RClsase02

{r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE)

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 estaadísticas

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="yellow")

altura<-c(2.25,2.00,1.80,1.70,1.60,1.50,1.25)
tiempo<-c(0.729,0.690,0.623,0.607,0.586,0.553,0.503)
h<-seq(1.0,2.50,0.1)
t<-sqrt(h*2/9.8)

t2=tiempo*tiempo

plot(t2,altura,xlim=c(0.4,0.90),ylim=c(0,3.0),main="Altura(cm) vs Tiempo(s)",xlab = "t(seg)",ylab="altura(cm)")
lines(t,h,col="black")
abline(-0.8785,4.2723,col="red" )
abline(v=0.7,col="yellow")
abline(h=2.0,col="blue")
abline(v=0.5,col="blue")

modelo<-lm(altura~tiempo)
summary(modelo)

## 
## Call:
## lm(formula = altura ~ tiempo)
## 
## Residuals:
##         1         2         3         4         5         6         7 
##  0.030647 -0.054349  0.029120 -0.003186 -0.014338  0.025281 -0.013175 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.8650     0.1106  -7.823 0.000547 ***
## tiempo        4.2309     0.1792  23.616 2.54e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03397 on 5 degrees of freedom
## Multiple R-squared:  0.9911, Adjusted R-squared:  0.9893 
## F-statistic: 557.7 on 1 and 5 DF,  p-value: 2.535e-06

Linealizado altura vs \(t^2\)

altura<-c(2.25,2.00,1.80,1.70,1.60,1.50,1.25)
tiempo<-c(0.729,0.690,0.623,0.607,0.586,0.553,0.503)
h<-seq(1.0,2.50,0.1)
t<-sqrt(h*2/9.8)

t2=tiempo*tiempo

plot(t2,altura,main="Altura(cm) vs Tiempo(s)")
abline(0.4698,3.3319)

modelo<-lm(altura~t2)
summary(modelo)

## 
## Call:
## lm(formula = altura ~ t2)
## 
## Residuals:
##          1          2          3          4          5          6          7 
##  0.0088906 -0.0526873  0.0468317  0.0138371 -0.0008638  0.0271105 -0.0431189 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.43169    0.06582   6.559  0.00124 ** 
## t2           3.40475    0.16828  20.233 5.45e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03958 on 5 degrees of freedom
## Multiple R-squared:  0.9879, Adjusted R-squared:  0.9855 
## F-statistic: 409.4 on 1 and 5 DF,  p-value: 5.454e-06

\(\sigma\)

\(\alpha^{3x}\)

\(\int{\frac{3a}{1-x}}\)

\(\sqrt{9x^2}\)