> x = women
> x
   height weight
1      58    115
2      59    117
3      60    120
4      61    123
5      62    126
6      63    129
7      64    132
8      65    135
9      66    139
10     67    142
11     68    146
12     69    150
13     70    154
14     71    159
15     72    164
> fit = lm(weight ~ height, data=x)
> summary(fit)

Call:
lm(formula = weight ~ height, data = x)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.7333 -1.1333 -0.3833  0.7417  3.1167 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -87.51667    5.93694  -14.74 1.71e-09 ***
height        3.45000    0.09114   37.85 1.09e-14 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.525 on 13 degrees of freedom
Multiple R-squared:  0.991,    Adjusted R-squared:  0.9903 
F-statistic:  1433 on 1 and 13 DF,  p-value: 1.091e-14

> fitted(fit)
       1        2        3        4        5        6        7        8        9 
112.5833 116.0333 119.4833 122.9333 126.3833 129.8333 133.2833 136.7333 140.1833 
      10       11       12       13       14       15 
143.6333 147.0833 150.5333 153.9833 157.4333 160.8833 
> women$weight
 [1] 115 117 120 123 126 129 132 135 139 142 146 150 154 159 164
> residuals(fit)
          1           2           3           4           5           6           7 
 2.41666667  0.96666667  0.51666667  0.06666667 -0.38333333 -0.83333333 -1.28333333 
          8           9          10          11          12          13          14 
-1.73333333 -1.18333333 -1.63333333 -1.08333333 -0.53333333  0.01666667  1.56666667 
         15 
 3.11666667 
> plot(women$height, women$weight)
> abline(fit)

> x = runif(100)
> y = 0.2*x + 0.1*rnorm(100)
> fit = lm(y~x)
> summary(fit)

Call:
lm(formula = y ~ x)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.299493 -0.056850  0.004709  0.066714  0.237272 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.002891   0.019688  -0.147    0.884    
x            0.236938   0.036158   6.553 2.64e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1037 on 98 degrees of freedom
Multiple R-squared:  0.3047,    Adjusted R-squared:  0.2976 
F-statistic: 42.94 on 1 and 98 DF,  p-value: 2.639e-09

> plot(x,y)
> abline(fit)

> y = 0.2*x + 0.01*rnorm(100)
> fit = lm(y~x)
> summary(fit)

Call:
lm(formula = y ~ x)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.019936 -0.005549 -0.001135  0.004598  0.026435 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.002684   0.001837  -1.461    0.147    
x            0.203561   0.003374  60.326   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.009678 on 98 degrees of freedom
Multiple R-squared:  0.9738,    Adjusted R-squared:  0.9735 
F-statistic:  3639 on 1 and 98 DF,  p-value: < 2.2e-16

> plot(x,y)
> abline(fit)

> fit2 = lm(weight ~ height + I(height^2), data=women)
> summary(fit2)

Call:
lm(formula = weight ~ height + I(height^2), data = women)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.50941 -0.29611 -0.00941  0.28615  0.59706 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 261.87818   25.19677  10.393 2.36e-07 ***
height       -7.34832    0.77769  -9.449 6.58e-07 ***
I(height^2)   0.08306    0.00598  13.891 9.32e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3841 on 12 degrees of freedom
Multiple R-squared:  0.9995,    Adjusted R-squared:  0.9994 
F-statistic: 1.139e+04 on 2 and 12 DF,  p-value: < 2.2e-16

> plot(women$height, women$weight)
> lines(women$height, fitted(fit2))

> y = 0.4*x**2 + 0.2*x + 0.01*rnorm(100)
> fit = lm(y~x + I(x^2))
> summary(fit)

Call:
lm(formula = y ~ x + I(x^2))

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0243909 -0.0058432 -0.0000949  0.0056788  0.0245737 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.003611   0.002727   1.324    0.189    
x           0.189098   0.013571  13.934   <2e-16 ***
I(x^2)      0.400631   0.013806  29.018   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.009857 on 97 degrees of freedom
Multiple R-squared:  0.9966,    Adjusted R-squared:  0.9965 
F-statistic: 1.418e+04 on 2 and 97 DF,  p-value: < 2.2e-16

> plot(x,y)

> states = as.data.frame(state.x77[, c("Murder", "Population", "Illiteracy", "Income", "Frost")])
> cor(states)
               Murder Population Illiteracy     Income      Frost
Murder      1.0000000  0.3436428  0.7029752 -0.2300776 -0.5388834
Population  0.3436428  1.0000000  0.1076224  0.2082276 -0.3321525
Illiteracy  0.7029752  0.1076224  1.0000000 -0.4370752 -0.6719470
Income     -0.2300776  0.2082276 -0.4370752  1.0000000  0.2262822
Frost      -0.5388834 -0.3321525 -0.6719470  0.2262822  1.0000000

> install.packages("car")
> library(car)
> scatterplotMatrix(states, spread=FALSE, lty.smooth=2, main="Scatter Plot Matrix")

> fit = lm(Murder ~ Population + Illiteracy + Income + Frost, data=states)
> summary(fit)

Call:
lm(formula = Murder ~ Population + Illiteracy + Income + Frost, 
    data = states)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.7960 -1.6495 -0.0811  1.4815  7.6210 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 1.235e+00  3.866e+00   0.319   0.7510    
Population  2.237e-04  9.052e-05   2.471   0.0173 *  
Illiteracy  4.143e+00  8.744e-01   4.738 2.19e-05 ***
Income      6.442e-05  6.837e-04   0.094   0.9253    
Frost       5.813e-04  1.005e-02   0.058   0.9541    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.535 on 45 degrees of freedom
Multiple R-squared:  0.567,    Adjusted R-squared:  0.5285 
F-statistic: 14.73 on 4 and 45 DF,  p-value: 9.133e-08

> fit = lm(mpg ~ hp + wt + hp:wt, data=mtcars)
> summary(fit)

Call:
lm(formula = mpg ~ hp + wt + hp:wt, data = mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.0632 -1.6491 -0.7362  1.4211  4.5513 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 49.80842    3.60516  13.816 5.01e-14 ***
hp          -0.12010    0.02470  -4.863 4.04e-05 ***
wt          -8.21662    1.26971  -6.471 5.20e-07 ***
hp:wt        0.02785    0.00742   3.753 0.000811 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.153 on 28 degrees of freedom
Multiple R-squared:  0.8848,    Adjusted R-squared:  0.8724 
F-statistic: 71.66 on 3 and 28 DF,  p-value: 2.981e-13

> install.packages("effects")
> library(effects)
> plot(effect("hp:wt", fit, list(wt=c(2.2, 3.2, 4.2))), multiline=TRUE)