STAT 101 Statistics

What can we conclude from the researchers’ findings that there is an association between consuming chocolate frequently and lower BMI?  How do we interpret regression models?

Introduction

The aim of this research was to bring into light the various health effects of chocolate that are beneficial. From various different studies, it has been observed that chocolate consumption has significant relationship with lower blood pressure, lower bad cholesterol, improved insulin sensitivity and reductions in the risks of diabetes, heart disease and stroke. This research has put into light that chocolate is helpful in reducing body fat despite of the high calorific content.

The data that has been used to conduct this study has been extracted from a clinical study which had examined the non-cardiac effects of cholesterol-lowering drugs in healthy adults. The information of the variables that are included in the dataset are Body Mass Index (BMI), Frequency of chocolate consumption, Sex and age of the respondents, Frequency of physical activity, depression and some other dietary variables. With the help of the research conducted on this data, the following information has been extracted.

Confounders

A variable which creates an outside influence and changes the effect of the independent variable on the dependent variable is known as a confounding variable or a confounder. This external influence can alter the results of an experimental design. In other words, a confounder is a third variable which explains association of an outcome to an observed exposure. This association can be correct or even incorrect in some cases. With the help of a confounder variable, association between two variables can be established when actually there is no relation. Thus, it can be said that an exposure which is unobserved can be associated with the exposure which is of interest and affects the outcome which is of interest. Hence, confounders are one of the causes for biasness (Best & Kahn, 2016).

The main aim of this research was to establish the effect of chocolate consumption on lower body weight. Thus, age and sex of the participants can be confounder variables. According to the study, it has been observed that the relationship between chocolate consumption and BMI is negative with a significance of 0.008. Thus, it can be said chocolate consumption significantly affects BMI. It can also be observed that with the inclusion of age and sex of the individuals in the model, the significance becomes 0.02. Thus, the significance is increasing and hence they are confounder variables as it is changing the effect of chocolate consumption on BMI.

Education level and BMI

According to different studies, it has been observed that education level affects the BMI of an individual inversely (Golomb, Koperski & White, 2012). With the increase in the education level, the BMI of an individual decreases. In this study, 58.8 percent of the subjects are college graduates. Thus, 58.8 percent of the subjects are high degree holders. Thus, if education is included in the model of predicting BMI, the result will give a much decreased BMI than usual. Thus, the model will be affected with the influence of education level. From this discussion, it can be clearly stated that education have controlled the regression.

Other possible variables that can control the regression model are calorie intake of an individual and activities performed by an individual. More intake of calories is supposed to increase the body weight of an individual and hence the BMI will be increased. Thus, inclusion of this variable in the model is supposed to influence the BMI. Similarly, activity performed by an individual is supposed to keep the BMI of the individual perfect. Thus, a person intaking a lot of calories and burning it by performing some activities should not have any effect in the BMI. Thus, performing activities will also be affecting the model to a great extent.

Chocolate Consumption and BMI

According to study by Golomb, Koperski & White (2012), frequent chocolate consumption leads to lower Body mass index (BMI). This is also helpful in adjusting for the intake of calorie, intake of saturated fat and swinging of moods. Chocolate consumption also helps in reducing depression in people. Chocolate itself contains a lot of calorific value. As the product is rich in chocolate, any individual lacking the desired amount of calorie intake in a day can compensate that with the consumption of chocolate. Thus, the calorie intake can be adjusted by the consumption of chocolates.

On the other hand, there are chocolates which do not have much high calorific values, such as dark chocolates. The chocolates rich in calories are effective in increasing the body weight while the chocolates with low calorific value decreases the body weight. This has resulted in the rise of the debate whether consumption of chocolates is adjustable for calories. According to research study by Golomb, Koperski & White (2012), lower BMI is observed in people consuming more chocolates and higher BMI is observed in people consuming less chocolates. It has been observed that with more consumption of chocolates, the amount of chocolate intake is more but despite of this higher calorie intake, the BMI does not increase. Even in case of performing activities regularly, lower BMI has been observed in people consuming chocolates frequently.

There is no absolute surety among the researchers in identifying the reasons behind this relationship.  According to a study by Farhat et al. (2014), the compounds that are contained in chocolates such as mitochondria which is needed to burn body fat can help to reduce the body weight. A lot of more research has to be done in future to identify the factors that are responsible in reducing the body weight on consumption of chocolates. On the other hand, a lot of researches has to be done in order to understand the relationship between the frequency of consumption of chocolates and body weight. It has also been considered that the healthiest form of chocolates is dark chocolates.

According to a study conducted by Cleveland Clinic, eating of chocolates contributes to a health benefit of 1.5 – 3 ounces per serving. Some studies have shown that consuming chocolates daily is beneficial for health but this is not the exact suggestion. What exactly can be suggested on this regard is still under the study. The highest level of antioxidants is contained in dark chocolates. Thus, dark chocolates are considered as the gold star for health benefits. Milk chocolates contain a very low amount of antioxidants and a much higher amount of sugar. There is no health benefit for white chocolates as it does not contain any cocoa bean in its ingredients. Hence, the chocolate that can be consumed in order to benefit health is dark chocolate and this is only beneficial in reducing the body weight (Yeh et al., 2016).

