datos1<-read.table("ma2.csv", sep = ",", header=T)
datos1
## densidad masa
## 1 1566 0.1481
## 2 1566 0.1954
## 3 1562 0.2204
## 4 1562 0.1207
## 5 1542 0.2920
## 6 1542 0.3892
## 7 1540 0.3837
## 8 1540 0.2994
## 9 1538 0.2892
## 10 1538 0.1347
## 11 1536 0.2254
## 12 1536 0.7405
## 13 1518 0.4069
## 14 1518 0.1213
## 15 1516 0.2477
## 16 1516 0.3641
## 17 1514 0.4780
## 18 1514 0.3243
## 19 1512 0.7489
## 20 1512 0.8562
## 21 1494 0.5270
## 22 1494 0.4817
## 23 1492 0.3918
## 24 1492 0.3449
## 25 1490 0.3349
## 26 1490 0.6067
## 27 1488 0.5888
## 28 1488 1.0516
## 29 1470 0.4802
## 30 1470 1.7754
## 31 1468 1.4030
## 32 1468 0.9107
## 33 1466 0.5893
## 34 1466 1.2156
## 35 1464 1.3592
## 36 1464 1.8306
## 37 1446 1.6102
## 38 1446 1.6628
## 39 1446 1.3939
## 40 1446 1.8325
## 41 1444 1.7633
## 42 1444 1.2809
## 43 1444 1.7984
## 44 1444 2.0020
## 45 1442 1.4276
## 46 1442 1.9924
## 47 1442 1.8784
## 48 1442 1.2773
## 49 1440 1.2808
## 50 1440 1.7115
## 51 1440 1.9192
## 52 1440 1.6359
## 53 1422 2.8007
## 54 1422 2.7597
## 55 1422 2.2568
## 56 1419 1.9971
## 57 1419 1.4329
## 58 1419 2.8216
## 59 1419 2.4322
## 60 1416 2.8792
## 61 1416 1.7876
## 62 1416 1.8798
## 63 1416 2.0045
attach(datos1)
plot (masa, densidad, ylim=c(1350, 1600))
fit1<-lm(densidad~masa)
fit1
##
## Call:
## lm(formula = densidad ~ masa)
##
## Coefficients:
## (Intercept) masa
## 1534.77 -50.34
abline(fit1)
segments(masa, fitted(fit1), masa, densidad)
summary(fit1)
##
## Call:
## lm(formula = densidad ~ masa)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.638 -16.823 -0.239 19.048 41.070
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1534.766 4.814 318.82 <2e-16 ***
## masa -50.337 3.439 -14.64 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 21.82 on 61 degrees of freedom
## Multiple R-squared: 0.7784, Adjusted R-squared: 0.7748
## F-statistic: 214.3 on 1 and 61 DF, p-value: < 2.2e-16
anova(fit1)
## Analysis of Variance Table
##
## Response: densidad
## Df Sum Sq Mean Sq F value Pr(>F)
## masa 1 102063 102063 214.3 < 2.2e-16 ***
## Residuals 61 29051 476
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
layout(matrix(1:4,2,2))
plot(fit1)
layout(1)
shapiro.test(fit1$residuals)
##
## Shapiro-Wilk normality test
##
## data: fit1$residuals
## W = 0.97721, p-value = 0.2922
datos1.tra<-transform(datos1,densidad=log10(densidad), masa=log10(masa))
detach(datos1)
attach(datos1.tra)
plot (masa, densidad)
fit1<-lm(densidad~masa)
fit1
##
## Call:
## lm(formula = densidad ~ masa)
##
## Coefficients:
## (Intercept) masa
## 3.16651 -0.03094
abline(fit1)
segments(masa, fitted(fit1), masa, densidad)
summary(fit1)
##
## Call:
## lm(formula = densidad ~ masa)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0135848 -0.0031897 -0.0000396 0.0029161 0.0158433
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.1665110 0.0007173 4414.35 <2e-16 ***
## masa -0.0309402 0.0017819 -17.36 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.005564 on 61 degrees of freedom
## Multiple R-squared: 0.8317, Adjusted R-squared: 0.829
## F-statistic: 301.5 on 1 and 61 DF, p-value: < 2.2e-16
anova(fit1)
## Analysis of Variance Table
##
## Response: densidad
## Df Sum Sq Mean Sq F value Pr(>F)
## masa 1 0.0093346 0.0093346 301.5 < 2.2e-16 ***
## Residuals 61 0.0018886 0.0000310
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
layout(matrix(1:4,2,2))
plot(fit1)
layout(1)
shapiro.test(fit1$residuals)
##
## Shapiro-Wilk normality test
##
## data: fit1$residuals
## W = 0.98995, p-value = 0.889