Чуть не забыл про ответы. Правильный ответ только 2.
Код:
> set.seed(999)
> e<-rnorm(50)
> x4<-x3<-x2<-x1<-rnorm(50)
> y1<-rnorm(50)
> summary(lm(y1~x1))
Call:
lm(formula = y1 ~ x1)
Residuals:
Min 1Q Median 3Q Max
-2.37460 -0.61702 -0.09342 0.64846 1.74851
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.1564 0.1400 -1.118 0.269
x1 -0.2282 0.1607 -1.419 0.162
Residual standard error: 0.9885 on 48 degrees of freedom
Multiple R-squared: 0.04028, Adjusted R-squared: 0.02029
F-statistic: 2.015 on 1 and 48 DF, p-value: 0.1622
> y2<-0.5*x2+e
> summary(lm(y2~x2))
Call:
lm(formula = y2 ~ x2)
Residuals:
Min 1Q Median 3Q Max
-1.8442 -0.8824 0.1773 0.7091 2.6597
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.2589 0.1416 -1.829 0.07363 .
x2 0.5282 0.1626 3.249 0.00212 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.9997 on 48 degrees of freedom
Multiple R-squared: 0.1803, Adjusted R-squared: 0.1632
F-statistic: 10.56 on 1 and 48 DF, p-value: 0.002117
> y3<-0.05*x3+e
> summary(lm(y3~x3))
Call:
lm(formula = y3 ~ x3)
Residuals:
Min 1Q Median 3Q Max
-1.8442 -0.8824 0.1773 0.7091 2.6597
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.2589 0.1416 -1.829 0.0736 .
x3 0.0782 0.1626 0.481 0.6327
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.9997 on 48 degrees of freedom
Multiple R-squared: 0.004797, Adjusted R-squared: -0.01594
F-statistic: 0.2314 on 1 and 48 DF, p-value: 0.6327
> y4<-x4*x4+e
> summary(lm(y4~x4))
Call:
lm(formula = y4 ~ x4)
Residuals:
Min 1Q Median 3Q Max
-2.4566 -0.7822 -0.0131 0.9171 3.2741
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.49891 0.18721 2.665 0.0105 *
x4 0.03735 0.21500 0.174 0.8628
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.322 on 48 degrees of freedom
Multiple R-squared: 0.0006285, Adjusted R-squared: -0.02019
F-statistic: 0.03019 on 1 and 48 DF, p-value: 0.8628
> oldpar<-par(mfrow=c(2,2))
> plot(y1~x1,pch=19,main="Задача 1")
> plot(y2~x2,pch=19,main="Задача 2")
> plot(y3~x3,pch=19,main="Задача 3")
> plot(y4~x4,pch=19,main="Задача 4")
> par(oldpar)