Ejercicios R 61-76
Nair González
16/6/2019
##Ejercicio 61
x<- 1:10
time<-x[-9]
speed<- c(1210, 1866,2301, 2564, 2724, 2881, 2879, 2915, 3010)
plot(x=time, y=speed)
model<- nls(speed~b*(1-exp(1)^(c*time)),start = list(b=3000,c=-1))
summary(model)##
## Formula: speed ~ b * (1 - exp(1)^(c * time))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## b 2996.28869 19.14635 156.49 1.15e-13 ***
## c -0.49291 0.01134 -43.46 8.91e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 30.9 on 7 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 7.559e-07curve(2996.28869*(1-exp(1)^(-0.49291*x)),add=T)
##Ejercicio 62
year<- 1990:1994
temperature<- c(18, 19,21,17,20)
df <-data.frame(year,temperature)
##Stem plot
library(ggplot2)## Registered S3 methods overwritten by 'ggplot2':
## method from
## [.quosures rlang
## c.quosures rlang
## print.quosures rlang
p <- ggplot(data=df) +
geom_hline(aes(yintercept=0)) +
geom_segment(aes(year,temperature,xend=year,yend=temperature-temperature)) +
geom_point(aes(year,temperature),size=3)
p
##Barplot
barplot(temperature~year)
##Stairplot
plot(temperature~year,type = "s")
##Ejercicio 63
v<-function(r){(4/3)*pi*r^3}
a<-function(r){4*pi*r^2}
par(mfrow=c(1,2))
plot(v,xlim = c(0.1,100))
plot(a,xlim = c(0.1,100))
par(mfrow=c(1,2))
plot(v,xlim = c(1,10^4))
plot(a,xlim = c(1,10^4))
##Ejercicio 64
#a
x<-seq(25,45,5)
y<-c(5,260,480,745,1100)
plot(x,y)
model<-lm(y~x)
abline(model)
#b
x<-c(2.5,3,3.5,4,4.5,5,5.5,6:10)
y<-c(1500,1220,1050,915,810,745,690,620,520,480,410,390)
plot(x,y)
model<-lm(log10(y)~x)
summary(model)##
## Call:
## lm(formula = log10(y) ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.038203 -0.033347 -0.008348 0.014708 0.082259
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.282514 0.032613 100.65 2.30e-16 ***
## x -0.075472 0.005332 -14.16 6.09e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04254 on 10 degrees of freedom
## Multiple R-squared: 0.9525, Adjusted R-squared: 0.9477
## F-statistic: 200.4 on 1 and 10 DF, p-value: 6.093e-08curve(1916.523*10^(-0.075472*x),add=T)
#c
x<-seq(550,750,50)
y<-c(41.2,18.62,8.62,3.92,1.86)
plot(x,y)
model<-lm(log10(y)~x)
summary(model)##
## Call:
## lm(formula = log10(y) ~ x)
##
## Residuals:
## 1 2 3 4 5
## 0.004768 -0.003403 -0.001129 -0.006604 0.006369
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.314e+00 2.613e-02 203.4 2.62e-07 ***
## x -6.735e-03 3.996e-05 -168.5 4.61e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.006319 on 3 degrees of freedom
## Multiple R-squared: 0.9999, Adjusted R-squared: 0.9999
## F-statistic: 2.84e+04 on 1 and 3 DF, p-value: 4.606e-07curve(206063*10^(-6.735e-03*x),add=T)
##Ejercicio 65
year<-2002:2007
population<-c(10,10.8,11.7,12.7,13.8,14.9)
plot(year,population)
model<-lm(population~year)
model$coefficients## (Intercept) year
## -1963.5476190 0.9857143curve(-1963.5476190+ 0.9857143*x,add=T)
#En que año se duplicara
año=20+1963.5476190/0.9857143
points(2012.005,20)
##Ejercicio 67
time<-0:6
temperature<-c(300,150,75,35,12,5,2)
plot(time,temperature)
model<-lm(log10(temperature)~time)
summary(model)##
## Call:
## lm(formula = log10(temperature) ~ time)
##
## Residuals:
## 1 2 3 4 5 6 7
## -0.074353 -0.008297 0.057758 0.093850 -0.003951 -0.017076 -0.047931
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.55147 0.04347 58.70 2.71e-08 ***
## time -0.36709 0.01206 -30.45 7.17e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06379 on 5 degrees of freedom
## Multiple R-squared: 0.9946, Adjusted R-squared: 0.9936
## F-statistic: 927.2 on 1 and 5 DF, p-value: 7.167e-07curve(356.0164*10^(-0.36709*x),add=T)
##Ejercicio 68
a<-0:9
t<-c(130,115,110,90,89,89,95,100, 110,125)
plot(a,t,type="l")
model <- lm(t ~ poly(a,4))
summary(model)##
## Call:
## lm(formula = t ~ poly(a, 4))
##
## Residuals:
## 1 2 3 4 5 6 7 8
## 0.04545 -1.76573 5.52739 -4.93298 -0.40676 0.44406 2.55536 -0.53904
## 9 10
## -1.70746 0.77972
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 105.3000 1.1723 89.825 3.24e-09 ***
## poly(a, 4)1 -6.3305 3.7071 -1.708 0.148
## poly(a, 4)2 43.7805 3.7071 11.810 7.66e-05 ***
## poly(a, 4)3 0.5938 3.7071 0.160 0.879
## poly(a, 4)4 -3.1975 3.7071 -0.863 0.428
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.707 on 5 degrees of freedom
