Diet & Health Analysis with Health & Nutrition Survey Data-FINAL PROJECT By Cindy Cisneros Barajas
2025-12-04
Diet & Health Analysis with Health & Nutrition Survey Data
Final Project:
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## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.0.4
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsPART A: LINEAR REGRESSION WITH A SUGAR OUTCOME:
GOAL: is to see how sugar intake is related to diet and demographic variables, and to understand the meaning of a multiple linear regression model
PART A:1 Exploring Your Sugar Target and its Relationship
GOAL:Getting a sense of how sugar density behaves and how it relates to several continuing predictors.
Part A:1:A: Distribution of Sugar Density
#Histogram of sugar density
hist(
dat_core$sugar_den,
main = "Histogram of Sugar Density",
xlab = "Sugar Density"
)
Part A:1:B: Correlations with continuous Predictors
#Selecting continuous variables and remove missing values
cont_vars=dat_core %>%
select(
sugar_den,
fiber_den,
satfat_den,
sodium_den,
age,
INDFMPIR,
DR1TKCAL
) %>%
na.omit()
#Correlation between sugar density and predictors
cor_sugar=cor(cont_vars$sugar_den,
cont_vars %>% select(-sugar_den))
cor_sugar## fiber_den satfat_den sodium_den age INDFMPIR DR1TKCAL
## [1,] -0.06124463 -0.2634305 -0.1794895 0.008018612 -0.1170348 -0.04280339#Correlation matrix from predictors
cor_predictors=cor(cont_vars %>% select(-sugar_den))
round(cor_predictors, 3)## fiber_den satfat_den sodium_den age INDFMPIR DR1TKCAL
## fiber_den 1.000 -0.265 0.006 0.114 0.070 -0.173
## satfat_den -0.265 1.000 -0.001 0.002 0.034 0.152
## sodium_den 0.006 -0.001 1.000 -0.019 0.036 -0.084
## age 0.114 0.002 -0.019 1.000 0.056 -0.145
## INDFMPIR 0.070 0.034 0.036 0.056 1.000 0.018
## DR1TKCAL -0.173 0.152 -0.084 -0.145 0.018 1.000Part A:1:C: Coplot: Sugar Versus one Predictor within Groups
#Conditional plot of sugar density vs saturated fat by income level
coplot(
sugar_den ~ satfat_den | INDFMPIR,
data = dat_core,
xlab = "Saturated Fat Density",
ylab = "Sugar Density"
)##
## Missing rows: 27, 30, 31, 52, 65, 66, 68, 75, 91, 92, 93, 99, 103, 106, 114, 115, 118, 121, 126, 167, 176, 185, 213, 216, 225, 228, 232, 234, 236, 255, 261, 270, 272, 280, 283, 302, 309, 322, 332, 345, 369, 375, 379, 385, 405, 409, 410, 414, 431, 447, 453, 456, 465, 480, 511, 526, 537, 540, 547, 579, 585, 590, 591, 600, 620, 627, 629, 656, 663, 673, 676, 687, 692, 697, 701, 702, 711, 715, 719, 728, 740, 743, 744, 752, 758, 759, 770, 781, 791, 810, 822, 829, 838, 844, 846, 854, 866, 868, 872, 874, 882, 891, 904, 941, 964, 970, 972, 973, 989, 1012, 1014, 1018, 1048, 1049, 1055, 1060, 1066, 1074, 1108, 1121, 1124, 1129, 1139, 1163, 1178, 1180, 1184, 1191, 1193, 1195, 1206, 1225, 1230, 1237, 1243, 1246, 1247, 1249, 1251, 1253, 1262, 1265, 1266, 1283, 1323, 1327, 1366, 1379, 1380, 