Problema 1

Mujer<-c(75,77,78,79,77,73,78,79,78,80)
Hombre<-c(74,72,77,76,76,73,75,73,74,75)
Sexo<-c(rep("Mujer",10), rep("Hombre",10))
Temp<-c(Mujer, Hombre)
datos<-data.frame(Sexo=Sexo, T=Temp)

resultado <- t.test(Mujer, Hombre,
                    alternative = "two.sided",
                    var.equal = FALSE)
print(resultado)
## 
##  Welch Two Sample t-test
## 
## data:  Mujer and Hombre
## t = 3.5254, df = 16.851, p-value = 0.002626
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.163304 4.636696
## sample estimates:
## mean of x mean of y 
##      77.4      74.5
datos
##      Sexo  T
## 1   Mujer 75
## 2   Mujer 77
## 3   Mujer 78
## 4   Mujer 79
## 5   Mujer 77
## 6   Mujer 73
## 7   Mujer 78
## 8   Mujer 79
## 9   Mujer 78
## 10  Mujer 80
## 11 Hombre 74
## 12 Hombre 72
## 13 Hombre 77
## 14 Hombre 76
## 15 Hombre 76
## 16 Hombre 73
## 17 Hombre 75
## 18 Hombre 73
## 19 Hombre 74
## 20 Hombre 75
datos$Sexo<-factor(datos$Sexo)
boxplot(T~Sexo,data=datos,col=c("orange","green"))

library("car")
## Cargando paquete requerido: carData
leveneTest(T~Sexo,data=datos,center=mean)
## Levene's Test for Homogeneity of Variance (center = mean)
##       Df F value Pr(>F)
## group  1  0.2085 0.6534
##       18

##Problema 2

actual<-c(1.88, 1.84, 1.83, 1.90, 2.19, 1.89, 2.27, 2.03, 1.96,
1.98, 2.00, 1.92, 1.83, 1.94, 1.94, 1.95, 1.93, 2.01)
nuevo<-c(1.88, 1.84, 1.83, 1.90, 2.19, 1.89, 2.27, 2.03, 1.96,
1.98, 2.00, 1.92, 1.83, 1.94, 1.94, 1.95, 1.93, 2.01)
resultado <- t.test(actual, nuevo,
                    alternative = "two.sided",paired=TRUE,
                    var.equal = FALSE)

print(resultado)
## 
##  Paired t-test
## 
## data:  actual and nuevo
## t = NaN, df = 17, p-value = NA
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  NaN NaN
## sample estimates:
## mean difference 
##               0
desgaste<-c(264, 260, 258, 241, 262, 255,208, 220, 216, 200, 213, 206,220, 263, 219, 225, 230, 228,217, 226, 215, 227, 220, 222)
tipoCuero<-c(rep("A",6),rep("B",6),rep("C",6),rep("D",6))
datos<-data.frame(tipoCuero=tipoCuero,desgaste=desgaste)
datos
##    tipoCuero desgaste
## 1          A      264
## 2          A      260
## 3          A      258
## 4          A      241
## 5          A      262
## 6          A      255
## 7          B      208
## 8          B      220
## 9          B      216
## 10         B      200
## 11         B      213
## 12         B      206
## 13         C      220
## 14         C      263
## 15         C      219
## 16         C      225
## 17         C      230
## 18         C      228
## 19         D      217
## 20         D      226
## 21         D      215
## 22         D      227
## 23         D      220
## 24         D      222
datos$tipoCuero<-factor(datos$tipoCuero)
modelo<-aov(desgaste~tipoCuero, data=datos)
summary(modelo)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## tipoCuero    3   7019  2339.8   22.75 1.18e-06 ***
## Residuals   20   2056   102.8                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
boxplot(desgaste~tipoCuero, data=datos, col=c("green","red","purple", "pink"))

plot(modelo)

shapiro.test(modelo$residuals)
## 
##  Shapiro-Wilk normality test
## 
## data:  modelo$residuals
## W = 0.88326, p-value = 0.00967
hist(modelo$residuals, breaks=5)

TukeyHSD(modelo)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = desgaste ~ tipoCuero, data = datos)
## 
## $tipoCuero
##           diff        lwr        upr     p adj
## B-A -46.166667 -62.552998 -29.780336 0.0000008
## C-A -25.833333 -42.219664  -9.447002 0.0014117
## D-A -35.500000 -51.886331 -19.113669 0.0000349
## C-B  20.333333   3.947002  36.719664 0.0118160
## D-B  10.666667  -5.719664  27.052998 0.2926431
## D-C  -9.666667 -26.052998   6.719664 0.3742863

##Regresión Lineal

x1<-seq(0, 10,length=10)
y<-0.8+2.3*x1
y<-y+rnorm(10, 0, 1.5)
plot(x1,y)

modelo<-lm(y~x1)
summary(modelo)
## 
## Call:
## lm(formula = y ~ x1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.57518 -0.95974 -0.06919  0.98433  2.57276 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.7479     1.0360   0.722    0.491    
## x1            2.3653     0.1747  13.543 8.49e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.763 on 8 degrees of freedom
## Multiple R-squared:  0.9582, Adjusted R-squared:  0.953 
## F-statistic: 183.4 on 1 and 8 DF,  p-value: 8.488e-07
plot(modelo)

yajustado<-modelo$fitted.values
plot(x1,y)
lines(x1, yajustado, col="purple", lwd=2)