> 
> O58;
 [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[17] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[33] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
[65] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
> summary(lm(CALORIES ~ SUGARS + FAT +  PROTEIN + CARBO + O58))

Call:
lm(formula = CALORIES ~ SUGARS + FAT + PROTEIN + CARBO + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.2166  -3.0019  -0.1584   2.5043  16.5380 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.04175    3.92730   0.011    0.992    
SUGARS       3.94232    0.16534  23.844  < 2e-16 ***
FAT          8.59671    0.63562  13.525  < 2e-16 ***
PROTEIN      4.15389    0.59962   6.928 1.59e-09 ***
CARBO        4.06656    0.17194  23.651  < 2e-16 ***
O58TRUE     70.00425    6.07124  11.530  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 4.987 on 71 degrees of freedom
Multiple R-squared: 0.9388,	Adjusted R-squared: 0.9345 
F-statistic: 217.8 on 5 and 71 DF,  p-value: < 2.2e-16 

> plot(lm(CALORIES ~ SUGARS + FAT +  PROTEIN + CARBO + O58))
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Warning messages:
1: Not plotting observations with leverage one:
  58 
2: Not plotting observations with leverage one:
  58 
> cereal[30:40,]
                          NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
30              Fruity_Pebbles      110       1   1    135   0.0  13.0     12     2
31                Golden_Crisp      100       2   0     45   0.0  11.0     15     1
32              Golden_Grahams      110       1   1    280   0.0  15.0      9     2
33           Grape_Nuts_Flakes      100       3   1    140   3.0  15.0      5     3
34                  Grape-Nuts      110       3   0    170   3.0  17.0      3     3
35          Great_Grains_Pecan      120       3   3     75   3.0  13.0      4     3
36            Honey_Graham_Ohs      120       1   2    220   1.0  12.0     11     2
37          Honey_Nut_Cheerios      110       3   1    250   1.5  11.5     10     1
38                  Honey-comb      110       1   0    180   0.0  14.0     11     1
39 Just_Right_Crunchy__Nuggets      110       2   1    170   1.0  17.0      6     3
40      Just_Right_Fruit_&_Nut      140       3   1    170   2.0  20.0      9     3
> cereal[68,]
        NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
68 Special_K      110       6   0    230     1    16      3     1
> plot(lm(CALORIES ~ SUGARS + factor(SHELF)))
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
> lm(CALORIES ~ SUGARS + factor(SHELF))

Call:
lm(formula = CALORIES ~ SUGARS + factor(SHELF))

Coefficients:
   (Intercept)          SUGARS  factor(SHELF)2  factor(SHELF)3  
       89.5592          2.6960         -5.9683          0.6197  

> summary(lm(CALORIES ~ SUGARS + factor(SHELF)))

Call:
lm(formula = CALORIES ~ SUGARS + factor(SHELF))

Residuals:
     Min       1Q   Median       3Q      Max 
-40.1789  -7.9228   0.4408  11.7331  34.7732 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     89.5592     4.2393  21.126  < 2e-16 ***
SUGARS           2.6960     0.4579   5.887 1.11e-07 ***
factor(SHELF)2  -5.9683     5.5249  -1.080    0.284    
factor(SHELF)3   0.6197     4.5898   0.135    0.893    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 16.21 on 73 degrees of freedom
Multiple R-squared: 0.3351,	Adjusted R-squared: 0.3078 
F-statistic: 12.26 on 3 and 73 DF,  p-value: 1.389e-06 

> summary(lm(CALORIES ~ SUGARS + factor(SHELF) + O58))

Call:
lm(formula = CALORIES ~ SUGARS + factor(SHELF) + O58)

Residuals:
    Min      1Q  Median      3Q     Max 
-39.749  -8.415   0.918  11.965  34.347 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     88.5316     4.4198  20.031  < 2e-16 ***
SUGARS           2.7619     0.4655   5.933 9.52e-08 ***
factor(SHELF)2  -5.5742     5.5557  -1.003    0.319    
factor(SHELF)3   1.2174     4.6535   0.262    0.794    
O58TRUE         14.2303    16.9061   0.842    0.403    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 16.24 on 72 degrees of freedom
Multiple R-squared: 0.3416,	Adjusted R-squared: 0.305 
F-statistic: 9.337 on 4 and 72 DF,  p-value: 3.894e-06 

> summary(lm(CALORIES ~ SUGARS + factor(SHELF) + O58))

Call:
lm(formula = CALORIES ~ SUGARS + factor(SHELF) + O58)

Residuals:
    Min      1Q  Median      3Q     Max 
-39.749  -8.415   0.918  11.965  34.347 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     88.5316     4.4198  20.031  < 2e-16 ***
SUGARS           2.7619     0.4655   5.933 9.52e-08 ***
factor(SHELF)2  -5.5742     5.5557  -1.003    0.319    
factor(SHELF)3   1.2174     4.6535   0.262    0.794    
O58TRUE         14.2303    16.9061   0.842    0.403    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 16.24 on 72 degrees of freedom
Multiple R-squared: 0.3416,	Adjusted R-squared: 0.305 
F-statistic: 9.337 on 4 and 72 DF,  p-value: 3.894e-06 

> summary(lm(CALORIES ~ SUGARS + factor(SHELF)*SUGARS + O58))

Call:
lm(formula = CALORIES ~ SUGARS + factor(SHELF) * SUGARS + O58)

Residuals:
      Min        1Q    Median        3Q       Max 
-35.01861  -5.93020  -0.01600   9.14169  29.75349 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            98.3314     4.9146  20.008  < 2e-16 ***
SUGARS                  0.8423     0.7318   1.151 0.253626    
factor(SHELF)2          0.8613     9.2711   0.093 0.926243    
factor(SHELF)3        -24.6802     6.7502  -3.656 0.000491 ***
O58TRUE                 2.5109    14.9629   0.168 0.867217    
SUGARS:factor(SHELF)2   0.2317     1.0506   0.221 0.826073    
SUGARS:factor(SHELF)3   4.3856     0.9548   4.593 1.88e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.92 on 70 degrees of freedom
Multiple R-squared:  0.53,	Adjusted R-squared: 0.4897 
F-statistic: 13.15 on 6 and 70 DF,  p-value: 6.572e-10 

> summary(lm(CALORIES ~ SUGARS + (SHELF==3)*SUGARS + O58))

Call:
lm(formula = CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-35.0186  -5.7355  -0.2465   8.8490  29.7535 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            98.1539     4.0495  24.238  < 2e-16 ***
SUGARS                  1.0831     0.4570   2.370 0.020466 *  
SHELF == 3TRUE        -24.5027     6.1082  -4.011 0.000146 ***
O58TRUE                 2.9292    14.4543   0.203 0.839981    
SUGARS:SHELF == 3TRUE   4.1448     0.7591   5.460 6.43e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.75 on 72 degrees of freedom
Multiple R-squared: 0.5279,	Adjusted R-squared: 0.5016 
F-statistic: 20.12 on 4 and 72 DF,  p-value: 3.696e-11 

> plot(lm(CALORIES ~ SUGARS + (SHELF==3)*SUGARS + O58))
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Warning messages:
1: Not plotting observations with leverage one:
  58 
2: Not plotting observations with leverage one:
  58 
> cereal[53,]
                    NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
53 Post_Nat._Raisin_Bran      120       3   1    200     6    11     14     3
> plot(lm(CALORIES ~ SUGARS + FAT + (SHELF==3)*SUGARS + O58))
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Warning messages:
1: Not plotting observations with leverage one:
  58 
2: Not plotting observations with leverage one:
  58 
> summary(lm(CALORIES ~ SUGARS + FAT + (SHELF==3)*SUGARS + O58))

