Laboratorios 7 y 8 - Estadística y Probabilidad SAMUEL GONZALEZ

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1 MI CURSO DE ESTADÍSTICA Y PROBABILIDAD - 2026

1.1 SEMANA 7. Mi página Web en Estadistica

1.2 Clase N° 28. AQUI COMIENZA EL LABORATORIO 7

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1.2.0.0.1 <-========== PASO 3. =========->

1.2.1 (i)Datos de muestra simulados

set.seed(2026)
n <- 121
DATOS2026 <- data.frame(
  SEXO = sample(c("MASCULINO", "FEMENINO"), n, replace = TRUE, prob = c(0.55, 0.45)),
  CURSO = sample(c("CURSO A", "CURSO B", "CURSO C"), n, replace = TRUE),
  ESTRATO = sample(c("ESTRATO 1", "ESTRATO 2", "ESTRATO 3", "ESTRATO 4", "ESTRATO 5"), n, replace = TRUE),
  EDAD = round(rnorm(n, mean = 20, sd = 2)),
  ESTATURA = round(rnorm(n, mean = 170, sd = 8)),
  PESO = round(rnorm(n, mean = 68, sd = 10))
)
head(DATOS2026)

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1.2.1.0.1 <-========== PASO 4. =========->

1.2.2 (2i)Usando la aplicación para hacer la tabla

table_sexo <- table(DATOS2026$SEXO)
table_sexo

 FEMENINO MASCULINO 
       50        71 

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1.2.2.0.1 <-========== PASO 5. =========->

1.2.3 (3i)Gráfico de torta para SEXO

pie(table_sexo, col = c("lightblue", "pink"),
    main = "Estudio de Pastel.\n Distribución por sexos.", labels = table_sexo)

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1.2.3.0.1 <-========== PASO 6. =========->

1.2.4 (4i)Construimos el diagrama de barras y el diagrama de Pastel para esta variable cualitativa

barp <- barplot(table_sexo, col = rainbow(2), border = "darkred",
                main = "Gráfico de Barras", sub = "UTB", xlab = "SEXO", ylab = "Conteo",
                ylim = c(0, max(table_sexo) + 15))
text(barp, table_sexo + 5, labels = table_sexo)

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1.2.4.0.1 <-========== PASO 7. =========->

1.2.4.1 (5i)Usando la aplicación para hacer la tabla porcentual redondeando al entero mas cercano

table_sexo2 <- round(table(DATOS2026$SEXO) / nrow(DATOS2026) * 100)
table_sexo2

 FEMENINO MASCULINO 
       41        59 

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1.2.4.1.1 <-========== PASO 8. =========->

1.2.5 (6i)Construimos el diagrama de barras % y de pastel para esta variable cualitativa

barp2 <- barplot(table_sexo2, col = rainbow(2), border = "darkred",
                 main = "Gráfico de Barras Porcentual", sub = "UTB", xlab = "SEXO", ylab = "Porcentaje",
                 ylim = c(0, max(table_sexo2) + 15))
text(barp2, table_sexo2 + 5, labels = paste0(table_sexo2, "%"))

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1.2.5.0.1 <-========== PASO 9. =========->

1.2.6 (7i)Las tablas de frecuencias y las representaciones gráficas son dos maneras equivalentes de presentar la información

pie(table_sexo2, col = c("lightblue", "pink"),
    main = "Estudio de Pastel.\n Distribución Porcentual por Sexo.", labels = paste0(table_sexo2, "%"))

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1.2.6.0.1 <-========== PASO 10. =========->

1.2.7 (8i)Usando la aplicación para hacer la tabla con dos variables SEXO y CURSO

table_3 <- table(DATOS2026$SEXO, DATOS2026$CURSO)
table_3

           
            CURSO A CURSO B CURSO C
  FEMENINO       13      23      14
  MASCULINO      29      24      18

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1.2.7.0.1 <-========== PASO 11. =========->

1.2.8 (9i)Usando la aplicación para hacer el gráfico con dos variables SEXO y CURSO

barp3 <- barplot(table_3,
                 main = "Gráfico de barras CURSO vs SEXO",
                 xlab = "CURSO", ylab = "Frecuencia",
                 col = c("pink", "blue"),
                 legend.text = rownames(table_3),
                 beside = TRUE,
                 ylim = c(0, max(table_3) + 10))
text(barp3, table_3 + 2, labels = table_3)

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1.2.8.0.1 <-========== PASO 12. =========->