1381, 1383, 1388, 1393, 1420, 1421, 1425, 1437, 1447, 1453, 1455, 1456, 1459, 1462, 1468, 1477, 1479, 1495, 1502, 1504, 1516, 1538, 1541, 1544, 1557, 1579, 1587, 1593, 1595, 1596, 1603, 1604, 1605, 1626, 1628, 1638, 1639, 1649, 1653, 1661, 1682, 1685, 1691, 1717, 1718, 1729, 1744, 1754, 1767, 1772, 1790, 1794, 1799, 1813, 1836, 1849, 1850, 1853, 1868, 1872, 1875, 1898, 1912, 1913, 1916, 1922, 1926, 1935, 1942, 1943, 1946, 1956, 1958, 1960, 1971, 1980, 1996, 2018, 2028, 2040, 2048, 2053, 2063, 2070, 2076, 2097, 2106, 2108, 2110, 2116, 2119, 2120, 2130, 2135, 2136, 2137, 2138, 2139, 2143, 2144, 2149, 2151, 2168, 2175, 2190, 2192, 2204, 2207, 2224, 2233, 2235, 2244, 2249, 2250, 2252, 2256, 2265, 2269, 2271, 2274, 2282, 2286, 2300, 2308, 2313, 2317, 2326, 2327, 2331, 2336, 2337, 2338, 2350, 2353, 2357, 2377, 2381, 2387, 2388, 2401, 2405, 2417, 2424, 2429, 2432, 2447, 2453, 2468, 2480, 2488, 2489, 2492, 2496, 2497, 2501, 2508, 2514, 2518, 2524, 2527, 2530, 2535, 2548, 2556, 2557, 2567, 2576, 2579, 2593, 2597, 2600, 2606, 2626, 2634, 2645, 2646, 2648, 2658, 2662, 2677, 2684, 2686, 2693, 2715, 2723, 2729, 2732, 2744, 2755, 2757, 2762, 2780, 2781, 2789, 2794, 2798, 2800, 2804, 2809, 2811, 2818, 2827, 2837, 2860, 2861, 2867, 2880, 2897, 2900, 2904, 2907, 2908, 2913, 2916, 2918, 2924, 2940, 2946, 2966, 2971, 2977, 2982, 2984, 2998, 3000, 3009, 3020, 3027, 3031, 3032, 3034, 3047, 3049, 3056, 3074, 3111, 3112, 3143, 3146, 3164, 3166, 3179, 3213, 3214, 3220, 3222, 3241, 3250, 3257, 3262, 3278, 3294, 3304, 3305, 3318, 3341, 3343, 3347, 3349, 3369, 3370, 3372, 3383, 3386, 3388, 3395, 3419, 3424, 3443, 3444, 3452, 3455, 3460, 3467, 3473, 3479, 3484, 3486, 3487, 3488, 3490, 3496, 3500, 3519, 3535, 3547, 3550, 3552, 3563, 3573, 3595, 3598, 3599, 3601, 3617, 3653, 3664, 3668, 3670, 3692, 3697, 3705, 3712, 3732, 3763, 3774, 3775, 3782, 3790, 3791, 3794, 3809, 3812, 3815, 3818, 3819, 3820, 3842, 3845, 3846, 3848, 3880, 3886, 3910, 3912, 3915, 3925, 3927, 3945, 3957, 3962, 3968, 3970, 3974, 3978, 3988, 3990, 4003, 4008, 4026, 4029, 4031, 4040, 4092, 4093, 4100, 4103, 4112, 4146, 4167, 4168, 4169, 4178, 4191, 4193, 4195, 4216, 4222, 4229, 4246, 4260, 4261, 4277, 4278, 4280, 4303, 4307, 4312, 4324, 4333, 4347, 4359, 4363, 4372, 4383, 4415, 4462, 4463, 4470, 4477, 4484, 4486, 4491, 4493, 4501, 4512, 4530, 4540, 4574, 4579, 4591, 4607, 4615, 4622, 4623, 4638, 4640, 4648, 4658, 4665, 4667, 4669, 4675, 4681, 4689title("Sugar Density vs. Saturated Fat Intake by Income Level")
Part A:2: FITTING MULTIPLE LINEAR REGRESSION MODEL:
Part A:2:A:Coplot: Sugar Versus one Predictor within Groups:
GOAL: Use a multiple linear regression model to describe how your Sugar Density outcome changes with several predictors at once
#Multiple linear regression model
model_full=lm(
sugar_den ~ fiber_den + satfat_den + sodium_den +
age + sex + race + INDFMPIR + DR1TKCAL,
