Tugas Statsos Kelompok 10 eBook

7/31/2019 Tugas Statsos Kelompok 10 eBook

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The U.S. Food and Drug Administration (FDA) requires nutrition labeling for most foods. Under

FDA regulations, manufacturers are required to list the amounts of certain nutrients in their

foods, such are calories, sugar, fat, and carbohydrates. This nutritional information is displayed

in the “Nutrition Facts” panel on the food’s package.

The table shows the following nutritional content for one cup of each of 21 different breakfast

cereals.

C = calories

S = sugar in grams

F = fat in grams

R = carbohydrates in grams

Cereal C S F R

Apple Jack 100 12 0.5 25Berry Burst Cheerios 130 11 1.5 29Cheerios 100 1 2 20Cocoa Puffs 130 15 2 31Cookie Crisp 130 13 1.5 29Corn Chex 120 3 0.5 26Corn Flakes 100 2 0 24Corn Pops 120 10 0 29Count Chocula 150 16 1.5 31Crispix 110 4 0 25Froot Loops 110 12 1 25Frosted Flakes 150 15 0 36Golden Grahams 160 15 1.5 35Honey Nut Cheerios 150 12 2 29Lucky Charms 150 15 1.5 29Multi Grain Cheerios 110 6 1 23Raisin Bran 190 19 1.5 45Rice Krispies 100 3 0 23Special K 120 4 0.5 23Trix 120 11 1.5 28Wheaties 130 5 0.5 29



USING TECHNOLOGY

1. Use a technology tool to draw a scatter plot of the following (x, y ) pairs in the data

set.

(a) (calories, sugar)

(b) (calories, fat)

Calories

200180160140120100

S u g a r ( i n g r a m s )

20

15

10

5

0

Calories

200180160140120100

F a t ( i n

g r a m s )

2.0

1.5

1.0

0.5

0.0



(c) (calories, carbohydrates)

(d) (sugar, fat)

Calories

200180160140120100

C a r b o h y d r a t e ( i n g r a m s )

45

40

35

30

25

20

Sugar (in grams)

20151050

F a t ( i n g r a m s )

2.0

1.5

1.0

0.5

0.0



(e) (sugar, carbohydrates)

(f) (fat, carbohydrates)

2. From the scatter plot in Exercise 1, which pairs of variables appear to have a strong

linear correlation?

Dari scatter plot di atas, dapat diamati pasangan variabel (calories, sugar), (calories,

carbohydrates), dan (sugar, carbohydrates) memiliki korelasi linear yang kuat. Dilihat dari

Sugar (in grams)

20151050

C a r b o h y d r a t e ( i n g r a m s )

45

40

35

30

25

20

Fat (in grams)

2.01.51.00.50.0

C a r

b o h y d r a t e ( i n g r a m s )

45

40

35

30

25

20



bentuk dan persebaran titik pada scatter plot. Hubungan linear yang terbentuk adalah

hubungan positif.

3. Use a technology tool to find the correlation coefficient for each pair of variables in

Exercise 1. Which has the strongest linear correlation?

(a) (calories, sugar), r = 0.766

(b) (calories, fat), r = 0.415

(c) (calories, carbohydrates), r = 0.913

Correlations

1 .766**

.000

21 21

.766** 1

.000

21 21

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Calories

Sugar (in grams)

Calories

Sugar (in

grams)

Correlation is s ignificant a t the 0.01 level (2- tailed).**.

Correlations

1 .415

.061

21 21

.415 1

.061

21 21

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Calories

Fat (in grams)

Calories Fat (in grams)

Correlations

1 .913**.000

21 21

.913** 1

.000

21 21

Pearson CorrelationSig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Calories

Carbohydrate ( in g rams)

Calories

Carbohydrate

(in grams)

Correlation is significant at the 0.01 level (2-tailed).**.



(d) (sugar, fat), r = 0.461

(e) (sugar, carbohydrates), r = 0.793

(f) (fat, carbohydrates), r = 0.230

4. Use a technology tool to find an equation of a regression line for the following

variables.


Correlations

1 .461*

.035

21 21.461* 1

.035

21 21

Pearson Correlation

Sig. (2-tailed)

NPearson Correlation

Sig. (2-tailed)

N

Sugar (in grams)

Fat (in grams)

Sugar (in

grams) Fat ( in grams)

Correlation is s ignificant at the 0.05 level (2-tailed).*.