1.2.9 (10i)Usando la aplicación para hacer la tabla con dos variables SEXO y CURSO pero usando las frecuencias relativas aproximadas

table_4 <- round(table(DATOS2026$SEXO, DATOS2026$CURSO) / nrow(DATOS2026) * 100)
table_4

           
            CURSO A CURSO B CURSO C
  FEMENINO       11      19      12
  MASCULINO      24      20      15

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1.2.9.0.1 <-========== PASO 13. =========->

1.2.10 (11i)Usando la aplicación para hacer el gráfico con dos variables SEXO y CURSO pero usando las frecuencias relativas aproximadas

barp4 <- barplot(table_4,
                 main = "Gráfico de barras CURSO vs SEXO en porcentajes",
                 xlab = "CURSO", ylab = "Porcentaje (%)",
                 col = c("pink", "blue"),
                 legend.text = rownames(table_4),
                 beside = TRUE,
                 ylim = c(0, max(table_4) + 10))
text(barp4, table_4 + 2, labels = paste0(table_4, "%"))

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1.2.10.0.1 <-========== PASO 14. =========->

1.2.11 (12i)Usando la aplicación para hacer la tabla con dos variables ESTRATO y CURSO

table_5 <- table(DATOS2026$ESTRATO, DATOS2026$CURSO)
table_5

           
            CURSO A CURSO B CURSO C
  ESTRATO 1       9       7      11
  ESTRATO 2      10      14      10
  ESTRATO 3       8       7       3
  ESTRATO 4       6      11       6
  ESTRATO 5       9       8       2

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1.2.11.0.1 <-========== PASO 15. =========->

1.2.12 (13i)Usando la aplicación para hacer el gráfico con dos variables ESTRATO y CURSO

barp5 <- barplot(table_5,
                 main = "Gráfico de barras CURSO vs ESTRATO",
                 xlab = "CURSO", ylab = "Frecuencia",
                 col = rainbow(nrow(table_5)),
                 legend.text = rownames(table_5),
                 beside = TRUE,
                 ylim = c(0, max(table_5) + 5))
text(barp5, table_5 + 1, labels = table_5)

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1.2.12.0.1 <-========== PASO 16. =========->

1.2.13 (14i)Usando la aplicación para hacer la tabla con dos variables ESTRATO y SEXO

table_6 <- table(DATOS2026$ESTRATO, DATOS2026$SEXO)
table_6

           
            FEMENINO MASCULINO
  ESTRATO 1       11        16
  ESTRATO 2       17        17
  ESTRATO 3        8        10
  ESTRATO 4        5        18
  ESTRATO 5        9        10

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1.2.13.0.1 <-========== PASO 17. =========->

1.2.14 (15i)Usando la aplicación para hacer el gráfico con dos variables ESTRATO y SEXO

barp6 <- barplot(table_6,
                 main = "Gráfico de barras SEXO vs ESTRATO",
                 xlab = "SEXO", ylab = "Frecuencia",
                 col = rainbow(nrow(table_6)),
                 legend.text = rownames(table_6),
                 beside = TRUE,
                 ylim = c(0, max(table_6) + 5))
text(barp6, table_6 + 1, labels = table_6)

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1.2.14.0.1 <-========== PASO 18. =========->

1.2.15 (16i)Tabla de Frecuencias Usando el paquete summarytools

library(summarytools)
tabla_8 <- freq(DATOS2026$EDAD, plain.ascii = FALSE, style = "rmarkdown")
tabla_8

### Frequencies  
#### DATOS2026$EDAD  
**Type:** Numeric  

|       | Freq | % Valid | % Valid Cum. | % Total | % Total Cum. |
|-----------:|-----:|--------:|-------------:|--------:|-------------:|
|     **15** |    2 |    1.65 |         1.65 |    1.65 |         1.65 |
|     **16** |    4 |    3.31 |         4.96 |    3.31 |         4.96 |
|     **17** |    7 |    5.79 |        10.74 |    5.79 |        10.74 |
|     **18** |   12 |    9.92 |        20.66 |    9.92 |        20.66 |
|     **19** |   22 |   18.18 |        38.84 |   18.18 |        38.84 |
|     **20** |   24 |   19.83 |        58.68 |   19.83 |        58.68 |
|     **21** |   25 |   20.66 |        79.34 |   20.66 |        79.34 |
|     **22** |   11 |    9.09 |        88.43 |    9.09 |        88.43 |
|     **23** |   10 |    8.26 |        96.69 |    8.26 |        96.69 |
|     **24** |    2 |    1.65 |        98.35 |    1.65 |        98.35 |
|     **25** |    2 |    1.65 |       100.00 |    1.65 |       100.00 |
| **\<NA\>** |    0 |         |              |    0.00 |       100.00 |
|  **Total** |  121 |  100.00 |       100.00 |  100.00 |       100.00 |