data = dat_core
)
model_full##
## Call:
## lm(formula = sugar_den ~ fiber_den + satfat_den + sodium_den +
## age + sex + race + INDFMPIR + DR1TKCAL, data = dat_core)
##
## Coefficients:
## (Intercept)
## 84.0471173
## fiber_den
## -0.6429814
## satfat_den
## -1.7679756
## sodium_den
## -0.0040056
## age
## 0.0188055
## sexFemale
## 3.8716178
## raceOther Hispanic
## 1.7090347
## raceNon-Hispanic White
## 4.0922383
## raceNon-Hispanic Black
## 3.2310434
## raceNon-Hispanic Asian
## -4.5609113
## raceOther Race - Including Multi-Racial
## 4.2503907
## INDFMPIR
## -1.2447684
## DR1TKCAL
## -0.0002689Part A:2:B: The regression Output
#Display of regression summary
summary(model_full)##
## Call:
## lm(formula = sugar_den ~ fiber_den + satfat_den + sodium_den +
## age + sex + race + INDFMPIR + DR1TKCAL, data = dat_core)
##
## Residuals:
## Min 1Q Median 3Q Max
## -90.21 -16.28 -1.45 12.79 243.85
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 84.0471173 2.4796427 33.895 < 2e-16
## fiber_den -0.6429814 0.0875465 -7.344 2.48e-13
## satfat_den -1.7679756 0.0875072 -20.204 < 2e-16
## sodium_den -0.0040056 0.0003418 -11.718 < 2e-16
## age 0.0188055 0.0225105 0.835 0.40354
## sexFemale 3.8716178 0.7973600 4.856 1.25e-06
## raceOther Hispanic 1.7090347 1.6700095 1.023 0.30619
## raceNon-Hispanic White 4.0922383 1.2747591 3.210 0.00134
## raceNon-Hispanic Black 3.2310434 1.3564942 2.382 0.01727
## raceNon-Hispanic Asian -4.5609113 1.5264328 -2.988 0.00283
## raceOther Race - Including Multi-Racial 4.2503907 1.9899648 2.136 0.03275
## INDFMPIR -1.2447684 0.2430188 -5.122 3.16e-07
## DR1TKCAL -0.0002689 0.0003962 -0.679 0.49734
##
## (Intercept) ***
## fiber_den ***
## satfat_den ***
## sodium_den ***
## age
## sexFemale ***
## raceOther Hispanic
## raceNon-Hispanic White **
## raceNon-Hispanic Black *
## raceNon-Hispanic Asian **
## raceOther Race - Including Multi-Racial *
## INDFMPIR ***
## DR1TKCAL
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 24.31 on 4124 degrees of freedom
## (554 observations deleted due to missingness)
## Multiple R-squared: 0.1454, Adjusted R-squared: 0.1429
## F-statistic: 58.49 on 12 and 4124 DF, p-value: < 2.2e-16Part A:2:C:Linking Back To Correlations and Coplots
NOTE: In write Up
Part A:3: HOW WELL DOES THE LINEAR MODEL FIT?:
Part A:3:A R² and adjusted R²
#Extract components used by the model
yhat=fitted(model_full)
res=residuals(model_full)
y=yhat + res
#Compute SSE and SST
SSE=sum(res^2)
SST=sum((y - mean(y))^2)
#R-squared
R2=1 - SSE / SST
R2## [1] 0.1454357#Adjusted R-squared
n=nrow(dat_core)
p=length(coefficients(model_full))
Adjusted_R2= 1 - ((n-1)/(n-p)) * (SSE/SST)
Adjusted_R2## [1] 0.1432435Part A:3:B Residual Standard Error (RSE)
# Compute residual standard error
RSE=sqrt(mean(residuals(model_full)^2))
RSE## [1] 24.26785Part A:3:C Residuals versus fitted values.
