y" debido a un cambio de una unidad en "X".
# En caso que "X1" es una variable dummy entonces, si "X1 = 1, "Y" aumenta en 100(e^b1 - 1) porciento.
# Como ejemplo usemos el archivo "mtcars" y calcular la regresion:
# ln(mpg) = b0 + b1(wt) + b2(hp) + b3 (am)
# Creamos una nueva variable para el ln(mpg)
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
mtcars$logmpg = log(mtcars$mpg)
# Nueva base de datos con variable mtcars$logmpg
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
## logmpg
## Mazda RX4 3.044522
## Mazda RX4 Wag 3.044522
## Datsun 710 3.126761
## Hornet 4 Drive 3.063391
## Hornet Sportabout 2.928524
## Valiant 2.895912
## Duster 360 2.660260
## Merc 240D 3.194583
## Merc 230 3.126761
## Merc 280 2.954910
## Merc 280C 2.879198
## Merc 450SE 2.797281
## Merc 450SL 2.850707
## Merc 450SLC 2.721295
## Cadillac Fleetwood 2.341806
## Lincoln Continental 2.341806
## Chrysler Imperial 2.687847
## Fiat 128 3.478158
## Honda Civic 3.414443
## Toyota Corolla 3.523415
## Toyota Corona 3.068053
## Dodge Challenger 2.740840
## AMC Javelin 2.721295
## Camaro Z28 2.587764
## Pontiac Firebird 2.954910
## Fiat X1-9 3.306887
## Porsche 914-2 3.258097
## Lotus Europa 3.414443
## Ford Pantera L 2.760010
## Ferrari Dino 2.980619
## Maserati Bora 2.708050
## Volvo 142E 3.063391
# Calculamos la regresion
regsemilog <- lm(mtcars$logmpg ~ mtcars$wt + mtcars$hp + mtcars$am, data=mtcars)
summary(regsemilog)
##
## Call:
## lm(formula = mtcars$logmpg ~ mtcars$wt + mtcars$hp + mtcars$am,
## data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.17137 -0.06955 -0.03865 0.07218 0.26567
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.7491397 0.1165798 32.159 < 2e-16 ***
## mtcars$wt -0.1757558 0.0399224 -4.402 0.000142 ***
## mtcars$hp -0.0016850 0.0004237 -3.976 0.000448 ***
## mtcars$am 0.0516749 0.0607202 0.851 0.401970
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1119 on 28 degrees of freedom
## Multiple R-squared: 0.8724, Adjusted R-squared: 0.8587
## F-statistic: 63.79 on 3 and 28 DF, p-value: 1.24e-12
# Interpretacion de coeficientes
# Si el wt aumenta en una unidad, mpg se reduce en 17.6%
# Si hp aumenta en una unidad, mpg se reduce en 0.17%.
# Si el carro es mecanico, mpg aumenta en 5.3% ([e^0.0517 -1]100).
#### Ejercicio en clase ####
# Usando los mismos datos, y la misma regresion semi-log, partan usando todas las variables hasta llegar a una regresion con la mas alta R^2 ajustada. Publiquen sus resultados en una pagina de internet usando Rpubs [https://rpubs.com].