Regression Analysis

In the first model, only two subjects are involved one is the dependent variable (BMI) and the other is the independent variable (Chocolate consumption frequency). In the second model, there are four subjects included – age, sex and chocolate consumption frequency as independent variables and BMI as dependent variable. In the third model, there are 5 subjects included. They are age, sex, activity and chocolate consumption frequency as independent variables and BMI as dependent variable. In the fourth model, there are 6 subjects included. They are age, sex, activity, calorie and chocolate consumption frequency as independent variables and BMI as dependent variable. In the fifth model, there are 5 subjects included. They are age, sex, saltfat and chocolate consumption frequency as independent variables and BMI as dependent variable. In the sixth model, there are 7 subjects included. They are age, sex, activity, saltfat, CES-D and chocolate consumption frequency as independent variables and BMI as dependent variable. In the seventh model, there are 8 subjects included. They are age, sex, activity, saltfat, fruit and vegetable, CES-D and chocolate consumption frequency as independent variables and BMI as dependent variable. In the last model, there are 10 subjects included. They are age, sex, activity, saltfat, fruit and vegetable, CES-D, calories and chocolate consumption frequency as independent variables and BMI as dependent variable.

All the regression models should be based on the same sample size (n) as regression cannot be done considering different number of samples for different variables. Thus, it is important that all the variables have the same sample size.

Unadjusted Regression Model

• The slope (b) of the regression line in the unadjusted regression model is -0.142.
• The y-intercept (A) can be given by the formula A = M_Y- bM_X = 28 – (-0.142) * 2 = 28.284.
• The equation for the regression line of the unadjusted model is BMI = 28.284 – (0.142 * Frequency of Chocolate Consumption)
• The predicted BMI of a subject who eats chocolate 3 times per week is 28.284 – (0.142 * 3) = 27.858.
• The correlation coefficient (r) between chocolate consumption frequency and BMI can be given by the following formula:

r = b(SD_X/SD_Y) = -0.142(2.5/4.5) = -0.0789

• The proportion of variance explained in the unadjusted model is given by the value of r-square, which is 1%.

Adjusted Model for Age, Sex and Activity

• The regression coefficient for the chocolate consumption frequency considering the adjusted model with the factors age, sex and activity is -0.130. This means that with one unit increase in the frequency of chocolate consumption, the BMI decreases 0.130 times.
• Based on this model, if two subjects were the same sex and age and engaged in the same frequency of vigorous physical activity, but differed by 3 in the number of times they consumed chocolate per week, the BMI will decrease by (0.130 * 3) = 0.39 times for the subject who consumes chocolate three more times in a week.
• For the unadjusted model, the BMI of the subject consuming three more chocolates in a week will decrease (0.142 * 3) = 0.426 times more than the one consuming 3 less chocolates.
• Since there is a negative relation between Chocolate consumption frequency and BMI, thus, it can be said that a person consuming chocolate frequently has a less BMI. From the model in (b), with the adjustments by age, sex and physical activity, it can be seen that the decrease rate of the BMI is less than the unadjusted model. Thus, maintaining all the conditions in the model (b), the decrease in BMI would be less.

Cross-Sectional Studies

It has been observed that eating more chocolates has resulted in lower BMI levels, though any causal relationship has not been identified on this issue. However, it has been understood that there must be some causal issues that has been influencing this result. Chocolates contain antioxidants in a huge amount and this ingredient helps to reduce oxidative stress. These antioxidants have a chance of reducing the inflammation of the body calories. Dark chocolate especially, can be of great help in balancing the hormones which help in the growth of weight. Thus, this can be a causal reason for this relationship between chocolate consumption and BMI (Rose, Koperski & Golomb, 2010).

It has also been observed from the study that consumption of chocolates decreases the depression levels of people. Thus, less depression will enhance the body weight and prevent the body from weight loss.

Designing Experiment

It has been observed that chocolate therapy reduces depression. This in turn helps to increase the body weight. The most appropriate population for this research study can be the people of a community. A sample of the people can be collected from that area and their weights can be recorded before and after chocolate consumption for time gap of 1 month. The rate of increase or decrease in the body weight will give a clear idea of the relationship.

Conclusion

In this study, confounder variables have been introduced as the variable which intervenes in the relationship between a dependent and an independent variable. The relationship between the frequency of chocolate consumption and BMI levels of the individuals have been established. From the relationship it has been observed that chocolate consumption negatively affects BMI. Even with the intervention of the confounding variables identified earlies, the negative effect remains unaltered. Causal relationship between eating of chocolates and lower BMI is not much present. However, regular activities, calorie intake, age, sex, saltfat, CES-D have been supposed to affect the outcome of the relationship between chocolate consumption and BMI. This is not the case here. No matter what the confounding variable is, the relation between chocolate consumption and BMI remained negative. This study has only identified the negative relation between the factors. The causes behind the negative relation has to be established by further study.

References

Best, J. W., & Kahn, J. V. (2016). Research in education. Pearson Education India.

Farhat, G., Al-Dujaili, E., Drummond, S., & Fyfe, L. (2014). Dark chocolate low in polyphenols increases BMI in normal weight and overweight adults (121.3). The FASEB Journal, 28(1 Supplement), 121-3.

Golomb, B. A., Koperski, S., & White, H. L. (2012). Association between more frequent chocolate consumption and lower body mass index. Archives of internal medicine, 172(6), 519-521.

Rose, N., Koperski, S., & Golomb, B. A. (2010). Mood food: chocolate and depressive symptoms in a cross-sectional analysis. Archives of internal medicine, 170(8), 699-703.

Yeh, M. C., Platkin, C., Estrella, P., MacShane, C., & Allinger, D. (2016). Chocolate Consumption and Health Beliefs and its Relation to BMI in College Students. J Obes Weight Loss, 2(004).