Call:
lm(formula = CALORIES ~ SUGARS + FAT + (SHELF == 3) * SUGARS + 
    O58)

Residuals:
      Min        1Q    Median        3Q       Max 
-34.07000  -5.64836   0.03962   8.64092  26.08366 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            95.6484     3.8885  24.598  < 2e-16 ***
SUGARS                  0.8626     0.4353   1.981  0.05143 .  
FAT                     5.3600     1.6660   3.217  0.00195 ** 
SHELF == 3TRUE        -23.8562     5.7499  -4.149 9.14e-05 ***
O58TRUE                -5.5059    13.8486  -0.398  0.69213    
SUGARS:SHELF == 3TRUE   3.6237     0.7323   4.949 4.85e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 12.94 on 71 degrees of freedom
Multiple R-squared: 0.5879,	Adjusted R-squared: 0.5589 
F-statistic: 20.26 on 5 and 71 DF,  p-value: 1.667e-12 

> summary(lm(CALORIES ~ SUGARS + CARBO + (SHELF==3)*SUGARS + O58))

Call:
lm(formula = CALORIES ~ SUGARS + CARBO + (SHELF == 3) * SUGARS + 
    O58)

Residuals:
    Min      1Q  Median      3Q     Max 
-17.963  -4.297  -1.578   4.399  30.536 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            38.2898     7.4631   5.131 2.41e-06 ***
SUGARS                  3.0037     0.3897   7.709 5.80e-11 ***
CARBO                   3.0187     0.3480   8.675 9.39e-13 ***
SHELF == 3TRUE         -9.8832     4.6052  -2.146   0.0353 *  
O58TRUE                67.7327    12.5963   5.377 9.19e-07 ***
SUGARS:SHELF == 3TRUE   2.4498     0.5673   4.318 5.01e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 9.651 on 71 degrees of freedom
Multiple R-squared: 0.7708,	Adjusted R-squared: 0.7546 
F-statistic: 47.75 on 5 and 71 DF,  p-value: < 2.2e-16 

> plot(lm(CALORIES ~ SUGARS + CARBO + (SHELF==3)*SUGARS + O58))
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Warning messages:
1: Not plotting observations with leverage one:
  58 
2: Not plotting observations with leverage one:
  58 
> cereal[35,]
                 NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
35 Great_Grains_Pecan      120       3   3     75     3    13      4     3
> O35
Error: object 'O35' not found
> O35=(NAME==NAME[35])
> plot(lm(CALORIES ~ SUGARS + CARBO + (SHELF==3)*SUGARS + O58 + O35))
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Warning messages:
1: Not plotting observations with leverage one:
  35, 58 
2: Not plotting observations with leverage one:
  35, 58 
> summar(lm(CALORIES ~ SUGARS + CARBO + (SHELF==3)*SUGARS + O58 + O35))
Error: could not find function "summar"
> summary(lm(CALORIES ~ SUGARS + CARBO + (SHELF==3)*SUGARS + O58 + O35))

Call:
lm(formula = CALORIES ~ SUGARS + CARBO + (SHELF == 3) * SUGARS + 
    O58 + O35)

Residuals:
    Min      1Q  Median      3Q     Max 
-18.041  -3.999  -0.910   4.534  24.920 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            36.8990     6.9515   5.308 1.24e-06 ***
SUGARS                  3.0484     0.3626   8.408 3.24e-12 ***
CARBO                   3.0889     0.3242   9.527 2.88e-14 ***
SHELF == 3TRUE        -11.4541     4.3061  -2.660 0.009682 ** 
O58TRUE                69.2383    11.7213   5.907 1.14e-07 ***
O35TRUE                31.9376     9.1783   3.480 0.000868 ***
SUGARS:SHELF == 3TRUE   2.5672     0.5286   4.856 7.03e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 8.975 on 70 degrees of freedom
Multiple R-squared: 0.8046,	Adjusted R-squared: 0.7878 
F-statistic: 48.04 on 6 and 70 DF,  p-value: < 2.2e-16 

> cereal[35,]
                 NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
35 Great_Grains_Pecan      120       3   3     75     3    13      4     3
> plot(lm(CALORIES ~ SUGARS + CARBO + (SHELF==3)*SUGARS + O58))
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Warning messages:
1: Not plotting observations with leverage one:
  58 
2: Not plotting observations with leverage one:
  58 
> summary(lm(CALORIES ~ SUGARS + FAT +  PROTEIN + CARBO + O58))

Call:
lm(formula = CALORIES ~ SUGARS + FAT + PROTEIN + CARBO + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.2166  -3.0019  -0.1584   2.5043  16.5380 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.04175    3.92730   0.011    0.992    
SUGARS       3.94232    0.16534  23.844  < 2e-16 ***
FAT          8.59671    0.63562  13.525  < 2e-16 ***
PROTEIN      4.15389    0.59962   6.928 1.59e-09 ***
CARBO        4.06656    0.17194  23.651  < 2e-16 ***
O58TRUE     70.00425    6.07124  11.530  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 4.987 on 71 degrees of freedom
Multiple R-squared: 0.9388,	Adjusted R-squared: 0.9345 
F-statistic: 217.8 on 5 and 71 DF,  p-value: < 2.2e-16 

> plot(lm(CALORIES ~ (SHELF==3) + O58))
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Warning messages:
1: Not plotting observations with leverage one:
  58 
2: Not plotting observations with leverage one:
  58 
> summary(lm(CALORIES ~ (SHELF==3) + O58))

Call:
lm(formula = CALORIES ~ (SHELF == 3) + O58)

Residuals:
    Min      1Q  Median      3Q     Max 
-57.778  -7.778   3.750   3.750  52.222 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     106.250      3.117  34.087   <2e-16 ***
SHELF == 3TRUE    1.528      4.529   0.337    0.737    
O58TRUE          -6.250     19.959  -0.313    0.755    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 19.71 on 74 degrees of freedom
Multiple R-squared: 0.003197,	Adjusted R-squared: -0.02374 
F-statistic: 0.1187 on 2 and 74 DF,  p-value: 0.8883 

> cor(CALORIES, cereal)
     NAME CALORIES    PROTEIN       FAT    SODIUM      FIBER     CARBO    SUGARS      SHELF
[1,]   NA        1 0.01906607 0.4986098 0.3006492 -0.2934128 0.2506809 0.5623403 0.09723437
Warning message:
In cor(CALORIES, cereal) : NAs introduced by coercion
> cor(residuals(lm(CALORIES ~ (SHELF==3) + O58))), cereal)
Error: unexpected ',' in "cor(residuals(lm(CALORIES ~ (SHELF==3) + O58))),"
> cor(residuals(lm(CALORIES ~ (SHELF==3) + O58)))), cereal)
Error: unexpected ')' in "cor(residuals(lm(CALORIES ~ (SHELF==3) + O58))))"
> cor(residuals(lm(CALORIES ~ (SHELF==3) + O58)), cereal)
     NAME  CALORIES    PROTEIN       FAT    SODIUM      FIBER     CARBO    SUGARS      SHELF
[1,]   NA 0.9984005 0.01784847 0.4947938 0.2935511 -0.3083158 0.2365196 0.5590068 0.05585689
Warning message:
In cor(residuals(lm(CALORIES ~ (SHELF == 3) + O58)), cereal) :
  NAs introduced by coercion
> cor(residuals(lm(CALORIES ~ SUGARS + (SHELF==3) + O58)), cereal)
     NAME  CALORIES   PROTEIN       FAT    SODIUM      FIBER     CARBO       SUGARS       SHELF
[1,]   NA 0.8170976 0.1977709 0.3741946 0.3208757 -0.3091423 0.5960541 3.820425e-17 -0.04730387
Warning message:
In cor(residuals(lm(CALORIES ~ SUGARS + (SHELF == 3) + O58)), cereal) :
  NAs introduced by coercion
> cor(residuals(lm(CALORIES ~ SUGARS + (SHELF==3)*SUGARS + O58)), cereal)
     NAME  CALORIES    PROTEIN       FAT    SODIUM      FIBER     CARBO       SUGARS      SHELF
[1,]   NA 0.6871275 0.01075755 0.3157862 0.3449438 -0.4405689 0.5332898 5.334131e-18 0.02359141
Warning message:
In cor(residuals(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS +  :
  NAs introduced by coercion
> summary(lm(CALORIES ~ SUGARS + (SHELF==3)*SUGARS + O58))

