> summary(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN)) Call: lm(formula = CALORIES ~ SUGARS + FAT + FIBER + PROTEIN) Residuals: Min 1Q Median 3Q Max -35.3305 -8.2901 0.4364 8.3081 33.2686 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 76.7918 5.4020 14.215 < 2e-16 *** SUGARS 2.3543 0.3881 6.066 5.52e-08 *** FAT 5.6355 1.6631 3.389 0.00114 ** FIBER -3.1632 0.7381 -4.286 5.56e-05 *** PROTEIN 5.8509 1.7799 3.287 0.00157 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 13.17 on 72 degrees of freedom Multiple R-squared: 0.567, Adjusted R-squared: 0.5429 F-statistic: 23.57 on 4 and 72 DF, p-value: 1.76e-12 > plot(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN)) Hit to see next plot: Hit to see next plot: Hit to see next plot: Hit to see next plot: > summary(lm(CALORIES ~ SUGARS + (FAT>0))) Call: lm(formula = CALORIES ~ SUGARS + (FAT > 0)) Residuals: Min 1Q Median 3Q Max -38.4018 -8.4018 -0.6899 7.8221 37.0758 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 86.1675 3.6554 23.573 < 2e-16 *** SUGARS 2.0746 0.4364 4.754 9.59e-06 *** FAT > 0TRUE 9.7865 4.0387 2.423 0.0178 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 15.72 on 74 degrees of freedom Multiple R-squared: 0.3665, Adjusted R-squared: 0.3494 F-statistic: 21.41 on 2 and 74 DF, p-value: 4.621e-08 > plot(CALORIES ~ SUGARS) > abline(lm(CALORIES ~ SUGARS + (FAT>0))) Warning message: In abline(lm(CALORIES ~ SUGARS + (FAT > 0))) : only using the first two of 3regression coefficients > abline(lm(CALORIES + 9.8 ~ SUGARS + (FAT>0))) Warning message: In abline(lm(CALORIES + 9.8 ~ SUGARS + (FAT > 0))) : only using the first two of 3regression coefficients > plot(lm(CALORIES ~ SUGARS + (FAT>0))) Hit to see next plot: Hit to see next plot: Hit to see next plot: Hit to see next plot: > summary(lm(CALORIES ~ SUGARS + (FAT>0) + SUGARS*(FAT>0))) Call: lm(formula = CALORIES ~ SUGARS + (FAT > 0) + SUGARS * (FAT > 0)) Residuals: Min 1Q Median 3Q Max -38.4754 -8.4754 -0.7149 7.6818 37.2451 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 85.96550 4.33919 19.811 < 2e-16 *** SUGARS 2.11757 0.65721 3.222 0.00190 ** FAT > 0TRUE 10.27028 6.84463 1.500 0.13780 SUGARS:FAT > 0TRUE -0.07764 0.88372 -0.088 0.93023 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 15.82 on 73 degrees of freedom Multiple R-squared: 0.3666, Adjusted R-squared: 0.3405 F-statistic: 14.08 on 3 and 73 DF, p-value: 2.466e-07 > SUGARS*(FAT>0) [1] 6 8 5 0 8 10 0 8 6 0 12 1 9 7 13 0 0 0 13 7 0 0 10 0 13 0 0 10 0 12 0 9 5 [34] 0 4 11 10 0 6 9 3 6 12 3 11 11 13 6 9 7 0 10 14 0 0 0 6 -1 12 8 0 0 0 0 0 0 [67] 15 0 0 3 14 3 3 12 3 3 8 > summary(lm(CALORIES ~ SUGARS + (FAT>0))) Call: lm(formula = CALORIES ~ SUGARS + (FAT > 0)) Residuals: Min 1Q Median 3Q Max -38.4018 -8.4018 -0.6899 7.8221 37.0758 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 86.1675 3.6554 23.573 < 2e-16 *** SUGARS 2.0746 0.4364 4.754 9.59e-06 *** FAT > 0TRUE 9.7865 4.0387 2.423 0.0178 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 15.72 on 74 degrees of freedom Multiple R-squared: 0.3665, Adjusted R-squared: 0.3494 F-statistic: 21.41 on 2 and 74 DF, p-value: 4.621e-08 > summary(lm(CALORIES ~ SUGARS + FAT)) Call: lm(formula = CALORIES ~ SUGARS + FAT) Residuals: Min 1Q Median 3Q Max -35.5623 -7.0534 0.2883 9.7544 33.6903 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 85.5623 3.2792 26.092 < 2e-16 *** SUGARS 2.0213 0.3941 5.129 2.26e-06 *** FAT 7.2349 1.7406 4.157 8.58e-05 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 14.7 on 74 degrees of freedom Multiple R-squared: 0.4457, Adjusted R-squared: 0.4307 F-statistic: 29.75 on 2 and 74 DF, p-value: 3.31e-10 > summary(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN)) Call: lm(formula = CALORIES ~ SUGARS + FAT + FIBER + PROTEIN) Residuals: Min 1Q Median 3Q Max -35.3305 -8.2901 0.4364 8.3081 33.2686 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 76.7918 5.4020 14.215 < 2e-16 *** SUGARS 2.3543 0.3881 6.066 5.52e-08 *** FAT 5.6355 1.6631 3.389 0.00114 ** FIBER -3.1632 0.7381 -4.286 5.56e-05 *** PROTEIN 5.8509 1.7799 3.287 0.00157 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 13.17 on 72 degrees of freedom Multiple R-squared: 0.567, Adjusted R-squared: 0.5429 F-statistic: 23.57 on 4 and 72 DF, p-value: 1.76e-12 > plot(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN)) Hit to see next plot: Hit to see next plot: Hit to see next plot: Hit to see next plot: > cereal[55:56,] NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF 55 Puffed_Rice 50 1 0 0 0 13 0 3 56 Puffed_Wheat 50 2 0 0 1 10 0 3 > cereal[50:60,] NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF 50 Nutri-Grain_Almond-Raisin 140 3 2 220 3.0 21.0 7 3 51 Nutri-grain_Wheat 90 3 0 170 3.0 18.0 2 3 52 Oatmeal_Raisin_Crisp 130 3 2 170 1.5 13.5 10 3 53 Post_Nat._Raisin_Bran 120 3 1 200 6.0 11.0 14 3 54 Product_19 100 3 0 320 1.0 20.0 3 3 55 Puffed_Rice 50 1 0 0 0.0 13.0 0 3 56 Puffed_Wheat 50 2 0 0 1.0 10.0 0 3 57 Quaker_Oat_Squares 100 4 1 135 2.0 14.0 6 3 58 Quaker_Oatmeal 100 5 2 0 2.7 -1.0 -1 1 59 Raisin_Bran 120 3 1 210 5.0 14.0 12 2 60 Raisin_Nut_Bran 100 3 2 140 2.5 10.5 8 3 > O55=(NAME==NAME[55]) > O55 [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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE [65] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE > O56=(NAME==NAME[56]) > summary(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN + O55 + O56)) Call: lm(formula = CALORIES ~ SUGARS + FAT + FIBER + PROTEIN + O55 + O56) Residuals: Min 1Q Median 3Q Max -22.098 -7.614 -1.221 4.859 36.054 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 85.1815 5.2158 16.331 < 2e-16 *** SUGARS 1.8700 0.3650 5.123 2.54e-06 *** FAT 5.4825 1.4917 3.675 0.000462 *** FIBER -3.2701 0.6621 -4.939 5.14e-06 *** PROTEIN 4.4333 1.6327 2.715 0.008334 ** O55TRUE -39.6147 12.4867 -3.173 0.002244 ** O56TRUE -40.7779 12.2303 -3.334 0.001371 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 11.81 on 70 degrees of freedom Multiple R-squared: 0.6617, Adjusted R-squared: 0.6327 F-statistic: 22.82 on 6 and 70 DF, p-value: 1.004e-14 > PUFFED = O55 | O56 > summary(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN + O55 + O56)) Call: lm(formula = CALORIES ~ SUGARS + FAT + FIBER + PROTEIN + O55 + O56) Residuals: Min 1Q Median 3Q Max -22.098 -7.614 -1.221 4.859 