Apunts practica 2 estadistica EEBE
Pere Lopez Brosa
25 marc de 2019
Codi
library(readr)
venecia <- read_csv("C:/Users/Pere/Downloads/Datos_Sesion3/venecia.txt")
names(venecia) <- c("nivell", "any")
plot(venecia[2:1])
summary(lm(nivell~any, data=venecia))
plot(nivell~any, data=venecia)
abline(lm(nivell~any, data=venecia), col="red")
reg <- read_delim("C:/Users/Pere/Downloads/Datos_Sesion3/reg.txt",
";", escape_double = FALSE, trim_ws = TRUE)
plot(y1~x1, data=reg)
abline(lm(y1~x1, data=reg), col="red")
summary(lm(y1~x1, data=reg))
plot(y2~x2, data=reg)
abline(lm(y2~x2, data=reg), col="red")
summary(lm(y2~x2, data=reg))
plot(y3~x3, data=reg)
abline(lm(y3~x3, data=reg), col="red")
summary(lm(y3~x3, data=reg))
plot(y4~x4, data=reg)
abline(lm(y4~x4, data=reg), col="red")
summary(lm(y4~x4, data=reg))
summary(lm(nivell~any, data=venecia[-c(36,49),]))
plot(nivell~any, data=venecia[-c(36,49),])
abline(lm(nivell~any, data=venecia[-c(36,49),]), col="red")
petroli <- read.table("~/petroleo.txt",
sep=",",
header=TRUE)
plot(petroli)
petroli$lMbbl <- log(petroli$Mbbl)
model <- lm(lMbbl~Year, data=petroli)
summary(model)
predict(model, newdata=data.frame(Year=2000))
exp(predict(model, newdata=data.frame(Year=2000)))
1880:1990
exp(predict(model, newdata=data.frame(Year=1880:1990)))
lines(1880:1990,
exp(predict(model, newdata=data.frame(Year=1880:1990))),
col="red")
cemento <- read_delim("C:/Users/Pere/Downloads/Datos_Sesion3/cemento.txt",
";", escape_double = FALSE, col_names = FALSE,
locale = locale(decimal_mark = ","),
trim_ws = TRUE)
names(cemento) <- c("dies", "MPa")
plot(cemento)
summary(lm(MPa~dies, data=cemento))
plot(MPa~dies, data=cemento)
abline(lm(MPa~dies, data=cemento), col="red")
summary(lm(MPa~I(sqrt(1/dies)), data=cemento))
plot(MPa~I(sqrt(1/dies)), data=cemento)
abline(lm(MPa~I(sqrt(1/dies)), data=cemento), col="red")
summary(lm(log10(MPa)~I(sqrt(1/dies)), data=cemento))
plot(log10(MPa)~I(sqrt(1/dies)), data=cemento)
abline(lm(log10(MPa)~I(sqrt(1/dies)), data=cemento), col="red")Codi i resultats
library(readr)
venecia <- read_csv("C:/Users/Pere/Downloads/Datos_Sesion3/venecia.txt")## Parsed with column specification:
## cols(
## nivel = col_double(),
## `a<f1>o` = col_double()
## )names(venecia) <- c("nivell", "any")
plot(venecia[2:1])
summary(lm(nivell~any, data=venecia))##
## Call:
## lm(formula = nivell ~ any, data = venecia)
##
## Residuals:
## Min 1Q Median 3Q Max
## -33.813 -11.211 -3.309 9.515 68.722
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -989.3822 346.4770 -2.856 0.00628 **
## any 0.5670 0.1771 3.201 0.00241 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.62 on 49 degrees of freedom
## Multiple R-squared: 0.1729, Adjusted R-squared: 0.1561
## F-statistic: 10.25 on 1 and 49 DF, p-value: 0.002406plot(nivell~any, data=venecia)
abline(lm(nivell~any, data=venecia), col="red")
reg <- read_delim("C:/Users/Pere/Downloads/Datos_Sesion3/reg.txt",
";", escape_double = FALSE, trim_ws = TRUE)## Parsed with column specification:
## cols(
## x1 = col_double(),
## y1 = col_number(),
## x2 = col_double(),
## y2 = col_number(),
## x3 = col_double(),
## y3 = col_number(),
## x4 = col_double(),
## y4 = col_number()
## )plot(y1~x1, data=reg)
abline(lm(y1~x1, data=reg), col="red")
summary(lm(y1~x1, data=reg))##
## Call:
## lm(formula = y1 ~ x1, data = reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -192.127 -45.577 -4.136 70.941 183.882
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 300.01 112.47 2.667 0.02573 *
## x1 50.01 11.79 4.241 0.00217 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 123.7 on 9 degrees of freedom
## Multiple R-squared: 0.6665, Adjusted R-squared: 0.6295
## F-statistic: 17.99 on 1 and 9 DF, p-value: 0.00217plot(y2~x2, data=reg)
abline(lm(y2~x2, data=reg), col="red")