Call:
lm(formula = CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-35.0186  -5.7355  -0.2465   8.8490  29.7535 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            98.1539     4.0495  24.238  < 2e-16 ***
SUGARS                  1.0831     0.4570   2.370 0.020466 *  
SHELF == 3TRUE        -24.5027     6.1082  -4.011 0.000146 ***
O58TRUE                 2.9292    14.4543   0.203 0.839981    
SUGARS:SHELF == 3TRUE   4.1448     0.7591   5.460 6.43e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.75 on 72 degrees of freedom
Multiple R-squared: 0.5279,	Adjusted R-squared: 0.5016 
F-statistic: 20.12 on 4 and 72 DF,  p-value: 3.696e-11 

> cor(residuals(lm(CALORIES ~ SUGARS + (SHELF==3)*SUGARS + O58)), cereal)
     NAME  CALORIES    PROTEIN       FAT    SODIUM      FIBER     CARBO       SUGARS      SHELF
[1,]   NA 0.6871275 0.01075755 0.3157862 0.3449438 -0.4405689 0.5332898 5.334131e-18 0.02359141
Warning message:
In cor(residuals(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS +  :
  NAs introduced by coercion
> cor(residuals(lm(CALORIES ~ SUGARS + (SHELF==3)*SUGARS + CARBO+ O58)), cereal)
     NAME  CALORIES   PROTEIN       FAT    SODIUM       FIBER       CARBO       SUGARS      SHELF
[1,]   NA 0.4787633 0.3012435 0.6828687 0.1225120 -0.09037323 4.41713e-17 5.945216e-17 0.04371924
Warning message:
In cor(residuals(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS +  :
  NAs introduced by coercion
> summary(lm(CALORIES ~ SUGARS + (SHELF==3)*SUGARS + CARBO + O58))

Call:
lm(formula = CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + CARBO + 
    O58)

Residuals:
    Min      1Q  Median      3Q     Max 
-17.963  -4.297  -1.578   4.399  30.536 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            38.2898     7.4631   5.131 2.41e-06 ***
SUGARS                  3.0037     0.3897   7.709 5.80e-11 ***
SHELF == 3TRUE         -9.8832     4.6052  -2.146   0.0353 *  
CARBO                   3.0187     0.3480   8.675 9.39e-13 ***
O58TRUE                67.7327    12.5963   5.377 9.19e-07 ***
SUGARS:SHELF == 3TRUE   2.4498     0.5673   4.318 5.01e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 9.651 on 71 degrees of freedom
Multiple R-squared: 0.7708,	Adjusted R-squared: 0.7546 
F-statistic: 47.75 on 5 and 71 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ SUGARS + (SHELF==3)*SUGARS + CARBO + (SHELF==3)*CARBO + O58))

Call:
lm(formula = CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + CARBO + 
    (SHELF == 3) * CARBO + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-16.9788  -4.1657  -0.2656   4.2266  31.1059 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            65.8016    15.5283   4.238 6.77e-05 ***
SUGARS                  2.1211     0.5821   3.644 0.000512 ***
SHELF == 3TRUE        -42.4545    16.8356  -2.522 0.013957 *  
CARBO                   1.6314     0.7704   2.118 0.037752 *  
O58TRUE                37.9509    19.2907   1.967 0.053111 .  
SUGARS:SHELF == 3TRUE   3.3578     0.7163   4.688 1.32e-05 ***
SHELF == 3TRUE:CARBO    1.7249     0.8590   2.008 0.048498 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 9.451 on 70 degrees of freedom
Multiple R-squared: 0.7833,	Adjusted R-squared: 0.7647 
F-statistic: 42.16 on 6 and 70 DF,  p-value: < 2.2e-16 

> plot(lm(CALORIES ~ SUGARS + (SHELF==3)*SUGARS + CARBO + (SHELF==3)*CARBO + O58))
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Warning messages:
1: Not plotting observations with leverage one:
  58 
2: Not plotting observations with leverage one:
  58 
> summary(lm(CALORIES ~ SUGARS + factor(SHELF) + O58))

Call:
lm(formula = CALORIES ~ SUGARS + factor(SHELF) + O58)

Residuals:
    Min      1Q  Median      3Q     Max 
-39.749  -8.415   0.918  11.965  34.347 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     88.5316     4.4198  20.031  < 2e-16 ***
SUGARS           2.7619     0.4655   5.933 9.52e-08 ***
factor(SHELF)2  -5.5742     5.5557  -1.003    0.319    
factor(SHELF)3   1.2174     4.6535   0.262    0.794    
O58TRUE         14.2303    16.9061   0.842    0.403    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 16.24 on 72 degrees of freedom
Multiple R-squared: 0.3416,	Adjusted R-squared: 0.305 
F-statistic: 9.337 on 4 and 72 DF,  p-value: 3.894e-06 

> summary(lm(CALORIES ~ SUGARS + factor(SHELF) + O58))

Call:
lm(formula = CALORIES ~ SUGARS + factor(SHELF) + O58)

Residuals:
    Min      1Q  Median      3Q     Max 
-39.749  -8.415   0.918  11.965  34.347 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     88.5316     4.4198  20.031  < 2e-16 ***
SUGARS           2.7619     0.4655   5.933 9.52e-08 ***
factor(SHELF)2  -5.5742     5.5557  -1.003    0.319    
factor(SHELF)3   1.2174     4.6535   0.262    0.794    
O58TRUE         14.2303    16.9061   0.842    0.403    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 16.24 on 72 degrees of freedom
Multiple R-squared: 0.3416,	Adjusted R-squared: 0.305 
F-statistic: 9.337 on 4 and 72 DF,  p-value: 3.894e-06 

> cor(CALORIES, ceral)
Error in inherits(x, "data.frame") : object 'ceral' not found
> cor(CALORIES, cereaal)
Error in inherits(x, "data.frame") : object 'cereaal' not found
> cor(CALORIES, cereal)
     NAME CALORIES    PROTEIN       FAT    SODIUM      FIBER     CARBO    SUGARS      SHELF
[1,]   NA        1 0.01906607 0.4986098 0.3006492 -0.2934128 0.2506809 0.5623403 0.09723437
Warning message:
In cor(CALORIES, cereal) : NAs introduced by coercion
> summary(lm(CALORIES ~ SUGARS + (SHELF==3)*SUGARS +  O58))

