The following data represent nutrition information for breakfast cereals produced by three American manufacturers: General Mills (G), Kellogg (K), and Quaker (Q).

Here is a list of the variables on the dataset:

• Brand of cereal
• Manufacturer = (G, K, or Q)

• X1 = Calories
• X2 = Protein
• X3 = Fat
• X4 = Sodium
• X5 = Fiber
• X6 = Carbohydrates
• X7 = Sugar
• X8 = Potassium

• Group (a numerical identification of manufacturer)

Tasks:

• Fit a linear discriminant function to the manufactuer response (in three levels)
• Explore alternative models and subsets of the variables
• Investigate the assumptions of the discriminant models

Here are the data:

Brand                   Man  X1 X2 X3   X4   X5   X6   X7   X8 Group
ACCheerios               G  110  2  2  180  1.5  10.5  10   70   1
Cheerios                 G  110  6  2  290  2.0  17.0   1  105   1
CocoaPuffs               G  110  1  1  180  0.0  12.0  13   55   1
CountChocula             G  110  1  1  180  0.0  12.0  13   65   1
GoldenGrahams            G  110  1  1  280  0.0  15.0   9   45   1
HoneyNutCheerios         G  110  3  1  250  1.5  11.5  10   90   1
Kix                      G  110  2  1  260  0.0  21.0   3   40   1
LuckyCharms              G  110  2  1  180  0.0  12.0  12   55   1
MultiGrainCheerios       G  100  2  1  220  2.0  15.0   6   90   1
OatmealRaisinCrisp       G  130  3  2  170  1.5  13.5  10  120   1
RaisinNutBran            G  100  3  2  140  2.5  10.5   8  140   1
TotalCornFlakes          G  110  2  1  200  0.0  21.0   3   35   1
TotalRaisinBran          G  140  3  1  190  4.0  15.0  14  230   1
TotalWholeGrain          G  100  3  1  200  3.0  16.0   3  110   1
Trix                     G  110  1  1  140  0.0  13.0  12   25   1
Cheaties                 G  100  3  1  200  3.0  17.0   3  110   1
WheatiesHoneyGold        G  110  2  1  200  1.0  16.0   8   60   1
AllBran                  K   70  4  1  260  9.0   7.0   5  320   2
AppleJacks               K  110  2  0  125  1.0  11.0  14   30   2
CornFlakes               K  100  2  0  290  1.0  21.0   2   35   2
CornPops                 K  110  1  0   90  1.0  13.0  12   20   2
CracklinOatBran          K  110  3  3  140  4.0  10.0   7  160   2
Crispix                  K  110  2  0  220  1.0  21.0   3   30   2
FrootLoops               K  110  2  1  125  1.0  11.0  13   30   2
FrostedFlakes            K  110  1  0  200  1.0  14.0  11   25   2
FrostedMiniWheats        K  100  3  0    0  3.0  14.0   7  100   2
FruitfulBran             K  120  3  0  240  5.0  14.0  12  190   2
JustRightCrunchyNuggets  K  110  2  1  170  1.0  17.0   6   60   2
MueslixCrispyBlend       K  160  3  2  150  3.0  17.0  13  160   2
NutNHoneyCrunch          K  120  2  1  190  0.0  15.0   9   40   2
NutriGrainAlmondRaisin   K  140  3  2  220  3.0  21.0   7  130   2
NutriGrainWheat          K   90  3  0  170  3.0  18.0   2   90   2
Product19                K  100  3  0  320  1.0  20.0   3   45   2
RaisinBran               K  120  3  1  210  5.0  14.0  12  240   2
RiceKrispies             K  110  2  0  290  0.0  22.0   3   35   2
Smacks                   K  110  2  1   70  1.0   9.0  15   40   2
SpecialK                 K  110  6  0  230  1.0  16.0   3   55   2
CapNCrunch               Q  120  1  2  220  0.0  12.0  12   35   3
HoneyGrahamOhs           Q  120  1  2  220  1.0  12.0  11   45   3
Life                     Q  100  4  2  150  2.0  12.0   6   95   3
PuffedRice               Q   50  1  0    0  0.0  13.0   0   15   3
PuffedWheat              Q   50  2  0    0  1.0  10.0   0   50   3
QuakerOatmeal            Q  100  5  2    0  2.7   1.0   1  110   3