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1.2.15.0.1 <-========== PASO 19. =========->

1.2.16 (17i)Resumen estadístico de la variable EDAD

summary(DATOS2026$EDAD)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  15.00   19.00   20.00   20.02   21.00   25.00 

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1.2.16.0.1 <-========== PASO 20. =========->

1.2.17 (18i)Una primera vista del diagrama de caja para la variable Edad

boxplot(DATOS2026$EDAD, horizontal = TRUE, col = rainbow(3), main = "Diagrama de Caja - EDAD")

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1.2.17.0.1 <-========== PASO 21. =========->

1.2.18 (19i)Identificamos donde queda la mediana

x <- DATOS2026$EDAD
boxplot(x, notch = TRUE, horizontal = TRUE, col = rainbow(3), main = "Diagrama de Caja con Muesca (Mediana)")

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1.2.18.0.1 <-========== PASO 22. =========->

1.2.19 (20i)EDAD vs SEXO

x <- DATOS2026$EDAD
y <- DATOS2026$SEXO
boxplot(x ~ y, horizontal = TRUE, col = rainbow(3), main = "EDAD vs SEXO")

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1.2.19.0.1 <-========== PASO 23. =========->

1.2.20 (21i)EDAD vs ESTRATO

library(ggplot2)
x <- DATOS2026$EDAD
z <- DATOS2026$ESTRATO
boxplot(x ~ z, horizontal = TRUE, col = rainbow(5), main = "EDAD vs ESTRATO")

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1.2.20.1 <-========== PASO 24. =========->

1.2.21 (22i)EDAD vs ESTRATO vs SEXO

ggplot(data = DATOS2026, mapping = aes(y = EDAD, x = ESTRATO, fill = SEXO)) +
  geom_boxplot() +
  scale_y_continuous(name = "EDAD") +
  scale_x_discrete(labels = abbreviate, name = "ESTRATO") +
  theme_minimal() +
  labs(title = "Distribución de EDAD por ESTRATO y SEXO")

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1.2.21.1 <-========== PASO 25. =========->

1.2.22 (23i)Estudiemos la variable ESTATURA y obtengamos sus seis medidas representativas

summary(DATOS2026$ESTATURA)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  151.0   165.0   170.0   169.9   176.0   186.0 

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1.2.22.1 <-========== PASO 26. =========->

1.2.22.2 (24i)Una primera vista del diagrama de caja para la variable ESTATURA

boxplot(DATOS2026$ESTATURA, horizontal = TRUE, col = rainbow(3), main = "Diagrama de Caja - ESTATURA")

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1.2.22.3 <-========== PASO 27. =========->

1.2.22.4 (25i)Identificamos donde queda la mediana

x <- DATOS2026$ESTATURA
boxplot(x, notch = TRUE, horizontal = TRUE, col = rainbow(3), main = "Mediana de ESTATURA")

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1.2.22.5 <-========== PASO 28. =========->

1.2.22.6 (26i)ESTATURA vs SEXO

x <- DATOS2026$ESTATURA
y <- DATOS2026$SEXO
boxplot(x ~ y, horizontal = TRUE, col = rainbow(3), main = "ESTATURA vs SEXO")

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1.2.22.7 <-========== PASO 29. =========->

1.2.22.8 (27)ESTATURA vs ESTRATO

x <- DATOS2026$ESTATURA
z <- DATOS2026$ESTRATO
boxplot(x ~ z, horizontal = TRUE, col = rainbow(5), main = "ESTATURA vs ESTRATO")

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1.2.22.9 <-========== PASO 30. =========->

1.2.23 (28i)ESTATURA vs ESTRATO vs SEXO

ggplot(data = DATOS2026, mapping = aes(y = ESTATURA, x = ESTRATO, fill = SEXO)) +
  geom_boxplot() +
  scale_y_continuous(name = "ESTATURA") +
  scale_x_discrete(labels = abbreviate, name = "ESTRATO") +
  theme_minimal() +
  labs(title = "Distribución de ESTATURA por ESTRATO y SEXO")

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1.2.23.1 <-========== PASO 31. =========->

