datos=c(6,3,7,4,5,3)
A=matrix(data=datos,nrow=3,ncol=2,byrow=FALSE)
print(A*3)
## [,1] [,2]
## [1,] 18 12
## [2,] 9 15
## [3,] 21 9
matA<-matrix(data = c("a", "b", "c", "d", "e", "f"), nrow = 3, ncol = 2,byrow=TRUE)
rownames(matA)<-c("Fila1","Fila2","Fila3")
colnames(matA)<-c("Col1","Col2")
print(matA)
## Col1 Col2
## Fila1 "a" "b"
## Fila2 "c" "d"
## Fila3 "e" "f"
class(matA)
## [1] "matrix" "array"
print(is.matrix(matA))
## [1] TRUE
Fórmulas estadísticas
x<-c(4,2,7,8,4,6,5,8,3)
media<-mean(x)
desvSTD<-sd(x)
varianza<-var(x)
print(media)
## [1] 5.222222
print(desvSTD)
## [1] 2.166667
print(varianza)
## [1] 4.694444
x<-c(0,1,2,3,4,5)
y<-c(0.5,1.4,1.98,3.1,3.8,5.4)
formula1<-formula(y~x)
modelo<-lm(formula1)
summary(modelo)
##
## Call:
## lm(formula = formula1)
##
## Residuals:
## 1 2 3 4 5 6
## 0.14762 0.10990 -0.24781 -0.06552 -0.30324 0.35905
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.35238 0.20485 1.72 0.160511
## x 0.93771 0.06766 13.86 0.000157 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.283 on 4 degrees of freedom
## Multiple R-squared: 0.9796, Adjusted R-squared: 0.9745
## F-statistic: 192.1 on 1 and 4 DF, p-value: 0.0001571
plot(x,y)
abline(0.35238,0.93771,col="blue")
altura<-c(2.25,2.00,1.80,1.70,1.60,1.50,1.25)
tiempo<-c(0.729,0.690,0.623,0.607,0.567,0.553,0.503)
h<-seq(1.0,2.50,0.1)
t<-sqrt(h*2/9.8)
t2=tiempo*tiempo
plot(t2,altura,xlim=c(0.5,0.75),ylim=c(1.0,2.5),main="Altura(cm) vs Tiempo(s)",xlab="t(seg)",ylab="altura(cm)")
abline(-0.8010 ,4.1449,col="orange")
abline(v=0.7,col="blue")
abline(h=2.0,col="green")
abline(v=0.5,col="green")
modelo<-lm(altura~tiempo)
summary(modelo)
##
## Call:
## lm(formula = altura ~ tiempo)
##
## Residuals:
## 1 2 3 4 5 6 7
## 0.02937 -0.05898 0.01873 -0.01495 0.05084 0.00887 -0.03389
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.8010 0.1330 -6.023 0.00181 **
## tiempo 4.1449 0.2164 19.157 7.15e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04178 on 5 degrees of freedom
## Multiple R-squared: 0.9866, Adjusted R-squared: 0.9839
## F-statistic: 367 on 1 and 5 DF, p-value: 7.146e-06
Linealizando altura vs \(t^2\)
altura<-c(2.25,2.00,1.80,1.70,1.60,1.50,1.25)
tiempo<-c(0.729,0.690,0.623,0.607,0.567,0.553,0.503)
h<-seq(1.0,2.50,0.1)
t<-sqrt(h*2/9.8)
t2=tiempo*tiempo
plot(t2,altura,main="Altura(m) vs T2(s2)")
abline(0.4698,3.3319)
modelo<-lm(altura~t2)
summary(modelo)
##
## Call:
## lm(formula = altura ~ t2)
##
## Residuals:
## 1 2 3 4 5 6 7
## 0.009426 -0.056182 0.036930 0.002503 0.058970 0.011214 -0.062860
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.4698 0.0800 5.873 0.00203 **
## t2 3.3319 0.2059 16.179 1.64e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04934 on 5 degrees of freedom
## Multiple R-squared: 0.9813, Adjusted R-squared: 0.9775
## F-statistic: 261.8 on 1 and 5 DF, p-value: 1.644e-05
\(\sigma\)
\(\alpha^{3x}\)
\(\int{\frac{3a}{1-x}}\)
\(\sqrt{9x^2}\)