1 Caffeine & Calories in Soda Statistics Anthony W Dick
2 Caffeine & Calories in Soda Description of Experiment Does the caffeine content in soda have anything to do with the calories? This is the question I wish to investigate in this project. I know that caffeine has no calories, so I do not believe that this is an explanatory relationship, but just an association. Because of this, neither variable is explanatory or response, but I will use caffeine as the x variable throughout the experiment. However, because the sodas with caffeine are intended to give energy, I believe that these sodas will also have higher sugar content, but I do not believe this will be a strong association. Data Collection To gather the data, I went to a local Wal-Mart and looked at the labels of caffeinated sodas. There were only 34 to choose from, so I assigned 1 34 to each of them and randomly chose 4 to exclude (with a random number generator). This should eliminate error from sampling method, but will only pertain to the sodas available at Wal-Mart, since this is the only location I went to. Data Presentation I organized the data from high to low values of caffeine, as displayed in figure 1 on page 3. The diet sodas form another group which is distinct from the rest of the sodas, and was a trait that was not considered as I chose the initial sample. Also, similar brands have essentially the same caloric content, so the scatter plot appears almost like a categorical plot. The scatterplot (figure 3, page 5)shows a positive direction, although the slope appears to be close to zero. If the diet sodas are excluded, there seems to be only one possible outlier at (69mg of caffeine, 69 calories); this is identified as Coke Blak. It appears to linear, although almost a horizontal line. It does not appear to be very strong, and with a r-squared value of 0.0136, this is conformed. I decided to take out all the diet sodas and do the same analysis, hoping to establish a stronger relationship; this data table (figure 2, page 4) and graph (figure 4, page 5) showed siginificant change from the initial r-squared value,and also affected the regression line. In the regression line with diet sodas omitted, the r-squared value increased to 0.0244, an increases of almost 79%, and the slope of the regression equation changed from a positive relationship to a negative relationship. The y-intercept also changed. From the scatterplot, the slope is meaningful (or rather the change of slope). Because the caloric content changes only slightly, but the caffeine content was a much wider range, the slope is relatively flat. This adds strength to the argument of a very weak relationship.
3 Figure 1 SODA Caffeine content per 12 oz. (mg) Calories per 12 oz. (mg) Vault 71 174 Jolt Cola 72 150 Mountain Dew MDX, regular 71 180 Coke Blak 69 69 Code Red 54 165 Mountain Dew 54 165 Pepsi One 54 1.5 Mello Yellow 53 177 Diet Coke 47 0 Diet Coke Lime 47 0 TAB 46.5 0 Dr. Pepper 42 150 Dr. Pepper diet 44 0 Pepsi 38 150 Pepsi Lime, regular or diet 38 150 Pepsi Vanilla 37 165 Pepsi Twist 38 165 Pepsi Wild Cherry, regular or diet 38 165 Diet Pepsi 36 0 Pepsi Twist diet 36 0 Coca-Cola Classic 35 145.5 Coke Black Cherry Vanilla, regular or diet 35 150 Pibb XTA 35 156 Coke Cherry, regular 35 156 Coke Lime 35 156 Coke Vanilla 35 157.5 Coke Zero 35 0 Barq's Diet Root Beer 23 0 Barq's Root Beer 23 166.5 Table of specific sodas with their corresponding data (includes diet sodas)
4 Figure 2 SODA Caffeine content per 12 oz. (mg) Calories per 12 oz. (mg) Vault 71 174 Jolt Cola 72 150 Mountain Dew MDX, regular 71 180 Coke Blak 69 69 Code Red 54 165 Mountain Dew 54 165 Mello Yellow 53 177 Dr. Pepper 42 150 Pepsi 38 150 Pepsi Lime, regular or diet 38 150 Pepsi Vanilla 37 165 Pepsi Twist 38 165 Pepsi Wild Cherry, regular or diet 38 165 Coca-Cola Classic 35 145.5 Coke Black Cherry Vanilla, regular or diet 35 150 Pibb XTA 35 156 Coke Cherry, regular 35 156 Coke Lime 35 156 Coke Vanilla 35 157.5 Barq's Root Beer 23 166.5 Table of specific sodas with their corresponding data (omits diet sodas)
Calories per 12 oz. Calories per 12 oz. 5 Figure 3 200 180 160 Calories & Caffeine in Soft Drinks 140 120 100 80 60 y = 0.6573x + 78.448 R² = 0.0136 40 20 0 0 20 40 60 80 Caffeine Content per 12 oz. (mg) Scatterplot of soda data including diet sodas Figure 4 Calories & Caffeine in Soft Drinks (w/o diet sodas) 200 150 100 50 0 y = -0.2367x + 166.37 R² = 0.0244 0 20 40 60 80 Caffeine content per 12 oz (mg) Revised scatterplot of soda data when omitting diet sodas
6 Models Two models were presented as part of my data analysis. The first, with all of the gathered data, gave the average predicted calories in 12oz. of soda to be equal to 78.448 more than the product 0.6573 and the caffeine content (mg) of the same quantity of soda. This regression line had a coefficient of determination of 0.0136. This would have a corresponding r value of +0.1136. This indicates a very weak positive relationship between caffeine content and calories per serving of soda. However, in contrast to the first model, when the diet sodas are omitted, the relationship strengthens slightly, although it is still weak, and it changes from a positive relationship to a negative one. As discussed previously, this indicates that as the calories remain relatively constant, the caffeine content rises across a much broader range of values. The regression line of this second model indicated the average predicted calories in 12oz. of soda to be equal to 166.37 more than the product -0.2367 and the caffeine content (mg) of the same quantity of soda. This has a corresponding r value of -0.1562. This indicates a very weak negative relationship between caffeine content and calories per serving of soda. Predictions In this particular model, a high caffeine prediction would be inappropriate, primarily because by U.S. federal law, a beverage with more than 71 mg of caffeine per 12 oz. serving must be marketed as an energy drink; I confined my data to soft drinks. Taking this into account, for a caffeine level of 180 mg (about the same level in a Rockstar juiced), the first model predicts a calorie content of 196.762 while the second model predicts a calorie content of 123.764; a Rockstar juiced actually has about 165 calories per 12 oz. serving. In the introductory section, no claim of causation was given and upon analysis of the data, none is found. However, I did initially suspect an association, but also found no evidence for that. Error Evaluation Error may have been introduced through the limited sampling method chosen. Only one store was visited, and four of the sodas there were omitted. However, given the data and the homogeneous nature of calorie content among the studied soft drinks, as well as those not studied, I strongly suspect that this would not change the overall conclusions given. Also, when looking at the same sodas online, the calorie, and more so the caffeine content, changed from what was published on the product. This may be another source of error, and may change the specifics, but I do not believe it would change the overall conclusions either. Conclusions As reiterated throughout the paper and by the data itself, I find little association in soft drinks between caffeine content and calories. This would also indicate no causative relationship either.