## Multiple R-squared: 0.9663, Adjusted R-squared: 0.9393
## F-statistic: 35.79 on 4 and 5 DF, p-value: 0.0007146points(model$fitted.values,type="l",col=2)
##R cuadrado 0.9663
##Ejercicio 70
temperature<-seq(10,90,10)
s<-c(35,35.6,36.25,36.9,37.5,38.1,38.8,39.4,40)
plot(temperature,s)
model<-lm(s~temperature)
summary(model)##
## Call:
## lm(formula = s ~ temperature)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.033889 -0.018889 0.001111 0.009444 0.037778
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.436e+01 1.749e-02 1965.2 < 2e-16 ***
## temperature 6.283e-02 3.107e-04 202.2 1.91e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02407 on 7 degrees of freedom
## Multiple R-squared: 0.9998, Adjusted R-squared: 0.9998
## F-statistic: 4.089e+04 on 1 and 7 DF, p-value: 1.91e-14curve(model$coefficients[1]+model$coefficients[2]*x,add=T)
#T=25 =35.93472
model$coefficients[1]+model$coefficients[2]*25## (Intercept)
## 35.93472
##Ejercicio 71
temperature<-seq(5,45,5)
s<-c(1.95,1.7,1.55,1.40,1.30,1.15,1.05,1,0.95)
plot(temperature,s)
model<-lm(s~temperature)
summary(model)##
## Call:
## lm(formula = s ~ temperature)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.06639 -0.04389 -0.03389 0.02861 0.12111
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.951389 0.053887 36.21 3.18e-09 ***
## temperature -0.024500 0.001915 -12.79 4.14e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07418 on 7 degrees of freedom
## Multiple R-squared: 0.959, Adjusted R-squared: 0.9531
## F-statistic: 163.6 on 1 and 7 DF, p-value: 4.135e-06abline(model)
#T8
1.951389-0.024500*8## [1] 1.755389#T50
1.951389-0.024500*50## [1] 0.726389
##Ejercicio 72
x<-1:10
y<-c(10,14,16,18,19,20,21,22,23,23)
plot(x,y)
model<-lm(y~log(x))
summary(model)##
## Call:
## lm(formula = y ~ log(x))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.23126 -0.16611 -0.00851 0.11077 0.44979
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.9123 0.1721 57.59 9.17e-12 ***
## log(x) 5.7518 0.1035 55.57 1.22e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2276 on 8 degrees of freedom
## Multiple R-squared: 0.9974, Adjusted R-squared: 0.9971
## F-statistic: 3088 on 1 and 8 DF, p-value: 1.22e-11curve(9.9123+ 5.7518*log(x),add=T)
##x=1.5
9.9123+ 5.7518*log(1.5)## [1] 12.24445#x=11
9.9123+ 5.7518*log(11)## [1] 23.70451
##Ejercicio 73
x <- seq(-10, 10, length= 30)
y <- x
f<-function(x,y){x^2-2*x*y+4*y^2}
z <- outer(x, y, f)
z[is.na(z)] <- 1
op <- par(bg = "white")
#superficie
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")
#Contorno
library(plotly)##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
##
## last_plot## The following object is masked from 'package:stats':
##
## filter## The following object is masked from 'package:graphics':
##
## layoutdata=data.frame(x,y,z)
p <- plot_ly(data = df, x=~x,y=~y, z=~z, type = "contour", colorscale='Jet')
p##Ejercicio 74
x <- seq(-10, 10, length= 30)
y <- x
f<-function(x,y){-x^2+2*x*y+3*y^2}
z <- outer(x, y, f)
z[is.na(z)] <- 1
op <- par(bg = "white")
#superficie
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "red")
#Contorno
library(plotly)
data=data.frame(x,y,z)
p <- plot_ly(data = df, x=~x,y=~y, z=~z, type = "contour", colorscale='Jet')
p
##Ejercicio 75
x <- seq(-10, 10, length= 30)
y <- x
f<-function(x,y){(x-y^2)*(x-3*y^2)}
z <- outer(x, y, f)
z[is.na(z)] <- 1
op <- par(bg = "white")
#superficie
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")
#Contorno
library(plotly)
data=data.frame(x,y,z)
p <- plot_ly(data = df, x=~x,y=~y, z=~z, type = "contour", colorscale='Jet')
p##Ejercicio 76
x <- seq(-1, 1, length= 30)
y <- x
f<-function(x,y){80*exp(1)^-((x-1)^(2))*exp(1)^-(3*(y-1)^2)}
z <- outer(x, y, f)
z[is.na(z)] <- 1
#superficie
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")
#Contorno
library(plotly)
data=data.frame(x,y,z)
p <- plot_ly(data = df, x=~x,y=~y, z=~z, type = "contour", colorscale='Jet')
p## Temperatura en la posicion x=0,y=0
80*exp(1)^-((0-1)^(2))*exp(1)^-(3*(0-1)^2)## [1] 1.465251