Call:
lm(formula = CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-35.0186  -5.7355  -0.2465   8.8490  29.7535 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            98.1539     4.0495  24.238  < 2e-16 ***
SUGARS                  1.0831     0.4570   2.370 0.020466 *  
SHELF == 3TRUE        -24.5027     6.1082  -4.011 0.000146 ***
O58TRUE                 2.9292    14.4543   0.203 0.839981    
SUGARS:SHELF == 3TRUE   4.1448     0.7591   5.460 6.43e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.75 on 72 degrees of freedom
Multiple R-squared: 0.5279,	Adjusted R-squared: 0.5016 
F-statistic: 20.12 on 4 and 72 DF,  p-value: 3.696e-11 

> cereal[58,]
             NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
58 Quaker_Oatmeal      100       5   2      0   2.7    -1     -1     1
> summary(lm(CALORIES ~ CARBO + (SHELF==3)*SUGARS +  O58))

Call:
lm(formula = CALORIES ~ CARBO + (SHELF == 3) * SUGARS + O58)

Residuals:
    Min      1Q  Median      3Q     Max 
-17.963  -4.297  -1.578   4.399  30.536 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            38.2898     7.4631   5.131 2.41e-06 ***
CARBO                   3.0187     0.3480   8.675 9.39e-13 ***
SHELF == 3TRUE         -9.8832     4.6052  -2.146   0.0353 *  
SUGARS                  3.0037     0.3897   7.709 5.80e-11 ***
O58TRUE                67.7327    12.5963   5.377 9.19e-07 ***
SHELF == 3TRUE:SUGARS   2.4498     0.5673   4.318 5.01e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 9.651 on 71 degrees of freedom
Multiple R-squared: 0.7708,	Adjusted R-squared: 0.7546 
F-statistic: 47.75 on 5 and 71 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ CARBO + (SHELF==3)*CARBO +  O58))

Call:
lm(formula = CALORIES ~ CARBO + (SHELF == 3) * CARBO + O58)

Residuals:
    Min      1Q  Median      3Q     Max 
-53.252  -9.234   1.498   9.553  44.680 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)          117.2880    12.1328   9.667 1.21e-14 ***
CARBO                 -0.7322     0.7829  -0.935  0.35277    
SHELF == 3TRUE       -53.2551    16.2252  -3.282  0.00159 ** 
O58TRUE              -18.0202    21.9845  -0.820  0.41511    
CARBO:SHELF == 3TRUE   3.7491     1.0597   3.538  0.00071 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 17.81 on 72 degrees of freedom
Multiple R-squared: 0.2089,	Adjusted R-squared: 0.1649 
F-statistic: 4.752 on 4 and 72 DF,  p-value: 0.001851 

> summary(lm(CALORIES ~ SUGAR + CARBO + (SHELF==3)*CARBO +  O58))
Error in eval(expr, envir, enclos) : object 'SUGAR' not found
> summary(lm(CALORIES ~ SUGARS + CARBO + (SHELF==3)*CARBO +  O58))

Call:
lm(formula = CALORIES ~ SUGARS + CARBO + (SHELF == 3) * CARBO + 
    O58)

Residuals:
    Min      1Q  Median      3Q     Max 
-24.529  -7.133  -2.558   5.372  28.117 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)           11.9786    11.8983   1.007   0.3175    
SUGARS                 4.3384     0.3861  11.236  < 2e-16 ***
CARBO                  4.1023     0.6394   6.416 1.36e-08 ***
SHELF == 3TRUE        19.8373    11.7647   1.686   0.0962 .  
O58TRUE               96.4621    16.7399   5.762 1.98e-07 ***
CARBO:SHELF == 3TRUE  -0.8166     0.7583  -1.077   0.2852    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 10.76 on 71 degrees of freedom
Multiple R-squared: 0.7152,	Adjusted R-squared: 0.6952 
F-statistic: 35.67 on 5 and 71 DF,  p-value: < 2.2e-16 

> plot(CALORIES ~ SUGARS)
> points(CALORIES[SHELF==1]  ~ SUGARS[SHELF==1])
> points(CALORIES[SHELF==1]  ~ SUGARS[SHELF==1], col='red')
> plot(CALORIES ~ SUGARS)
> points(CALORIES[SHELF==1]  ~ SUGARS[SHELF==1], col='red')
> points(CALORIES[SHELF==2]  ~ SUGARS[SHELF==2], col='blue')
> summary(lm(CALORIES ~ SUGARS  + (SHELF==3)*SUGARS +  O58))

Call:
lm(formula = CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-35.0186  -5.7355  -0.2465   8.8490  29.7535 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            98.1539     4.0495  24.238  < 2e-16 ***
SUGARS                  1.0831     0.4570   2.370 0.020466 *  
SHELF == 3TRUE        -24.5027     6.1082  -4.011 0.000146 ***
O58TRUE                 2.9292    14.4543   0.203 0.839981    
SUGARS:SHELF == 3TRUE   4.1448     0.7591   5.460 6.43e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.75 on 72 degrees of freedom
Multiple R-squared: 0.5279,	Adjusted R-squared: 0.5016 
F-statistic: 20.12 on 4 and 72 DF,  p-value: 3.696e-11 

> abline(lm(CALORIES ~ SUGARS  + (SHELF==3)*SUGARS +  O58))
Warning message:
In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58)) :
  only using the first two of 5regression coefficients
> abline(lm(CALORIES[SHELF==3] ~ SUGARS[SHELF==3] +  O58))
Error in model.frame.default(formula = CALORIES[SHELF == 3] ~ SUGARS[SHELF ==  : 
  variable lengths differ (found for 'O58')
> abline(lm(CALORIES[SHELF==3] ~ SUGARS[SHELF==3] +  O58[SHELF==3]))
Warning message:
In abline(lm(CALORIES[SHELF == 3] ~ SUGARS[SHELF == 3] + O58[SHELF ==  :
  only using the first two of 3regression coefficients
> abline(lm(CALORIES ~ SUGARS  + (SHELF==3)*SUGARS +  O58), col='purple')
Warning message:
In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58), col = "purple") :
  only using the first two of 5regression coefficients
> plot(CALORIES ~ SUGARS)
> points(CALORIES[58] ~ SUGARS[58])
> ?points
> points(CALORIES[58] ~ SUGARS[58], pch=22, col='green')
> points(CALORIES[58] ~ SUGARS[58], col='green', pch=22)
> points(CALORIES[58] ~ SUGARS[58], col='green', pch=18)
> points(CALORIES[58] ~ SUGARS[58], col='green', pch=25)
> points(CALORIES[58] ~ SUGARS[58], col='black', pch=25)
> points(CALORIES[58] ~ SUGARS[58], col='black', pch=25, bg='black')
> draw_picture=edit()
Error in edit(name, file, title, editor) : unable to open file to read
> draw_picture=edit(draw_picture)
Error in edit(draw_picture) : object 'draw_picture' not found
> draw_picture=function
+ ;
Error: unexpected ';' in:
"draw_picture=function
;"
> draw_picture=function()
+ {}
> draw_picture=edit(draw_picture)
> draw_picture
function()
{
	plot(CALORIES ~ SUGARS)
	points(CALORIES[58] ~ SUGARS[58], col='black', bg='black', pch=25)
	