Corre lations

1 .793**

.000

21 21

.793** 1

.000

21 21

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Sugar ( in grams)

Carbohydrate (in g rams)

Sugar (in

grams)

Carbohydrate

(in grams)

Correlation is significant at the 0.01 level (2-tailed).**.

Correlations

1 .230

.315

21 21

.230 1

.315

21 21

Pears on Correlation

Sig. (2-tailed)

N

Pears on Correlation

Sig. (2-tailed)

N

Carbohydrate (in grams)

Fat (in grams)

Carbohydrate

(in grams) Fat (in grams)

Coefficientsa

-12.836 4.406 -2.914 .009

.177 .034 .766 5.201 .000

(Constant)

Calories

Model1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.

Dependent Variable: Sugar (in grams)a.



Equation,

(b) (calories, carbohydrates)

Equation,

5. Use the results of Exercise 4 to predict the following.

(a) The sugar content of one cup of cereal that has caloric content of 120 calories.

Diketahui:

Ditanyakan:

Jawab:

()

Kandungan gula dalam satu cangkir sereal yang memiliki kandungan kalori sebesar

120 kalori adalah 8.404 gram.

(b) The carbohydrate content of one cup of cereal that has caloric content of 120

calories.

Diketahui:

Ditanyakan:

Jawab:

()

Coefficientsa

1.072 2.840 .377 .710

.213 .022 .913 9.739 .000

(Constant)

Calories

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.

Dependent Variable: Carbohydrate (in grams)a.



Kandungan karbohidrat dalam satu cangkir sereal yang memiliki kandungan kalori

sebesar 120 kalori adalah 26.632 gram.

6. Use a technology tool to find the multiple regression equations of the following

forms.

(a)

Maka persamaannya adalah

(b)


7. Use the equations from Exercise 6 to predict the caloric content of 1 cup of cereal

that has 7 grams of sugar, 0.5 gram of fat, and 31 grams of carbohydrates.

Diketahui:

Ditanyakan:

Jawab:

() () ()

Kandungan kalori dalam satu cangkir sereal yang memiliki kandungan gula sebesar 7

gram, lemak 0.5 gram, dan karbohidrat sebesar 31 gram diprediksikan sebesar 135.3025kalori.

Coefficientsa

12.929 13.543 .955 .353

-.268 .682 -.062 -.393 .699

7.567 3.176 .235 2.382 .029

3.886 .614 .908 6.330 .000

(Constant)

Sugar ( in grams)

Fat (in grams)


Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.

Dependent Var iable: Caloriesa.

Coefficientsa

23.279 14.397 1.617 .123

.496 .676 .114 .734 .4723.518 .667 .822 5.275 .000

(Constant)

Sugar ( in grams)Carbohydrate (in grams)

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.




MANUALLY CALCULATED

1. Use a technology tool to draw a scatter plot of the following (x, y ) pairs in the data

set.


(b) (calories, fat)

(c) (calories, carbohydrates)

y = 0.1767x - 12.836R² = 0.5875

0

5

10

15

20

25

0 50 100 150 200

S u g a r

Calories

y = 0.0129x - 0.6652R² = 0.1723

0

0.5

1

1.5

2

2.5

0 50 100 150 200

F a t

Calories

y = 0.2132x + 1.0716R² = 0.8331

0

5

10

15

20

25

30

35

40

45

50

0 50 100 150 200

C a r b o h y d r a t e s

Calories



(d) (sugar, fat)

(e) (sugar, carbohydrates)

(f) (fat, carbohydrates)

y = 0.062x + 0.3737R² = 0.2129

0

0.5

1

1.5

2

2.5

0 5 10 15 20

F a t

Sugar

y = 0.8038x + 20.477R² = 0.6292

0

510

15

20

25

30

35

40

45

50

0 5 10 15 20


Sugar

y = 1.7361x + 26.591R² = 0.053

0

5

10

15

20

25

30

35

40

45

50

0 0.5 1 1.5 2 2.5


Fat



2. From the scatter plot in Exercise 1, which pairs of variables appear to have a strong

linear correlation?

Dari scatter plot di atas, dapat diamati pasangan variabel (calories, sugar), (calories,

carbohydrates), dan (sugar, carbohydrates) memiliki korelasi linear yang kuat. Dilihat dari

bentuk dan persebaran titik pada scatter plot. Hubungan linear yang terbentuk adalah

hubungan positif.

