# Equations estimated in the NHANES 2003-2006, using SAS PROC REG

### For cup equivalents of fruits and vegetables:

E ([Fruits and Veg]^{1/2}) = b_{0}+ b_{1}([N_{FG1}P_{1} + N_{FG2}P_{2}+... + N_{FG10}P_{10}]^{1/2})

Cup equivalents of fruits and vegetables were square-root-transformed to approximate normality; N_{FGk} is the usual number of times per day an
individual consumed food group k; P_{k} is the median portion size in fruit and vegetable cup equivalents of group k; and k indexes the ten fruit
and vegetable food groups. We calculated weighted least-squares estimates of the regression coefficients b_{0} and b_{1} in the NHANES
2003-2006 samples, stratifying by sex, and excluding extreme exposure values.

### For cup equivalents of fruits:

E ([Fruits]^{1/2}) = b_{0}+ b_{1}([N_{FG1}P_{1} + N_{FG2}P_{2}]^{1/2})

Cup equivalents of fruits was square-root-transformed to approximate normality; N_{FGk} is the usual number of times per day an individual consumed
food group k; P_{k} is the median portion size in fruit cup equivalents of group k; and k indexes the two fruit food groups: fruit, and 100% fruit
juices. We calculated weighted least-squares estimates of the regression coefficients b_{0} and b_{1} in the NHANES 2003-2006 samples,
stratifying by sex, and excluding extreme exposure values.

### For cup equivalents of vegetables:

E ([Veg]^{1/2}) = b_{0}+ b_{1}([N_{FG3}P_{3} + N_{FG4}P_{4}+... + N_{FG10}P_{10}] ^{1/2})

Cup equivalents of vegetables was square-root-transformed to approximate normality; N_{FGk} is the usual number of times per day an individual
consumed food group k; P_{k} is the median portion size in vegetable cup equivalents of group k; and k indexes the eight vegetable food groups. We
calculated weighted least-squares estimates of the regression coefficients b_{0} and b_{1} in the NHANES 2003-2006 samples, stratifying by
sex, and excluding extreme exposure values.

### For cup equivalents of dairy:

E ([Dairy]^{1/2}) = b_{0}+ b_{1}([N_{FG1}P_{1}+ N_{FG2}P_{2}+...+ N_{FG4}P_{4}] ^{1/2})

Cup equivalents of dairy were square-root-transformed to approximate normality; N_{FGk} is the usual number of times per day an individual consumed
food group k; P_{k} is the median portion size in dairy cup equivalents of group k; and k indexes the four dairy food groups. We calculated
weighted least-squares estimates of the regression coefficients b_{0} and b_{1} on the NHANES 2003-2006 samples, stratifying by sex, and
excluding extreme exposure values.

### For teaspoons of added sugars:

E ([Added Sugars]^{.33}) = b_{0}+ b_{1}([N_{FG1}P_{1}+ N_{FG2}P_{2}+...+ N_{FG13}P_{13}]^{.33})

Teaspoons of added sugars were cube-root-transformed to approximate normality; N_{FGk} is the usual number of times per day that an individual
consumed food group k; P_{k} is the median portion size in added sugars teaspoons of group k; and k indexes the thirteen added sugars food groups.

We calculated weighted least-squares estimates of the regression coefficients b_{0 }and b_{1 }in the NHANES 2003-2006 samples, stratifying
by sex, and excluding extreme exposure values.

### For teaspoons of added sugars from sugar-sweetened beverages:

E ([Added Sugars_{ssb}]^{.5}) = b_{0}+ b_{1}([N_{FG1}P_{1}+ N_{FG2}P_{2}+ N_{FG3}P_{3}]^{.5})

The dependent variable added sugars from sugar-sweetened beverages included the following beverages: sodas, fruitades/sports drinks, and sugar in
coffee/tea. Teaspoons of added sugars were square-root-transformed to approximate normality; N_{FGk} is the usual number of times per day that an
individual consumed food group k; P_{k} is the median portion size in added sugars teaspoons of group k; and k indexes the three sugar-sweetened
beverage food groups.