36.054 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 85.1815 5.2158 16.331 < 2e-16 *** SUGARS 1.8700 0.3650 5.123 2.54e-06 *** FAT 5.4825 1.4917 3.675 0.000462 *** FIBER -3.2701 0.6621 -4.939 5.14e-06 *** PROTEIN 4.4333 1.6327 2.715 0.008334 ** O55TRUE -39.6147 12.4867 -3.173 0.002244 ** O56TRUE -40.7779 12.2303 -3.334 0.001371 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 11.81 on 70 degrees of freedom Multiple R-squared: 0.6617, Adjusted R-squared: 0.6327 F-statistic: 22.82 on 6 and 70 DF, p-value: 1.004e-14 > summary(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN + PUFFED)) Call: lm(formula = CALORIES ~ SUGARS + FAT + FIBER + PROTEIN + PUFFED) Residuals: Min 1Q Median 3Q Max -22.092 -7.603 -1.224 4.851 36.060 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 85.2078 5.1654 16.496 < 2e-16 *** SUGARS 1.8690 0.3622 5.160 2.15e-06 *** FAT 5.4853 1.4807 3.705 0.000416 *** FIBER -3.2698 0.6574 -4.974 4.41e-06 *** PROTEIN 4.4244 1.6162 2.737 0.007819 ** PUFFEDTRUE -40.2095 9.0179 -4.459 3.02e-05 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 11.72 on 71 degrees of freedom Multiple R-squared: 0.6617, Adjusted R-squared: 0.6379 F-statistic: 27.77 on 5 and 71 DF, p-value: 1.798e-15 > plot(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN + PUFFED)) Hit to see next plot: Hit to see next plot: Hit to see next plot: Hit to see next plot: > cereal[40:50,] NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF 40 Just_Right_Fruit_&_Nut 140 3 1 170 2 20 9 3 41 Kix 110 2 1 260 0 21 3 2 42 Life 100 4 2 150 2 12 6 2 43 Lucky_Charms 110 2 1 180 0 12 12 2 44 Maypo 100 4 1 0 0 16 3 2 45 Muesli_Raisins,_Dates,_&_Almonds 150 4 3 95 3 16 11 3 46 Muesli_Raisins,_Peaches,_&_Pecans 150 4 3 150 3 16 11 3 47 Mueslix_Crispy_Blend 160 3 2 150 3 17 13 3 48 Multi-Grain_Cheerios 100 2 1 220 2 15 6 1 49 Nut&Honey_Crunch 120 2 1 190 0 15 9 2 50 Nutri-Grain_Almond-Raisin 140 3 2 220 3 21 7 3 > summary(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN + CARBO)) Call: lm(formula = CALORIES ~ SUGARS + FAT + FIBER + PROTEIN + CARBO) 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 *** SUGARS 3.2461 0.2550 12.732 < 2e-16 *** FAT 8.3883 1.0643 7.881 2.77e-11 *** FIBER -1.0867 0.4975 -2.184 0.032234 * PROTEIN 5.7180 1.1057 5.172 2.06e-06 *** CARBO 2.8633 0.2663 10.752 < 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 ~ SUGARS + FAT + FIBER + PROTEIN + CARBO)) Hit to see next plot: Hit to see next plot: Hit to see next plot: Hit to see next plot: > O58=(NAME==NAME[58]) > plot(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN + CARBO + O58)) Hit to see next plot: Hit to see next plot: Hit to see next plot: Hit 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 + FIBER + PROTEIN + CARBO + O58)) Call: lm(formula = CALORIES ~ SUGARS + FAT + FIBER + PROTEIN + CARBO + 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 *** FIBER 0.2501 0.3277 0.763 0.448 PROTEIN 3.8860 0.6963 5.581 4.23e-07 *** CARBO 4.1446 0.2005 20.675 < 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 ~ 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 to see next plot: Hit to see next plot: Hit to see next plot: Hit to see next plot: Warning messages: 1: Not plotting observations with leverage one: 58 2: Not plotting observations with leverage one: 58 > cereal NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF 1 100%_Bran 70 4 1 130 10.0 5.0 6 3 2 100%_Natural_Bran 120 3 5 15 2.0 8.0 8 3 3 All-Bran 70 4 1 260 9.0 7.0 5 3 4 All-Bran_with_Extra_Fiber 50 4 0 140 14.0 8.0 0 3 5 Almond_Delight 110 2 2 200 1.0 14.0 8 3 6 Apple_Cinnamon_Cheerios 110 2 2 180 1.5 10.5 10 1 7 Apple_Jacks 110 2 0 125 1.0 11.0 14 2 8 Basic_4 130 3 2 210 2.0 18.0 8 3 9 Bran_Chex 90 2 1 200 4.0 15.0 6 1 10 Bran_Flakes 90 3 0 210 5.0 13.0 5 3 11 Cap'n'Crunch 120 1 2 220 0.0 12.0 12 2 12 Cheerios 110 6 2 290 2.0 17.0 1 1 13 Cinnamon_Toast_Crunch 120 1 3 210 0.0 13.0 9 2 14 Clusters 110 3 2 140 2.0 13.0 7 3 15 Cocoa_Puffs 110 1 1 180 0.0 12.0 13 2 16 Corn_Chex 110 2 0 280 0.0 22.0 3 1 17 Corn_Flakes 100 2 0 290 1.0 21.0 2 1 18 Corn_Pops 110 1 0 90 1.0 13.0 12 2 19 Count_Chocula 110 1 1 180 0.0 12.0 13 2 20 Cracklin'_Oat_Bran 110 3 3 140 4.0 10.0 7 3 21 Cream_of_Wheat_(Quick) 100 3 0 80 1.0 21.0 0 2 22 Crispix 110 2 0 220 1.0 21.0 3 3 23 Crispy_Wheat_&_Raisins 100 2 1 140 2.0 11.0 10 3 24 Double_Chex 100 2 0 190 1.0 18.0 5 3 25 Froot_Loops 110 2 1 125 1.0 11.0 13 2 26 Frosted_Flakes 110 1 0 200 1.0 14.0 11 1 27 Frosted_Mini-Wheats 100 3 0 0 3.0 14.0 7 2 28 Fruit_&_Fibre_Dates,_Walnuts,_and_Oats 120 3 2 160 5.0 12.0 10 3 29 Fruitful_Bran 120 3 0 240 5.0 14.0 12 3 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 41 Kix 110 2 1 260 0.0 21.0 3 2 42 Life 100 4 2 150 2.0 12.0 6 2 43 Lucky_Charms 110 2 1 180 0.0 12.0 12 2 44 Maypo 100 4 1 0 0.0 16.0 3 2 45 Muesli_Raisins,_Dates,_&_Almonds 150 4 3 95 3.0 16.0 11 3 46 Muesli_Raisins,_Peaches,_&_Pecans 150 4 3 150 3.0 16.0 11 3 47 Mueslix_Crispy_Blend 160 3 2 150 3.0 17.0 13 3 48 Multi-Grain_Cheerios 100 2 1 220 2.0 15.0 6 1 49 Nut&Honey_Crunch 120 2 1 190 0.0 15.0 9 2 50 Nutri-Grain_Almond-Raisin 140 3 2 220 3.0 21.0 7 3 51 Nutri-grain_Wheat 90 3 0 170 3.0 18.0 2 3 52 Oatmeal_Raisin_Crisp 130 3 2 170 1.5 13.5 10 3 53 Post_Nat._Raisin_Bran 120 3 1 200 6.0 11.0 14 3 54 Product_19 100 3 0 320 1.0 20.0 3 3 55 Puffed_Rice 50 1 0 0 0.0 13.0 0 3 56 Puffed_Wheat 50 2 0 0 1.0 10.0 0 3 57 Quaker_Oat_Squares 100 4 1 135 2.0 14.0 6 3 58 Quaker_Oatmeal 100 5 2 0 2.7 -1.0 -1 1 59 Raisin_Bran 120 3 1 210 5.0 14.0 12 2 60 Raisin_Nut_Bran 100 3 2 140 2.5 10.5 8 3 61 Raisin_Squares 90 2 0 0 2.0 15.0 6 3 62 Rice_Chex 110 1 0 240 0.0 23.0 2 1 63 Rice_Krispies 110 2 0 290 0.0 22.0 3 1 64 Shredded_Wheat 80 2 0 0 3.0 16.0 0 1 65 Shredded_Wheat_'n'Bran 90 3 0 0 4.0 19.0 0 1 66 Shredded_Wheat_spoon_size 90 3 0 0 3.0 20.0 0 1 67 Smacks 110 2 1 70 1.0 9.0 15 2 68 Special_K 110 6 0 230 1.0 16.0 3 1 69 Strawberry_Fruit_Wheats 90 2 0 15 3.0 15.0 5 2 70 Total_Corn_Flakes 110 2 1 200 0.0 21.0 3 3 71 Total_Raisin_Bran 140 3 1 190 4.0 15.0 14 3 72 Total_Whole_Grain 100 3 1 200 3.0 16.0 3 3 73 Triples 110 2 1 250 0.0 21.0 3 3 74 Trix 110 1 1 140 0.0 13.0 12 2 75 Wheat_Chex 100 3 1 230 3.0 17.0 3 1 76 Wheaties 100 3 1 200 3.0 17.0 3 1 77 Wheaties_Honey_Gold 110 2 1 200 1.0 16.0 8 1 > 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 >