3. Use a technology tool to find the correlation coefficient for each pair of variables inExercise 1. Which has the strongest linear correlation?

∑ (∑ )(∑ ) ∑ (∑ ) ∑ (∑ )

(a) (b)

() ()()√ () () √ () ()

() ()()√ () () √ () ()

C S xy x 2 y 2

C F xy x 2 y 2

x y x y

100 12 1200 10000 144 100 0.5 50 10000 0.25

130 11 1430 16900 121 130 1.5 195 16900 2.25

100 1 100 10000 1 100 2 200 10000 4

130 15 1950 16900 225 130 2 260 16900 4

130 13 1690 16900 169 130 1.5 195 16900 2.25

120 3 360 14400 9 120 0.5 60 14400 0.25

100 2 200 10000 4 100 0 0 10000 0

120 10 1200 14400 100 120 0 0 14400 0

150 16 2400 22500 256 150 1.5 225 22500 2.25

110 4 440 12100 16 110 0 0 12100 0110 12 1320 12100 144 110 1 110 12100 1

150 15 2250 22500 225 150 0 0 22500 0

160 15 2400 25600 225 160 1.5 240 25600 2.25

150 12 1800 22500 144 150 2 300 22500 4

150 15 2250 22500 225 150 1.5 225 22500 2.25

110 6 660 12100 36 110 1 110 12100 1

190 19 3610 36100 361 190 1.5 285 36100 2.25

100 3 300 10000 9 100 0 0 10000 0

120 4 480 14400 16 120 0.5 60 14400 0.25

120 11 1320 14400 121 120 1.5 180 14400 2.25

130 5 650 16900 25 130 0.5 65 16900 0.25

∑ 2680

∑ 204

∑ 28010

∑ 35320

0

∑ 2576

∑ 2680

∑ 20.5

∑ 2760

∑ 35320

0

∑ 30.75



(c) (d)

() ()()√ () () √ () ()

() ()()√ () () √ () ()

C R xy x 2 y 2

S F xy x 2 y 2

x y x y

100 25 2500 10000 625 12 0.5 6 144 0.25

130 29 3770 16900 841 11 1.5 16.5 121 2.25

100 20 2000 10000 400 1 2 2 1 4

130 31 4030 16900 961 15 2 30 225 4

130 29 3770 16900 841 13 1.5 19.5 169 2.25

120 26 3120 14400 676 3 0.5 1.5 9 0.25

100 24 2400 10000 576 2 0 0 4 0

120 29 3480 14400 841 10 0 0 100 0

150 31 4650 22500 961 16 1.5 24 256 2.25

110 25 2750 12100 625 4 0 0 16 0110 25 2750 12100 625 12 1 12 144 1

150 36 5400 22500 1296 15 0 0 225 0

160 35 5600 25600 1225 15 1.5 22.5 225 2.25

150 29 4350 22500 841 12 2 24 144 4

150 29 4350 22500 841 15 1.5 22.5 225 2.25

110 23 2530 12100 529 6 1 6 36 1

190 45 8550 36100 2025 19 1.5 28.5 361 2.25

100 23 2300 10000 529 3 0 0 9 0

120 23 2760 14400 529 4 0.5 2 16 0.25

120 28 3360 14400 784 11 1.5 16.5 121 2.25

130 29 3770 16900 841 5 0.5 2.5 25 0.25

∑ 2680

∑ 594

∑ 78190

∑ 35320

0

∑ 17412

∑ 204

∑ 20.5

∑ 236

∑ 2576

∑ 30.75



(e) (f)

() ()()√ () () √ () ()

() ()()√ () () √ () ()