}
> 
> draw_picture=edit(draw_picture)
> 
> draw_picture=edit(draw_picture)
> draw_picture
function()
{
	# Draw all points, set up plotting field
	plot(CALORIES ~ SUGARS)
	# draw the outlier (Quaker oats)with a different symbol
	points(CALORIES[58] ~ SUGARS[58], col='black', bg='black', pch=25)
	# draw the shelf 1 and shelf 2 cereals with a different color
	points(CALORIES[SHELF==1]  ~ SUGARS[SHELF==1], col='red')
	points(CALORIES[SHELF==2]  ~ SUGARS[SHELF==2], col='blue')
	
	# draw the regression line for the two interesting subpops
	abline(lm(CALORIES ~ SUGARS  + (SHELF==3)*SUGARS +  O58), col='purple')
	abline(lm(CALORIES[SHELF==3] ~ SUGARS[SHELF==3] +  O58[SHELF==3]))
}
> draw_picture()
Warning messages:
1: In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58), col = "purple") :
  only using the first two of 5regression coefficients
2: In abline(lm(CALORIES[SHELF == 3] ~ SUGARS[SHELF == 3] + O58[SHELF ==  :
  only using the first two of 3regression coefficients
> ?key
No documentation for 'key' in specified packages and libraries:
you could try '??key'
> ?plot
> ?legend
> draw_picture=edit(draw_picture)
> draw_picture=edit(draw_picture)
> draw_picture()
Warning messages:
1: In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58), col = "purple") :
  only using the first two of 5regression coefficients
2: In abline(lm(CALORIES[SHELF == 3] ~ SUGARS[SHELF == 3] + O58[SHELF ==  :
  only using the first two of 3regression coefficients
3: In legend(-1, 1.9, c("sin", "cos", "tan"), col = c("red", "blue",  :
  'merge = TRUE' has no effect when no line segments are drawn
> draw_picture=edit(draw_picture)
> draw_picture()
Warning messages:
1: In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58), col = "purple") :
  only using the first two of 5regression coefficients
2: In abline(lm(CALORIES[SHELF == 3] ~ SUGARS[SHELF == 3] + O58[SHELF ==  :
  only using the first two of 3regression coefficients
> draw_picture=edit(draw_picture)
> draw_picture()
Warning messages:
1: In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58), col = "purple") :
  only using the first two of 5regression coefficients
2: In abline(lm(CALORIES[SHELF == 3] ~ SUGARS[SHELF == 3] + O58[SHELF ==  :
  only using the first two of 3regression coefficients
> draw_picture=edit(draw_picture)
> draw_picture()
Warning messages:
1: In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58), col = "purple") :
  only using the first two of 5regression coefficients
2: In abline(lm(CALORIES[SHELF == 3] ~ SUGARS[SHELF == 3] + O58[SHELF ==  :
  only using the first two of 3regression coefficients
> draw_picture=edit(draw_picture)
> draw_picture()
Warning messages:
1: In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58), col = "purple") :
  only using the first two of 5regression coefficients
2: In abline(lm(CALORIES[SHELF == 3] ~ SUGARS[SHELF == 3] + O58[SHELF ==  :
  only using the first two of 3regression coefficients
> draw_picture=edit(draw_picture)
Error in edit(name, file, title, editor) : 
  unexpected ',' occurred on line 15
 use a command like
 x <- edit()
 to recover
> draw_picture=edit(draw_picture)
> draw_picture()
Warning messages:
1: In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58), col = "purple") :
  only using the first two of 5regression coefficients
2: In abline(lm(CALORIES[SHELF == 3] ~ SUGARS[SHELF == 3] + O58[SHELF ==  :
  only using the first two of 3regression coefficients
> ?pch
> draw_picture=edit(draw_picture)
> draw_picture()
Warning messages:
1: In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58), col = "purple") :
  only using the first two of 5regression coefficients
2: In abline(lm(CALORIES[SHELF == 3] ~ SUGARS[SHELF == 3] + O58[SHELF ==  :
  only using the first two of 3regression coefficients
> ?legend
> draw_picture=edit(draw_picture)
> draw_picture()
Warning messages:
1: In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58), col = "purple") :
  only using the first two of 5regression coefficients
2: In abline(lm(CALORIES[SHELF == 3] ~ SUGARS[SHELF == 3] + O58[SHELF ==  :
  only using the first two of 3regression coefficients
> draw_picture=edit(draw_picture)
> draw_picture()
Warning messages:
1: In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58), col = "purple") :
  only using the first two of 5regression coefficients
2: In abline(lm(CALORIES[SHELF == 3] ~ SUGARS[SHELF == 3] + O58[SHELF ==  :
  only using the first two of 3regression coefficients
> draw_picture
function()
{
	# Draw all points, set up plotting field
	plot(CALORIES ~ SUGARS)
	# draw the outlier (Quaker oats)with a different symbol
	points(CALORIES[58] ~ SUGARS[58], col='black', bg='black', pch=25)
	# draw the shelf 1 and shelf 2 cereals with a different color
	points(CALORIES[SHELF==1]  ~ SUGARS[SHELF==1], col='red')
	points(CALORIES[SHELF==2]  ~ SUGARS[SHELF==2], col='blue')
	
	# draw the regression line for the two interesting subpops
	abline(lm(CALORIES ~ SUGARS  + (SHELF==3)*SUGARS +  O58), col='purple')
	abline(lm(CALORIES[SHELF==3] ~ SUGARS[SHELF==3] +  O58[SHELF==3]))

	# Add a key
	legend(0, 160, c("Shelf 1", "Shelf 2", "Shelf 3"), col = c('red','blue','black'), pch=c(21,21,21), title='Key:')
}
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> plot(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN + O58))
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Warning messages:
1: Not plotting observations with leverage one:
  58 
2: Not plotting observations with leverage one:
  58 
> cereal[1,]
       NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
1 100%_Bran       70       4   1    130    10     5      6     3
> summary(lm(CALORIES ~ PROTEIN + FAT + SODIUM + FIBER + CARBO + SUGARS + factor(SHELF)))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + SODIUM + FIBER + CARBO + 
    SUGARS + factor(SHELF))

Residuals:
    Min      1Q  Median      3Q     Max 
-15.459  -3.777  -1.011   2.886  40.640 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    23.517108   6.492319   3.622 0.000558 ***
PROTEIN         5.562041   1.133009   4.909 6.02e-06 ***
FAT             8.520430   1.132547   7.523 1.61e-10 ***
SODIUM          0.001287   0.012950   0.099 0.921116    
FIBER          -1.061850   0.554075  -1.916 0.059513 .  
CARBO           2.837985   0.308606   9.196 1.50e-13 ***
SUGARS          3.302795   0.279079  11.835  < 2e-16 ***
factor(SHELF)2 -2.755322   2.928959  -0.941 0.350180    
factor(SHELF)3 -1.885309   2.565114  -0.735 0.464879    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 8.298 on 68 degrees of freedom
Multiple R-squared: 0.8377,	Adjusted R-squared: 0.8186 
F-statistic: 43.88 on 8 and 68 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS + factor(SHELF)))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS + 
    factor(SHELF))

Residuals:
    Min      1Q  Median      3Q     Max 
-15.625  -3.935  -1.003   2.755  40.660 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     23.4785     6.4340   3.649 0.000507 ***
PROTEIN          5.5610     1.1248   4.944 5.16e-06 ***
FAT              8.5323     1.1181   7.631 9.45e-11 ***
FIBER           -1.0541     0.5446  -1.936 0.057023 .  
CARBO            2.8513     0.2761  10.327 1.22e-15 ***
SUGARS           3.3107     0.2655  12.470  < 2e-16 ***
factor(SHELF)2  -2.8034     2.8680  -0.977 0.331756    
factor(SHELF)3  -1.9232     2.5183  -0.764 0.447662    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 8.238 on 69 degrees of freedom
Multiple R-squared: 0.8377,	Adjusted R-squared: 0.8212 
F-statistic: 50.88 on 7 and 69 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS ))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS)