summary(lm(y2~x2, data=reg))##
## Call:
## lm(formula = y2 ~ x2, data = reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -190.09 -76.09 12.91 94.91 126.91
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 300.1 112.5 2.667 0.02576 *
## x2 50.0 11.8 4.239 0.00218 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 123.7 on 9 degrees of freedom
## Multiple R-squared: 0.6662, Adjusted R-squared: 0.6292
## F-statistic: 17.97 on 1 and 9 DF, p-value: 0.002179plot(y3~x3, data=reg)
abline(lm(y3~x3, data=reg), col="red")
summary(lm(y3~x3, data=reg))##
## Call:
## lm(formula = y3 ~ x3, data = reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -115.86 -61.46 -23.03 15.40 324.11
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 300.25 112.45 2.670 0.02562 *
## x3 49.97 11.79 4.239 0.00218 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 123.6 on 9 degrees of freedom
## Multiple R-squared: 0.6663, Adjusted R-squared: 0.6292
## F-statistic: 17.97 on 1 and 9 DF, p-value: 0.002176plot(y4~x4, data=reg)
abline(lm(y4~x4, data=reg), col="red")
summary(lm(y4~x4, data=reg))##
## Call:
## lm(formula = y4 ~ x4, data = reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -175.1 -83.1 0.0 80.9 183.9
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 300.17 112.39 2.671 0.02559 *
## x4 49.99 11.78 4.243 0.00216 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 123.6 on 9 degrees of freedom
## Multiple R-squared: 0.6667, Adjusted R-squared: 0.6297
## F-statistic: 18 on 1 and 9 DF, p-value: 0.002165summary(lm(nivell~any, data=venecia[-c(36,49),]))##
## Call:
## lm(formula = nivell ~ any, data = venecia[-c(36, 49), ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -29.334 -9.165 -0.688 7.825 37.984
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -705.0774 289.5564 -2.435 0.01874 *
## any 0.4205 0.1481 2.840 0.00665 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.1 on 47 degrees of freedom
## Multiple R-squared: 0.1464, Adjusted R-squared: 0.1283
## F-statistic: 8.064 on 1 and 47 DF, p-value: 0.006653plot(nivell~any, data=venecia[-c(36,49),])
abline(lm(nivell~any, data=venecia[-c(36,49),]), col="red")
petroli <- read.table("C:/Users/Pere/Downloads/Datos_Sesion3/petroleo.txt",
sep=",",
header=TRUE)
plot(petroli)
petroli$lMbbl <- log(petroli$Mbbl)
model <- lm(lMbbl~Year, data=petroli)
summary(model)##
## Call:
## lm(formula = lMbbl ~ Year, data = petroli)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.53738 -0.06588 0.04655 0.12515 0.29507
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.154e+02 2.533e+00 -45.55 <2e-16 ***
## Year 6.342e-02 1.302e-03 48.71 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2046 on 25 degrees of freedom
## Multiple R-squared: 0.9896, Adjusted R-squared: 0.9892
## F-statistic: 2373 on 1 and 25 DF, p-value: < 2.2e-16predict(model, newdata=data.frame(Year=2000))## 1
## 11.43577exp(predict(model, newdata=data.frame(Year=2000)))## 1
## 92574.21880:1990## [1] 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893
## [15] 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907
## [29] 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921
## [43] 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935
## [57] 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949
## [71] 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963
## [85] 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977
## [99] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990exp(predict(model, newdata=data.frame(Year=1880:1990)))## 1 2 3 4 5 6
## 45.86034 48.86291 52.06207 55.47069 59.10247 62.97204
## 7 8 9 10 11 12
## 67.09496 71.48781 76.16827 81.15517 86.46857 92.12986
## 13 14 15 16 17 18
## 98.16180 104.58866 111.43631 118.73229 126.50595 134.78856
## 19 20 21 22 