1.2.24 (29i)Histograma y tabla de frecuencias usando Regla de Sturges

library(agricolae)
h2 <- graph.freq(DATOS2026$EDAD, col = colors()[75], main = "Histograma de EDAD (Regla de Sturges)", xlab = "EDAD")

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1.2.24.1 <-========== PASO 32. =========->

1.2.25 (30i)Tabla de frecuencias agrupadas Regla de Sturges

summary(h2)

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1.2.25.1 <-========== PASO 33. =========->

1.2.25.2 (31i)Polígono de frecuencia absolutas

plot(h2, col = colors()[70], frequency = 1, main = "Polígono de Frecuencias Absolutas", xlab = "EDAD")
polygon.freq(h2, col = "red", frequency = 1, lwd = 2)

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1.2.25.3 <-========== PASO 34. =========->

1.2.26 (32i)Polígono de frecuencia relativas

plot(h2, col = colors()[70], frequency = 2, main = "Polígono de Frecuencias Relativas", xlab = "EDAD")
polygon.freq(h2, col = "red", frequency = 2, lwd = 2)

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1.2.26.1 <-========== PASO 35. =========->

1.2.27 (33i)Ojivas - usando R

fr_por_clase2 <- h2$counts
total_n2 <- sum(h2$counts)
fr_relativos2 <- fr_por_clase2 / total_n2
fr_porcentuales2 <- 100 * fr_relativos2

data.frame(
  Acumulada_Absoluta = cumsum(fr_por_clase2),
  Acumulada_Relativa = round(cumsum(fr_relativos2), 4),
  Acumulada_Porcentual = round(cumsum(fr_porcentuales2), 2)
)

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1.2.27.1 <-========== PASO 36. =========->

1.3 (34i)Ojivas - frecuencias porcentuales

p4 <- cumsum(fr_porcentuales2)
plot(p4, type = "o", col = "red", main = "Ojiva de Frecuencias Porcentuales Acumuladas",
     xlab = "Clases", ylab = "Porcentaje Acumulado (%)")

1.3.0.1 <-========== AQUI FINALIZA EL LABORATORIO 7. =========->

1.3.0.2 <-========== AQUI INICIA EL LABORATORIO 8. VARIABLES RELACIONADAS =========->

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1.3.0.3 <-========== PASO 37. =========->

1.3.1 (35i)Algunas tablas bivariadas - Contamos Sexo vs Curso - ambas cualitativas

table_bv1 <- table(DATOS2026$SEXO, DATOS2026$CURSO)
table_bv1

           
            CURSO A CURSO B CURSO C
  FEMENINO       13      23      14
  MASCULINO      29      24      18

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1.3.1.1 <-========== PASO 38. =========->

1.3.2 (36i)Algunas tablas bivariadas - Diagrama de barras Contamos Sexo vs Curso

barp_bv1 <- barplot(table_bv1,
                    main = "Gráfico de barras CURSO vs SEXO",
                    xlab = "CURSO", ylab = "Frecuencia",
                    col = c("pink", "blue"),
                    legend.text = rownames(table_bv1),
                    beside = TRUE,
                    ylim = c(0, max(table_bv1) + 10))
text(barp_bv1, table_bv1 + 2, labels = table_bv1)

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1.3.2.1 <-========== PASO 39. =========->

1.3.3 (37i)Algunas tablas bivariadas - Diagrama de barras Contamos Estrato vs Curso

table_bv2 <- table(DATOS2026$ESTRATO, DATOS2026$CURSO)
table_bv2

           
            CURSO A CURSO B CURSO C
  ESTRATO 1       9       7      11
  ESTRATO 2      10      14      10
  ESTRATO 3       8       7       3
  ESTRATO 4       6      11       6
  ESTRATO 5       9       8       2

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1.3.3.1 <-========== PASO 40. =========->

barp_bv2 <- barplot(table_bv2,
                    main = "Gráfico de barras CURSO vs ESTRATO",
                    xlab = "CURSO", ylab = "Frecuencia",
                    col = rainbow(nrow(table_bv2)),
                    legend.text = rownames(table_bv2),
                    beside = TRUE,
                    ylim = c(0, max(table_bv2) + 5))
text(barp_bv2, table_bv2 + 1, labels = table_bv2)

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1.3.3.2 <-========== PASO 41. =========->

1.3.4 (38i)Una variable cualitativa y la otra cuantitativa: es necesario un boxplot

x <- DATOS2026$EDAD
y <- DATOS2026$SEXO
boxplot(x ~ y, horizontal = TRUE, col = rainbow(3), main = "EDAD vs SEXO")