Residuals:
    Min      1Q  Median      3Q     Max 
-14.844  -3.592  -1.051   2.923  41.773 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  21.9038     6.1090   3.586 0.000614 ***
PROTEIN       5.7180     1.1057   5.172 2.06e-06 ***
FAT           8.3883     1.0643   7.881 2.77e-11 ***
FIBER        -1.0867     0.4975  -2.184 0.032234 *  
CARBO         2.8633     0.2663  10.752  < 2e-16 ***
SUGARS        3.2461     0.2550  12.732  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 8.183 on 71 degrees of freedom
Multiple R-squared: 0.8352,	Adjusted R-squared: 0.8236 
F-statistic: 71.98 on 5 and 71 DF,  p-value: < 2.2e-16 

> plot(lm(CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS ))
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
> plot(lm(CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS + O58))
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Warning messages:
1: Not plotting observations with leverage one:
  58 
2: Not plotting observations with leverage one:
  58 
> summary(lm(CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS + O58))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS + 
    O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.1891  -2.9905  -0.9437   2.5162  16.4884 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -1.2589     4.2917  -0.293    0.770    
PROTEIN       3.8860     0.6963   5.581 4.23e-07 ***
FAT           8.6983     0.6512  13.356  < 2e-16 ***
FIBER         0.2501     0.3277   0.763    0.448    
CARBO         4.1446     0.2005  20.675  < 2e-16 ***
SUGARS        3.9681     0.1692  23.449  < 2e-16 ***
O58TRUE      71.8695     6.5612  10.954  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 5.002 on 70 degrees of freedom
Multiple R-squared: 0.9393,	Adjusted R-squared: 0.9341 
F-statistic: 180.5 on 6 and 70 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ PROTEIN + FAT + SODIUM + FIBER + CARBO + SUGARS + factor(SHELF) + O58))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + SODIUM + FIBER + CARBO + 
    SUGARS + factor(SHELF) + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-11.7207  -3.2005  -0.7102   2.4930  16.1621 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    -1.338819   4.627467  -0.289    0.773    
PROTEIN         3.880558   0.714465   5.431 8.38e-07 ***
FAT             8.616332   0.696483  12.371  < 2e-16 ***
SODIUM         -0.001528   0.007968  -0.192    0.849    
FIBER           0.204418   0.360963   0.566    0.573    
CARBO           4.151360   0.226493  18.329  < 2e-16 ***
SUGARS          3.980146   0.183075  21.741  < 2e-16 ***
factor(SHELF)2  0.069617   1.820600   0.038    0.970    
factor(SHELF)3  0.667894   1.595545   0.419    0.677    
O58TRUE        72.282944   6.804783  10.622 5.25e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 5.102 on 67 degrees of freedom
Multiple R-squared: 0.9395,	Adjusted R-squared: 0.9314 
F-statistic: 115.7 on 9 and 67 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ PROTEIN + FAT + SODIUM + FIBER + CARBO + SUGARS + SHELF==3 + O58))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + SODIUM + FIBER + CARBO + 
    SUGARS + SHELF == 3 + O58)

Residuals:
    Min      1Q  Median      3Q     Max 
-56.883  -6.883   3.117   3.117  53.117 

Coefficients: (1 not defined because of singularities)
                                                                       Estimate Std. Error t value
(Intercept)                                                              106.88       2.22   48.14
PROTEIN + FAT + SODIUM + FIBER + CARBO + SUGARS + SHELF == 3 + O58TRUE       NA         NA      NA
                                                                       Pr(>|t|)    
(Intercept)                                                              <2e-16 ***
PROTEIN + FAT + SODIUM + FIBER + CARBO + SUGARS + SHELF == 3 + O58TRUE       NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 19.48 on 76 degrees of freedom

> summary(lm(CALORIES ~ PROTEIN + FAT + SODIUM + FIBER + CARBO + SUGARS + ()SHELF==3) + O58))
Error: unexpected ')' in "summary(lm(CALORIES ~ PROTEIN + FAT + SODIUM + FIBER + CARBO + SUGARS + ()"
> summary(lm(CALORIES ~ PROTEIN + FAT + SODIUM + FIBER + CARBO + SUGARS + (SHELF==3) + O58))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + SODIUM + FIBER + CARBO + 
    SUGARS + (SHELF == 3) + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-11.7788  -3.2365  -0.6895   2.4926  16.1724 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    -1.285751   4.381918  -0.293    0.770    
PROTEIN         3.877669   0.705224   5.498 6.24e-07 ***
FAT             8.617857   0.690215  12.486  < 2e-16 ***
SODIUM         -0.001576   0.007809  -0.202    0.841    
FIBER           0.203293   0.357111   0.569    0.571    
CARBO           4.150476   0.223651  18.558  < 2e-16 ***
SUGARS          3.981661   0.177423  22.442  < 2e-16 ***
SHELF == 3TRUE  0.635291   1.338694   0.475    0.637    
O58TRUE        72.244935   6.682184  10.812  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 5.065 on 68 degrees of freedom
Multiple R-squared: 0.9395,	Adjusted R-squared: 0.9324 
F-statistic: 132.1 on 8 and 68 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS + (SHELF==3) + O58))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS + 
    (SHELF == 3) + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-11.7685  -3.2703  -0.7307   2.5755  16.1492 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -1.1769     4.3183  -0.273    0.786    
PROTEIN          3.8777     0.7003   5.537 5.19e-07 ***
FAT              8.6042     0.6821  12.615  < 2e-16 ***
FIBER            0.1918     0.3501   0.548    0.586    
CARBO            4.1322     0.2031  20.345  < 2e-16 ***
SUGARS           3.9726     0.1704  23.315  < 2e-16 ***
SHELF == 3TRUE   0.6538     1.3262   0.493    0.624    
O58TRUE         72.1671     6.6245  10.894  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 5.029 on 69 degrees of freedom
Multiple R-squared: 0.9395,	Adjusted R-squared: 0.9334 
F-statistic: 153.1 on 7 and 69 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS + O58))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS + 
    O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.1891  -2.9905  -0.9437   2.5162  16.4884 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -1.2589     4.2917  -0.293    0.770    
PROTEIN       3.8860     0.6963   5.581 4.23e-07 ***
FAT           8.6983     0.6512  13.356  < 2e-16 ***
FIBER         0.2501     0.3277   0.763    0.448    
CARBO         4.1446     0.2005  20.675  < 2e-16 ***
SUGARS        3.9681     0.1692  23.449  < 2e-16 ***
O58TRUE      71.8695     6.5612  10.954  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 5.002 on 70 degrees of freedom
Multiple R-squared: 0.9393,	Adjusted R-squared: 0.9341 
F-statistic: 180.5 on 6 and 70 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ PROTEIN + FAT + CARBO + SUGARS + O58))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + CARBO + SUGARS + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.2166  -3.0019  -0.1584   2.5043  16.5380 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.04175    3.92730   0.011    0.992    
PROTEIN      4.15389    0.59962   6.928 1.59e-09 ***
FAT          8.59671    0.63562  13.525  < 2e-16 ***
CARBO        4.06656    0.17194  23.651  < 2e-16 ***
SUGARS       3.94232    0.16534  23.844  < 2e-16 ***
O58TRUE     70.00425    6.07124  11.530  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 4.987 on 71 degrees of freedom
Multiple R-squared: 0.9388,	Adjusted R-squared: 0.9345 
F-statistic: 217.8 on 5 and 71 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ SUGARS + O58))

