[Hogfather]

Чуть не забыл про ответы. Правильный ответ только 2.

> 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)