We calculated weighted least-squares estimates of the regression coefficients b_{0 }and b_{1 }in the NHANES 2003-2006 samples, stratifying
by sex, and excluding extreme exposure values.

### For ounce-equivalents of whole grains:

E ([Whole Grains]^{ 1/2}) = b_{0} + b_{1} (N_{FG1}P_{1}) + b_{2}(N_{FG2}P_{2} ) + ... + b _{9}(N_{FG9}P_{9})^{ }

Ounce-equivalents of whole grains were square-root-transformed to approximate normality; N_{FGk} is the usual number of times per day an individual
consumed food group k; P_{k} is the median portion size in whole grain ounce-equivalents of group k; and k indexes the nine whole grain food
groups: hot cereals (2 groups), cold cereals (4 groups), brown rice, whole grain bread, and popcorn.

We calculated weighted least-squares estimates of the regression coefficients b_{0} and b_{k}, k = 0, ..., 9 on the NHANES 2003-2006 samples,
stratifying by sex, and excluding extreme exposure values.

### For grams of fiber:

E ([Fiber]^{ 1/4}) = b_{0} + b_{1}(N_{FG1}P_{1}) + b_{2}(N_{FG2}P_{2} ) + ... + b_{29}
(N_{FG29}P_{29})^{ }

Grams of fiber were quarter-root-transformed to approximate normality; N_{FGk} is the usual number of times per day an individual consumed food
group k; P_{k} is the median portion size in grams of group k; and k indexes the 28 food groups. Two food groups, tomato sauce, and dried beans,
were frequently consumed in mixed dishes. Because we wanted to represent only the particular food, we estimated the number of grams of tomatoes and
legumes, respectively, in these mixed dishes. For tomato sauce, this was done by multiplying the MPED 1 cup equivalent by 171 (1 MPED = 171 grams). For
legumes, this was done by estimating the MPED one cup equivalent for legumes and multiplying by 212 (1 MPED = 212 grams).

We calculated weighted least-squares estimates of the regression coefficients b_{0} and b_{k}, k = 0,..., 29 on the NHANES 2003-2006
samples, stratifying by sex, and excluding extreme exposure values. We first included all 29 food groups in the regression model. After examining the
results, we dropped food groups that failed to attain statistical significance at α = 0.25 to form more parsimonious final models. In the fiber model, soda
and sugar in coffee/tea were dropped for men, and salad and sugar in coffee/tea were dropped for women.

### For milligrams of calcium:

E ([Calcium]^{ 1/4}) = b_{0} + b_{1} (N_{FG1}P_{1}) + b_{2}(N_{FG2}P_{2} )+ ... + b _{29}(N_{FG29}P_{29})^{ }

Milligrams of calcium were quarter-root-transformed to approximate normality; N_{FGk} is the usual number of times per day an individual consumed
food group k; P_{k} is the median portion size in grams of group k; and k indexes the 29 food groups. Two food groups, tomato sauce, and dried
beans, were frequently consumed in mixed dishes. Because we wanted to represent only the particular food, we estimated the number of grams of tomatoes and
legumes, respectively, in these mixed dishes. For tomato sauce, this was done by multiplying the MPED 1 cup equivalent by 171 (1 MPED = 171 grams). For
legumes, this was done by estimating the MPED one cup equivalent for legumes and multiplying by 212 (1 MPED = 212 grams).

We calculated weighted least-squares estimates of the regression coefficients b_{0} and b_{k}, k = 0, ..., 29 on the NHANES 2003-06 samples,
stratifying by sex, and excluding extreme exposure values. We first included all 29 food groups in the regression model. After examining the results, we
dropped food groups that failed to attain statistical significance at α = 0.25 to form more parsimonious final models. In the calcium model, popcorn, brown
rice, soda, sugar in coffee/tea, and other potatoes were dropped for men; and popcorn, brown rice, fruitades/sports drinks, doughnuts, and tomato sauce
were dropped for women.

Last Modified: 11 Apr 2014