Question

In: Statistics and Probability

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

  1. 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 as calories, sugar, fat, and carbohydrates. This nutritional information is displayed on the food’s package.

Calories (C)

Sugar (S)

Fat (F)

Carbohydrates (R)

100

12

0.5

25

130

11

1.5

29

100

1

2

20

130

15

2

31

130

13

1.5

29

120

3

0.5

26

100

2

0

24

120

10

0

29

150

16

1.5

31

110

4

0

25

110

12

1

25

150

15

0

36

160

15

1.5

35

150

12

2

29

150

15

1.5

29

110

6

1

23

190

19

1.5

45

100

3

0

23

120

4

0.5

23

120

11

1.5

28

130

5

0.5

29

  1. Find the equation of a regression line for each pair of variables
  1. Calories, sugar
  1. Calories, carbohydrates

  1. Use the results of the previous exercise to predict each value.
  1. The sugar content of one cup of cereal that has 120 calories.

  1. The carbohydrate content of one cup of cereal that has 120 calories.

  1. Find the multiple regression equations of each form
  1. C=β0+ β1S+ β2F+ β3R

  1. C=a0+a1S+a2R
  1. Use the results from part iii) above, to predict the calories in 1 cup of cereal that has 7 grams of sugar, 0.5 grams of fat, and 31 grams of carbohydrates.

Solutions

Expert Solution

We will be applying the Linear regression model here, it can be done by using the function LINEST(y_value, x_value, TRUE, TRUE) where y_values contain values of Calories here and x_values have sugar values in the first case and carbohydrates in the second.

Select 5 rows and 2 columns and then write the formula in the first cell and after that, press Shift + Ctrl + Enter.    

The equations come out to be -

Sugar = -12.84 + 0.18*Calories      
carbohydrates = 1.07 + 0.21*Calories  

When calories = 120

Sugar = -12.84 + 0.18*120 = -12.84 + 21.6 = 8.76

carbohydrates = 1.07 + 0.21*120 = 1.07 + 25.2 = 26.27

The multiple regression equation comes out to be -

Calories = 12.92908 -0.26828*Sugar + 7.57*Fat + 3.89*carbohydrates  

When fat = 0.5, sugar = 7, carbohydrates = 31

Calories = 12.92908 -0.26828*7+ 7.57*0.5+ 3.89*31

Calories = 12.92908 - 1.87796 + 3.785 + 120.59

Calories = 135.42

orchestra answered 1 year ago
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