S R xy x 2 y 2

F R xy x 2 y 2

x y x y

12 25 300 144 625 0.5 25 12.5 0.25 625

11 29 319 121 841 1.5 29 43.5 2.25 8411 20 20 1 400 2 20 40 4 400

15 31 465 225 961 2 31 62 4 961

13 29 377 169 841 1.5 29 43.5 2.25 841

3 26 78 9 676 0.5 26 13 0.25 676

2 24 48 4 576 0 24 0 0 576

10 29 290 100 841 0 29 0 0 841

16 31 496 256 961 1.5 31 46.5 2.25 961

4 25 100 16 625 0 25 0 0 625

12 25 300 144 625 1 25 25 1 625

15 36 540 225 1296 0 36 0 0 1296

15 35 525 225 1225 1.5 35 52.5 2.25 1225

12 29 348 144 841 2 29 58 4 841

15 29 435 225 841 1.5 29 43.5 2.25 841

6 23 138 36 529 1 23 23 1 529

19 45 855 361 2025 1.5 45 67.5 2.25 2025

3 23 69 9 529 0 23 0 0 529

4 23 92 16 529 0.5 23 11.5 0.25 529

11 28 308 121 784 1.5 28 42 2.25 784

5 29 145 25 841 0.5 29 14.5 0.25 841∑ 204∑ 594

∑ 6248∑ 2576

∑ 17412∑ 20.5

∑ 594∑ 598.5

∑ 30.75∑ 17412



4. Use a technology tool to find an equation of a regression line for the following

variables.


∑ (∑ )(∑ ) ∑ (∑ ) () ()()

() ()

∑ ∑

()

C S xy x 2 y 2

x y

100 12 1200 10000 144130 11 1430 16900 121

100 1 100 10000 1

130 15 1950 16900 225

130 13 1690 16900 169

120 3 360 14400 9

100 2 200 10000 4

120 10 1200 14400 100

150 16 2400 22500 256

110 4 440 12100 16

110 12 1320 12100 144

150 15 2250 22500 225

160 15 2400 25600 225

150 12 1800 22500 144

150 15 2250 22500 225

110 6 660 12100 36

190 19 3610 36100 361

100 3 300 10000 9

120 4 480 14400 16

120 11 1320 14400 121

130 5 650 16900 25

∑ 2680 ∑ 204 ∑ 28010 ∑ 353200 ∑ 2576



(b) (calories, carbohydrates)

∑ (∑ )(∑ ) ∑ (∑ ) () ()()

() ()

∑

∑

()

C R xy x 2 y 2

x y

100 25 2500 10000 625

130 29 3770 16900 841

100 20 2000 10000 400

130 31 4030 16900 961

130 29 3770 16900 841

120 26 3120 14400 676

100 24 2400 10000 576

120 29 3480 14400 841

150 31 4650 22500 961

110 25 2750 12100 625

110 25 2750 12100 625

150 36 5400 22500 1296

160 35 5600 25600 1225150 29 4350 22500 841

150 29 4350 22500 841

110 23 2530 12100 529

190 45 8550 36100 2025

100 23 2300 10000 529

120 23 2760 14400 529

120 28 3360 14400 784

130 29 3770 16900 841

∑ 2680 ∑ 594 ∑ 78190 ∑ 353200 ∑ 17412



5. Use the results of Exercise 4 to predict the following.

(a) The sugar content of one cup of cereal that has caloric content of 120 calories.

Diketahui:

Ditanyakan:

Jawab:

()

Kandungan gula dalam satu cangkir sereal yang memiliki kandungan kalori sebesar

120 kalori adalah 8.404 gram.

(b) The carbohydrate content of one cup of cereal that has caloric content of 120

calories.

Diketahui:

Ditanyakan:

Jawab:

()

Kandungan karbohidrat dalam satu cangkir sereal yang memiliki kandungan kalori

sebesar 120 kalori adalah 26.632 gram.

6. Use a technology tool to find the multiple regression equations of the following

forms. (Perhitungan secara manual sangat rumit sehingga menggunakan teknologi)

(a)


Coefficientsa

12.929 13.543 .955 .353

-.268 .682 -.062 -.393 .699

7.567 3.176 .235 2.382 .029

3.886 .614 .908 6.330 .000

(Constant)

Sugar ( in grams)

Fat (in grams)


Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.




(b)


7. Use the equations from Exercise 6 to predict the caloric content of 1 cup of cereal

that has 7 grams of sugar, 0.5 gram of fat, and 31 grams of carbohydrates.

Diketahui:

Ditanyakan:

Jawab:

() () ()

Kandungan kalori dalam satu cangkir sereal yang memiliki kandungan gula sebesar 7 gram,

lemak 0.5 gram, dan karbohidrat sebesar 31 gram diprediksikan sebesar 135.3025 kalori.

Coefficientsa

23.279 14.397 1.617 .123

.496 .676 .114 .734 .4723.518 .667 .822 5.275 .000

(Constant)

Sugar ( in grams)Carbohydrate ( in grams)

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.


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Tugas Statsos Kelompok 10 eBook