23 24
## 143.61346 153.01614 163.03444 173.70866 185.08174 197.19944
## 25 26 27 28 29 30
## 210.11051 223.86690 238.52395 254.14063 270.77977 288.50830
## 31 32 33 34 35 36
## 307.39757 327.52355 348.96722 371.81486 396.15838 422.09573
## 37 38 39 40 41 42
## 449.73124 479.17612 510.54882 543.97555 579.59080 617.53786
## 43 44 45 46 47 48
## 657.96940 701.04808 746.94721 795.85146 847.95757 903.47519
## 49 50 51 52 53 54
## 962.62766 1025.65297 1092.80468 1164.35297 1240.58567 1321.80949
## 55 56 57 58 59 60
## 1408.35122 1500.55901 1598.80385 1703.48099 1815.01157 1933.84430
## 61 62 63 64 65 66
## 2060.45726 2195.35985 2339.09480 2492.24038 2655.41274 2829.26835
## 67 68 69 70 71 72
## 3014.50666 3211.87292 3422.16118 3646.21746 3884.94319 4139.29881
## 73 74 75 76 77 78
## 4410.30765 4699.06001 5006.71762 5334.51823 5683.78066 6055.91006
## 79 80 81 82 83 84
## 6452.40357 6874.85636 7324.96806 7804.54953 8315.53025 8859.96597
## 85 86 87 88 89 90
## 9440.04708 10058.10735 10716.63335 11418.27448 12165.85357 12962.37828
## 91 92 93 94 95 96
## 13811.05318 14715.29266 15678.73465 16705.25526 17798.98440 18964.32235
## 97 98 99 100 101 102
## 20205.95749 21528.88516 22938.42777 24440.25617 26040.41253 27745.33457
## 103 104 105 106 107 108
## 29561.88155 31497.36177 33559.56207 35756.77907 38097.85262 40592.20131
## 109 110 111
## 43249.86039 46081.52215 49098.57892lines(1880:1990,
exp(predict(model, newdata=data.frame(Year=1880:1990))),
col="red")
cemento <- read_delim("C:/Users/Pere/Downloads/Datos_Sesion3/cemento.txt",
";", escape_double = FALSE, col_names = FALSE,
locale = locale(decimal_mark = ","),
trim_ws = TRUE)## Parsed with column specification:
## cols(
## X1 = col_double(),
## X2 = col_double()
## )names(cemento) <- c("dies", "MPa")
plot(cemento)
summary(lm(MPa~dies, data=cemento))##
## Call:
## lm(formula = MPa ~ dies, data = cemento)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.4452 -2.0034 0.7848 3.4385 8.5059
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.5871 1.6831 13.420 3.84e-11 ***
## dies 0.6581 0.1187 5.546 2.38e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.739 on 19 degrees of freedom
## Multiple R-squared: 0.6182, Adjusted R-squared: 0.5981
## F-statistic: 30.76 on 1 and 19 DF, p-value: 2.382e-05plot(MPa~dies, data=cemento)
abline(lm(MPa~dies, data=cemento), col="red")
summary(lm(MPa~I(sqrt(1/dies)), data=cemento))##
## Call:
## lm(formula = MPa ~ I(sqrt(1/dies)), data = cemento)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7947 -1.2567 -0.0567 1.8954 3.1053
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 45.655 1.023 44.63 < 2e-16 ***
## I(sqrt(1/dies)) -32.599 1.764 -18.48 1.34e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.133 on 19 degrees of freedom
## Multiple R-squared: 0.9473, Adjusted R-squared: 0.9445
## F-statistic: 341.4 on 1 and 19 DF, p-value: 1.337e-13plot(MPa~I(sqrt(1/dies)), data=cemento)
abline(lm(MPa~I(sqrt(1/dies)), data=cemento), col="red")
summary(lm(log10(MPa)~I(sqrt(1/dies)), data=cemento))##
## Call:
## lm(formula = log10(MPa) ~ I(sqrt(1/dies)), data = cemento)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.083275 -0.031305 -0.002137 0.023595 0.075087
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.73240 0.02165 80.02 < 2e-16 ***
## I(sqrt(1/dies)) -0.57725 0.03734 -15.46 3.23e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04513 on 19 degrees of freedom
## Multiple R-squared: 0.9264, Adjusted R-squared: 0.9225
## F-statistic: 239 on 1 and 19 DF, p-value: 3.232e-12plot(log10(MPa)~I(sqrt(1/dies)), data=cemento)
abline(lm(log10(MPa)~I(sqrt(1/dies)), data=cemento), col="red")
Formigó
Evolució de la resistència del formigó segons el codi model:
\[\frac{f_{ck}(t)}{f_{ck}(28)}=exp(s(1-\sqrt{\frac{28}{t}}))\]