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1.3.4.1 <-========== PASO 42. =========->

1.3.5 (39i)Una variable cualitativa y la otra cuantitativa: es necesario un boxplot

x <- DATOS2026$EDAD
z <- DATOS2026$ESTRATO
boxplot(x ~ z, horizontal = TRUE, xlab = "EDAD", ylab = "ESTRATOS", col = rainbow(5), main = "EDAD vs ESTRATO")

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1.3.5.1 <-========== PASO 43. =========->

1.3.6 (40i)Una variable cualitativa y la otra cuantitativa: es necesario un boxplot

x <- DATOS2026$ESTATURA
z <- DATOS2026$SEXO
boxplot(x ~ z, horizontal = TRUE, xlab = "ESTATURA", ylab = "SEXO", col = rainbow(3), main = "ESTATURA vs SEXO")

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1.3.6.1 <-========== PASO 44. =========->

1.3.7 (41i)Dos variables cuantitativas: es necesario un diagrama de dispersión

x <- DATOS2026$ESTATURA
y <- DATOS2026$PESO
plot(x, y, xlab = "ESTATURA", ylab = "PESO", col = "blue", pch = 16, main = "Diagrama de Dispersión ESTATURA vs PESO")
abline(v = mean(x), lwd = 2, lty = 2, col = "red")
abline(h = mean(y), lwd = 2, lty = 2, col = "red")

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1.3.7.1 <-========== PASO 45. =========->

cat("Media ESTATURA:", mean(x), "\nMedia PESO:", mean(y))

Media ESTATURA: 169.8512 
Media PESO: 67.90083

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1.3.7.2 <-========== PASO 46. =========->

1.3.8 (42i)Recta de regresión lineal Simple

regresion1 <- lm(y ~ x, data = DATOS2026)
regresion1

Call:
lm(formula = y ~ x, data = DATOS2026)

Coefficients:
(Intercept)            x  
   56.85898      0.06501  

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1.3.8.1 <-========== PASO 47. =========->

1.3.9 (43i)Recta de regresión lineal Simple2

regresion2 <- lm(x ~ y, data = DATOS2026)
regresion2

Call:
lm(formula = x ~ y, data = DATOS2026)

Coefficients:
(Intercept)            y  
  166.22304      0.05343  

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1.3.9.1 <-========== PASO 48. =========->

1.3.10 (45i)Recta de regresión lineal Simple - Summary

summary(regresion2)

Call:
lm(formula = x ~ y, data = DATOS2026)

Residuals:
     Min       1Q   Median       3Q      Max 
-18.7497  -5.2306  -0.0703   6.6626  16.4641 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 166.22304    5.68062  29.261   <2e-16 ***
y             0.05343    0.08296   0.644    0.521    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 8.043 on 119 degrees of freedom
Multiple R-squared:  0.003474,  Adjusted R-squared:  -0.0049 
F-statistic: 0.4148 on 1 and 119 DF,  p-value: 0.5208

1.4 46i Diagrama de Dispersión y línea de regresión

x <- DATOS2026$ESTATURA
y <- DATOS2026$PESO
regresion1 <- lm(y ~ x, data = DATOS2026)

plot(x, y, xlab = "ESTATURA", ylab = "PESO", col = "darkgreen", pch = 16,
     main = "Regresión Lineal: ESTATURA vs PESO")
abline(v = mean(x), lwd = 2, lty = 2, col = "gray")
abline(h = mean(y), lwd = 2, lty = 2, col = "gray")
abline(regresion1, col = "steelblue", lwd = 2)

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1.4.0.1 <-========== PASO 49. =========->

1.4.1 Problema de aplicación:Taller Regresión Lineal

taller_rl <- data.frame(
  x = c(88, 77, 68, 80, 68, 55, 89, 61, 72, 72, 79, 75, 68, 65, 70, 52, 78, 55, 96, 75, 44, 57, 60, 50, 93),
  y = c(175, 183, 158, 165, 175, 160, 160, 156, 174, 171, 160, 184, 163, 176, 167, 172, 168, 167, 181, 175, 153, 154, 169, 168, 187)
)
head(taller_rl)

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1.4.1.1 <-========== PASO 50. =========->

1.4.2 (b)Diagrama de dispersión Taller

plot(taller_rl$x, taller_rl$y, xlab = "PESO", ylab = "ESTATURA", col = "purple", pch = 16, main = "Taller: PESO vs ESTATURA")
abline(v = mean(taller_rl$x), lwd = 2, lty = 2, col = "orange")
abline(h = mean(taller_rl$y), lwd = 2, lty = 2, col = "orange")