Call:
lm(formula = CALORIES ~ SUGARS + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-39.1578  -9.5849   0.4151  10.8422  37.8795 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  89.1578     3.5429  25.165  < 2e-16 ***
SUGARS        2.5356     0.4287   5.914 9.58e-08 ***
O58TRUE      13.3778    16.7222   0.800    0.426    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 16.26 on 74 degrees of freedom
Multiple R-squared: 0.3221,	Adjusted R-squared: 0.3038 
F-statistic: 17.58 on 2 and 74 DF,  p-value: 5.667e-07 

> cor(residuals(lm(CALORIES ~ SUGARS + O58)), cereal)
     NAME  CALORIES   PROTEIN       FAT    SODIUM      FIBER     CARBO       SUGARS      SHELF
[1,]   NA 0.8233531 0.2297927 0.4045617 0.3147774 -0.2596833 0.5774692 6.393162e-17 0.06345195
Warning message:
In cor(residuals(lm(CALORIES ~ SUGARS + O58)), cereal) :
  NAs introduced by coercion
> cor(residuals(lm(CALORIES ~ SUGARS + CARBO + O58)), cereal)
     NAME  CALORIES   PROTEIN       FAT     SODIUM     FIBER        CARBO       SUGARS     SHELF
[1,]   NA 0.5699005 0.5175758 0.7694434 0.07948173 0.1515787 8.590074e-18 5.176803e-17 0.2786484
Warning message:
In cor(residuals(lm(CALORIES ~ SUGARS + CARBO + O58)), cereal) :
  NAs introduced by coercion
> cor(residuals(lm(CALORIES ~ SUGARS + CARBO + FAT+ O58)), cereal)
     NAME  CALORIES   PROTEIN          FAT    SODIUM     FIBER         CARBO        SUGARS     SHELF
[1,]   NA 0.3202921 0.5534573 2.276893e-17 0.0368857 0.3238235 -4.434146e-17 -7.297588e-18 0.1309996
Warning message:
In cor(residuals(lm(CALORIES ~ SUGARS + CARBO + FAT + O58)), cereal) :
  NAs introduced by coercion
> cor(residuals(lm(CALORIES ~ SUGARS + CARBO + FAT + PROTEIN+ O58)), cereal)
     NAME  CALORIES       PROTEIN          FAT      SODIUM      FIBER         CARBO       SUGARS
[1,]   NA 0.2474111 -4.040225e-17 8.821112e-18 -0.01334798 0.06674655 -3.444116e-17 1.862463e-17
          SHELF
[1,] 0.07296655
Warning message:
In cor(residuals(lm(CALORIES ~ SUGARS + CARBO + FAT + PROTEIN +  :
  NAs introduced by coercion
Fri Apr 30 11:01:34 slick.local R[1801] <Error>: kCGErrorIllegalArgument: CGSShapeWindow
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> summary(lm(CALORIES ~ SUGAR + FAT + PROTEIN + CARBO + FIBER + O58))
Error in eval(expr, envir, enclos) : object 'SUGAR' not found
> summary(lm(CALORIES ~ SUGARS + FAT + PROTEIN + CARBO + FIBER + O58))

Call:
lm(formula = CALORIES ~ SUGARS + FAT + PROTEIN + CARBO + FIBER + 
    O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.1891  -2.9905  -0.9437   2.5162  16.4884 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -1.2589     4.2917  -0.293    0.770    
SUGARS        3.9681     0.1692  23.449  < 2e-16 ***
FAT           8.6983     0.6512  13.356  < 2e-16 ***
PROTEIN       3.8860     0.6963   5.581 4.23e-07 ***
CARBO         4.1446     0.2005  20.675  < 2e-16 ***
FIBER         0.2501     0.3277   0.763    0.448    
O58TRUE      71.8695     6.5612  10.954  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 5.002 on 70 degrees of freedom
Multiple R-squared: 0.9393,	Adjusted R-squared: 0.9341 
F-statistic: 180.5 on 6 and 70 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ SUGARS + FAT + PROTEIN + CARBO + O58))

Call:
lm(formula = CALORIES ~ SUGARS + FAT + PROTEIN + CARBO + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.2166  -3.0019  -0.1584   2.5043  16.5380 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.04175    3.92730   0.011    0.992    
SUGARS       3.94232    0.16534  23.844  < 2e-16 ***
FAT          8.59671    0.63562  13.525  < 2e-16 ***
PROTEIN      4.15389    0.59962   6.928 1.59e-09 ***
CARBO        4.06656    0.17194  23.651  < 2e-16 ***
O58TRUE     70.00425    6.07124  11.530  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 4.987 on 71 degrees of freedom
Multiple R-squared: 0.9388,	Adjusted R-squared: 0.9345 
F-statistic: 217.8 on 5 and 71 DF,  p-value: < 2.2e-16 

> 
> cereal[58,]
             NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
58 Quaker_Oatmeal      100       5   2      0   2.7    -1     -1     1
> summary(lm(CALORIES ~ SUGARS + factor(SHELF) + O58))

Call:
lm(formula = CALORIES ~ SUGARS + factor(SHELF) + O58)

Residuals:
    Min      1Q  Median      3Q     Max 
-39.749  -8.415   0.918  11.965  34.347 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     88.5316     4.4198  20.031  < 2e-16 ***
SUGARS           2.7619     0.4655   5.933 9.52e-08 ***
factor(SHELF)2  -5.5742     5.5557  -1.003    0.319    
factor(SHELF)3   1.2174     4.6535   0.262    0.794    
O58TRUE         14.2303    16.9061   0.842    0.403    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 16.24 on 72 degrees of freedom
Multiple R-squared: 0.3416,	Adjusted R-squared: 0.305 
F-statistic: 9.337 on 4 and 72 DF,  p-value: 3.894e-06 

> summary(lm(CALORIES ~ SUGARS + factor(SHELF) + factor(SHELF)*SUGARS+ O58))

Call:
lm(formula = CALORIES ~ SUGARS + factor(SHELF) + factor(SHELF) * 
    SUGARS + O58)

Residuals:
      Min        1Q    Median        3Q       Max 
-35.01861  -5.93020  -0.01600   9.14169  29.75349 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            98.3314     4.9146  20.008  < 2e-16 ***
SUGARS                  0.8423     0.7318   1.151 0.253626    
factor(SHELF)2          0.8613     9.2711   0.093 0.926243    
factor(SHELF)3        -24.6802     6.7502  -3.656 0.000491 ***
O58TRUE                 2.5109    14.9629   0.168 0.867217    
SUGARS:factor(SHELF)2   0.2317     1.0506   0.221 0.826073    
SUGARS:factor(SHELF)3   4.3856     0.9548   4.593 1.88e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.92 on 70 degrees of freedom
Multiple R-squared:  0.53,	Adjusted R-squared: 0.4897 
F-statistic: 13.15 on 6 and 70 DF,  p-value: 6.572e-10 

> summary(lm(CALORIES ~ SUGARS + (SHELF==3) + (SHELF==3)*SUGARS+ O58))

