Fitting lines exercise

This example from Gelman and Nolan 2002 Teaching Statistics: A bag of tricks, chapter 4.

# now make each figure and the corresponding r lm() output
x = c(1,2,3)
y = x
plot(x,y,xlab="",ylab="",bty="n",xlim=c(0,3),ylim=c(0,3))
lm.1 = lm(y~x)
abline(lm.1)

summary(lm.1)
## Warning in summary.lm(lm.1): essentially perfect fit: summary may be
## unreliable
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## 1 2 3
## 0 0 0
##
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)        0          0      NA       NA
## x                  1          0     Inf   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0 on 1 degrees of freedom
## Multiple R-squared:      1,  Adjusted R-squared:      1
## F-statistic:   Inf on 1 and 1 DF,  p-value: < 2.2e-16
# now make each figure and the corresponding r lm() output
x = c(1,1,2)
y = c(1,2,2)
plot(x,y,xlab="",ylab="",bty="n",xlim=c(0,3),ylim=c(0,3))
lm.1 = lm(y~x)
abline(lm.1)

summary(lm.1)
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
##          1          2          3
## -5.000e-01  5.000e-01  2.498e-16
##
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)    1.000      1.225   0.816    0.564
## x              0.500      0.866   0.577    0.667
##
## Residual standard error: 0.7071 on 1 degrees of freedom
## Multiple R-squared:   0.25,  Adjusted R-squared:   -0.5
## F-statistic: 0.3333 on 1 and 1 DF,  p-value: 0.6667
# now make each figure and the corresponding r lm() output
x = c(1,1,2,2)
y = c(1,2,1,2)
plot(x,y,xlab="",ylab="",bty="n",xlim=c(0,3),ylim=c(0,3))
lm.1 = lm(y~x)
abline(lm.1)

summary(lm.1)
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
##    1    2    3    4
## -0.5  0.5 -0.5  0.5
##
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.500e+00  1.118e+00   1.342    0.312
## x           1.110e-16  7.071e-01   0.000    1.000
##
## Residual standard error: 0.7071 on 2 degrees of freedom
## Multiple R-squared:  1.972e-31,  Adjusted R-squared:   -0.5
## F-statistic: 3.944e-31 on 1 and 2 DF,  p-value: 1
# now make each figure and the corresponding r lm() output
x = c(1,2,3,3,4,5)
y = c(2,3,1,3,2,3)
plot(x,y,xlab="",ylab="",bty="n",xlim=c(0,6),ylim=c(0,4))
lm.1 = lm(y~x)
abline(lm.1)

summary(lm.1)
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
##       1       2       3       4       5       6
## -0.1333  0.7667 -1.3333  0.6667 -0.4333  0.4667
##
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)   2.0333     0.9286   2.190   0.0937 .
## x             0.1000     0.2843   0.352   0.7428
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8991 on 4 degrees of freedom
## Multiple R-squared:   0.03,  Adjusted R-squared:  -0.2125
## F-statistic: 0.1237 on 1 and 4 DF,  p-value: 0.7428