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1.4.2.1 <-========== PASO 51. =========->

1.4.3 (51i)Coeficiente de Correlación de Pearson

cor(taller_rl$x, taller_rl$y)

[1] 0.5133798

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1.4.3.1 <-========== PASO 52. =========->

1.4.4 (d)Recta de regresión lineal Simple Taller

regresion3 <- lm(y ~ x, data = taller_rl)
summary(regresion3)

Call:
lm(formula = y ~ x, data = taller_rl)

Residuals:
    Min      1Q  Median      3Q     Max 
-15.656  -6.614   1.404   6.247  13.335 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 143.9296     8.8404  16.281 4.06e-14 ***
x             0.3565     0.1242   2.869  0.00867 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 8.315 on 23 degrees of freedom
Multiple R-squared:  0.2636,    Adjusted R-squared:  0.2315 
F-statistic: 8.231 on 1 and 23 DF,  p-value: 0.008673

plot(taller_rl$x, taller_rl$y, xlab = "PESO", ylab = "ESTATURA", col = "blue", pch = 16, main = "Ajuste de Regresión Taller")
abline(v = mean(taller_rl$x), lwd = 2, lty = 2, col = "gray")
abline(h = mean(taller_rl$y), lwd = 2, lty = 2, col = "gray")
abline(regresion3, col = "steelblue", lwd = 2)

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1.4.4.1 <-========== PASO 53. =========->

1.4.5 (52i)Lectura/Creación del conjunto de datos EdadPesoGrasas

grasas <- data.frame(
  edad = c(23, 27, 39, 41, 47, 49, 50, 52, 54, 54, 56, 57, 58, 58, 60, 61, 61, 61, 62, 63, 63, 64, 65, 66, 68),
  peso = c(60.0, 61.3, 65.2, 62.7, 65.0, 66.2, 65.8, 65.5, 67.2, 68.1, 68.8, 72.1, 74.2, 75.8, 73.6, 74.2, 76.0, 78.5, 80.1, 80.0, 79.5, 81.3, 81.0, 82.2, 85.0),
  grasas = c(225, 230, 240, 250, 280, 300, 310, 312, 320, 330, 335, 340, 350, 352, 360, 365, 370, 380, 385, 390, 395, 400, 405, 410, 425)
)
names(grasas)

[1] "edad"   "peso"   "grasas"

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1.4.5.1 <-========== PASO 54. =========->

1.4.6 (53i)Matriz de diagramas de dispersión

pairs(grasas, col = "darkblue", pch = 16)

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1.4.6.1 <-========== PASO 55. =========->

1.4.7 (54i)Matriz de correlación

cor(grasas)

            edad      peso    grasas
edad   1.0000000 0.8867815 0.9599667
peso   0.8867815 1.0000000 0.9579207
grasas 0.9599667 0.9579207 1.0000000

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1.4.7.1 <-========== PASO 56. =========->

1.4.8 (55i)Cálculo de la recta de mínimos cuadrados

regresion <- lm(grasas ~ edad, data = grasas)
summary(regresion)

Call:
lm(formula = grasas ~ edad, data = grasas)

Residuals:
    Min      1Q  Median      3Q     Max 
-23.583 -11.344  -5.686  14.578  39.310 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  73.7183    16.4457   4.483 0.000169 ***
edad          4.8683     0.2962  16.436 3.32e-14 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 16.73 on 23 degrees of freedom
Multiple R-squared:  0.9215,    Adjusted R-squared:  0.9181 
F-statistic: 270.1 on 1 and 23 DF,  p-value: 3.322e-14

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1.4.8.1 <-========== PASO 57. =========->

1.4.9 (56i)Representación gráfica de la recta de mínimos cuadrados

plot(grasas$edad, grasas$grasas, xlab = 'Edad', ylab = 'Grasas', col = "red", pch = 16, main = "Ajuste Grasas vs Edad")
abline(regresion, col = "blue", lwd = 2)

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1.4.9.1 <-========== PASO 58. =========->

1.4.10 (57i)Predicción para individuos de edades 30 a 50

nuevas.edades <- data.frame(edad = seq(30, 50))
predicciones <- predict(regresion, nuevas.edades)
data.frame(Edad = nuevas.edades$edad, Grasas_Predichas = round(predicciones, 2))

1.4.10.1 <-========== AQUI FINALIZA EL LABORATORIO 8 =========->