Call:
lm(formula = CALORIES ~ SUGARS + (SHELF == 3) + (SHELF == 3) * 
    SUGARS + O58)

Residuals:
     Min       1Q   Median       3Q      Max 
-35.0186  -5.7355  -0.2465   8.8490  29.7535 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            98.1539     4.0495  24.238  < 2e-16 ***
SUGARS                  1.0831     0.4570   2.370 0.020466 *  
SHELF == 3TRUE        -24.5027     6.1082  -4.011 0.000146 ***
O58TRUE                 2.9292    14.4543   0.203 0.839981    
SUGARS:SHELF == 3TRUE   4.1448     0.7591   5.460 6.43e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.75 on 72 degrees of freedom
Multiple R-squared: 0.5279,	Adjusted R-squared: 0.5016 
F-statistic: 20.12 on 4 and 72 DF,  p-value: 3.696e-11 

> draw_picture()
Warning messages:
1: In abline(lm(CALORIES ~ SUGARS + (SHELF == 3) * SUGARS + O58), col = "purple") :
  only using the first two of 5regression coefficients
2: In abline(lm(CALORIES[SHELF == 3] ~ SUGARS[SHELF == 3] + O58[SHELF ==  :
  only using the first two of 3regression coefficients
> draw_picture
function()
{
	# Draw all points, set up plotting field
	plot(CALORIES ~ SUGARS)
	# draw the outlier (Quaker oats)with a different symbol
	points(CALORIES[58] ~ SUGARS[58], col='black', bg='black', pch=25)
	# draw the shelf 1 and shelf 2 cereals with a different color
	points(CALORIES[SHELF==1]  ~ SUGARS[SHELF==1], col='red')
	points(CALORIES[SHELF==2]  ~ SUGARS[SHELF==2], col='blue')
	
	# draw the regression line for the two interesting subpops
	abline(lm(CALORIES ~ SUGARS  + (SHELF==3)*SUGARS +  O58), col='purple')
	abline(lm(CALORIES[SHELF==3] ~ SUGARS[SHELF==3] +  O58[SHELF==3]))

	# Add a key
	legend(0, 160, c("Shelf 1", "Shelf 2", "Shelf 3"), col = c('red','blue','black'), pch=c(21,21,21), title='Key:')
}
> cor(CALORIES , cereal)
     NAME CALORIES    PROTEIN       FAT    SODIUM      FIBER     CARBO    SUGARS      SHELF
[1,]   NA        1 0.01906607 0.4986098 0.3006492 -0.2934128 0.2506809 0.5623403 0.09723437
Warning message:
In cor(CALORIES, cereal) : NAs introduced by coercion
> summary(lm(CALORIES ~ SUGARS))

Call:
lm(formula = CALORIES ~ SUGARS)

Residuals:
     Min       1Q   Median       3Q      Max 
-39.8201  -9.4003   0.4598  12.6449  38.1347 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  89.8201     3.4366  26.137  < 2e-16 ***
SUGARS        2.4650     0.4185   5.889 1.02e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 16.22 on 75 degrees of freedom
Multiple R-squared: 0.3162,	Adjusted R-squared: 0.3071 
F-statistic: 34.69 on 1 and 75 DF,  p-value: 1.025e-07 

> cor(residuals(lm(CALORIES ~ SUGARS)), cereal)
     NAME CALORIES   PROTEIN      FAT   SODIUM      FIBER     CARBO       SUGARS      SHELF
[1,]   NA 0.826906 0.2468911 0.418811 0.294591 -0.2588049 0.5287055 4.920474e-17 0.04928505
Warning message:
In cor(residuals(lm(CALORIES ~ SUGARS)), cereal) :
  NAs introduced by coercion
> summary(lm(CALORIES ~ SUGARS + CARBO))

Call:
lm(formula = CALORIES ~ SUGARS + CARBO)

Residuals:
    Min      1Q  Median      3Q     Max 
-31.304  -8.511  -1.145   5.610  53.191 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  52.2253     7.0655   7.392 1.82e-10 ***
SUGARS        3.1792     0.3699   8.594 9.72e-13 ***
CARBO         2.2368     0.3843   5.821 1.41e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.52 on 74 degrees of freedom
Multiple R-squared: 0.531,	Adjusted R-squared: 0.5183 
F-statistic: 41.89 on 2 and 74 DF,  p-value: 6.822e-13 

> 
> cereal[1,]
       NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
1 100%_Bran       70       4   1    130    10     5      6     3
> summary(lm(CALORIES ~ PROTEIN + FAT + SODIUM + FIBER + CARBO + SUGARS + factor(SHELF)))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + SODIUM + FIBER + CARBO + 
    SUGARS + factor(SHELF))

Residuals:
    Min      1Q  Median      3Q     Max 
-15.459  -3.777  -1.011   2.886  40.640 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    23.517108   6.492319   3.622 0.000558 ***
PROTEIN         5.562041   1.133009   4.909 6.02e-06 ***
FAT             8.520430   1.132547   7.523 1.61e-10 ***
SODIUM          0.001287   0.012950   0.099 0.921116    
FIBER          -1.061850   0.554075  -1.916 0.059513 .  
CARBO           2.837985   0.308606   9.196 1.50e-13 ***
SUGARS          3.302795   0.279079  11.835  < 2e-16 ***
factor(SHELF)2 -2.755322   2.928959  -0.941 0.350180    
factor(SHELF)3 -1.885309   2.565114  -0.735 0.464879    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 8.298 on 68 degrees of freedom
Multiple R-squared: 0.8377,	Adjusted R-squared: 0.8186 
F-statistic: 43.88 on 8 and 68 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS + factor(SHELF)))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS + 
    factor(SHELF))

Residuals:
    Min      1Q  Median      3Q     Max 
-15.625  -3.935  -1.003   2.755  40.660 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     23.4785     6.4340   3.649 0.000507 ***
PROTEIN          5.5610     1.1248   4.944 5.16e-06 ***
FAT              8.5323     1.1181   7.631 9.45e-11 ***
FIBER           -1.0541     0.5446  -1.936 0.057023 .  
CARBO            2.8513     0.2761  10.327 1.22e-15 ***
SUGARS           3.3107     0.2655  12.470  < 2e-16 ***
factor(SHELF)2  -2.8034     2.8680  -0.977 0.331756    
factor(SHELF)3  -1.9232     2.5183  -0.764 0.447662    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 8.238 on 69 degrees of freedom
Multiple R-squared: 0.8377,	Adjusted R-squared: 0.8212 
F-statistic: 50.88 on 7 and 69 DF,  p-value: < 2.2e-16 

> summary(lm(CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS ))

Call:
lm(formula = CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS)

Residuals:
    Min      1Q  Median      3Q     Max 
-14.844  -3.592  -1.051   2.923  41.773 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  21.9038     6.1090   3.586 0.000614 ***
PROTEIN       5.7180     1.1057   5.172 2.06e-06 ***
FAT           8.3883     1.0643   7.881 2.77e-11 ***
FIBER        -1.0867     0.4975  -2.184 0.032234 *  
CARBO         2.8633     0.2663  10.752  < 2e-16 ***
SUGARS        3.2461     0.2550  12.732  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 8.183 on 71 degrees of freedom
Multiple R-squared: 0.8352,	Adjusted R-squared: 0.8236 
F-statistic: 71.98 on 5 and 71 DF,  p-value: < 2.2e-16 

> plot(lm(CALORIES ~ PROTEIN + FAT + FIBER + CARBO + SUGARS ))
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>