#Create dataframe for residual plot
library(ggplot2)
df_res=data.frame(
fitted = fitted(model_full),
residuals = residuals(model_full)
)
#Plot of residuals vs fitted values
ggplot(df_res, aes(x = fitted, y = residuals)) +
geom_point() +
geom_hline(yintercept = 0, color = "pink") +
labs(
title = "Residuals vs Fitted",
x = "Fitted Values",
y = "Residuals"
)
Part B: LOGISTIC REGRESSION WITH OBESITY:
Goal: we treat obesity as a yes/no outcome and use logistic regression to study how obesity is related to sugar measures and other predictors. We will look both at the size and direction of associations and at how well the model classifies individuals as obese or not.
Part B:1: Getting To Know The Obesity Outcome
GOAL: Understand how common obesity is in this sample and how it relates to your sugar outcome.
Part B:1:A. Overall prevalence of obesity
GOAL: Compute the proportion of participants who are obese
(obese = 1) in your analysis dataset.
Express this as a proportion and as a percentage. This gives a baseline:
if we always guessed “not
obese,” how often would we be wrong?
#Remove non obesity values
NUMBER_OF_OBESITY=dat_core %>%
filter(!is.na(obese))
## Percentage Obese
PORPORTION_OBESE=mean(NUMBER_OF_OBESITY$obese == 1)
PORPORTION_OBESE## [1] 0.425922#Percentage Obses
PERCENT_OBESE=PORPORTION_OBESE * 100
PERCENT_OBESE## [1] 42.5922B2: FITTING A LOGISTIC REGRESSION FOR OBESITY:
GOAL: Fit a logistic regression model and interpret the main coefficients in terms of odds and log-odds
Part B:2:A. Fitting a logistic regression model for obesity
Fit a logistic regression model with obese as the target and the following predictors: your chosen sugar outcome, fiber_den, satfat_den, sodium_den, age, sex, race, INDFMPIR, and DR1TKCAL.
#Fit logistic regression model for obesity
logit_model=glm(
obese ~ sugar_den + fiber_den + satfat_den + sodium_den +
age + sex + race + INDFMPIR + DR1TKCAL,
data = dat_core,
family = "binomial"
)Part B:2:B Logistic Regression Output
#Logistic Regression Output
summary(logit_model)##
## Call:
## glm(formula = obese ~ sugar_den + fiber_den + satfat_den + sodium_den +
## age + sex + race + INDFMPIR + DR1TKCAL, family = "binomial",
## data = dat_core)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.191e-01 2.690e-01 -1.186 0.235465
## sugar_den 3.799e-04 1.404e-03 0.271 0.786766
## fiber_den -4.123e-02 8.023e-03 -5.138 2.77e-07
## satfat_den 1.320e-02 7.880e-03 1.675 0.093858
## sodium_den 2.989e-04 6.315e-05 4.733 2.21e-06
## age -1.108e-03 1.931e-03 -0.574 0.566017
## sexFemale 2.537e-01 6.913e-02 3.669 0.000243
## raceOther Hispanic -3.643e-01 1.402e-01 -2.598 0.009372
## raceNon-Hispanic White -3.843e-01 1.068e-01 -3.597 0.000322
## raceNon-Hispanic Black -1.244e-01 1.133e-01 -1.098 0.272248
## raceNon-Hispanic Asian -1.889e+00 1.554e-01 -12.151 < 2e-16
## raceOther Race - Including Multi-Racial -2.162e-01 1.657e-01 -1.305 0.192042
## INDFMPIR 1.328e-02 2.109e-02 0.630 0.528974
## DR1TKCAL -9.031e-06 3.385e-05 -0.267 0.789610
##
## (Intercept)
## sugar_den
## fiber_den ***
## satfat_den .
## sodium_den ***
## age
## sexFemale ***
## raceOther Hispanic **
## raceNon-Hispanic White ***
## raceNon-Hispanic Black
## raceNon-Hispanic Asian ***
## raceOther Race - Including Multi-Racial
## INDFMPIR
## DR1TKCAL
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5643.9 on 4136 degrees of freedom
## Residual deviance: 5320.4 on 4123 degrees of freedom
## (554 observations deleted due to missingness)
## AIC: 5348.4
##
## Number of Fisher Scoring iterations: 4