Breakfast cereal is a common meal in the Western world that is made from processed grains. Cereal is commonly eaten with warm milk, but can also be eaten with other milk products, such as yoghurt or even plain (Saeedi et al., 2016; Ali & Abizari, 2018). The product has been in existence since before the late 19 th century and its market is highly competitive. As a result, the nutrient content of the products has diverged. As a result, apart from high calorific content, breakfast cereal brands have varying total fat content: saturates, polyunsaturated, and monounsaturated. The objective of this short report is to model the relationship between the total fat content and the calories per serving and use the model to make predictions about breakfast cereals. For uniformity, all measurements were recorded per 100 grams. The table below shows the dataset for ten popular cereal brands and their total fat content and total calorie count per serving.
Table 1 . Dataset for popular breakfast cereals
| Breakfast Cereal | Fat content (g) | Calories per serving |
| Golden Crisp |
1.3 |
390 |
| Frosted Flakes |
1.7 |
369 |
| Honey Smacks |
2.2 |
380 |
| Cocoa Krispies |
2.9 |
389 |
| Corn Flakes |
4 |
357 |
| Honet Nuts |
4.7 |
376 |
| General Mills |
5 |
379 |
| Honey Bunches |
5 |
393 |
| Cap'n Crunch |
5 |
398 |
| Kellogg's Krave |
11 |
397 |
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Building a linear model from the above data set would require two things. First is the set of input. In this case, the independent variable will be the total fat content for each of the ten brands of breakfast cereal. Secondly, there needs to be a dependent variable, which in this case is the calorie content per serving of the breakfast cereal brands.
Given that there is a data set, the first step in creating its linear model would be to find the line of best fit. From the line of best fit, it would be possible to calculate both the slope and y-intercept. Using simple regression, the slope for the line of best fit was established to be 1.8442 while the y-intercept was 374.91. Therefore, the linear model could be represented by the following linear equation:
where y is the calorie content per serving and x is the fat content for the cereal brands
The linear model and the original dataset at plotted in the graph below for comparison.
Figure 1 . Fat content against calories per serving
From the above dataset, it can be observed that the minimum calories per serving allowable with zero fat is 374.91. On the other hand, if a customer desires to have a breakfast cereal with 15g of fat, the linear model predicts that it needs to be paired with 402.573g of calories per serving.
Note, however, that the line of best fit does not closely follow the trend of the original dataset. Therefore, any prediction of interpolation made would have an associated error, that is significantly large. Despite the inaccuracy, the dataset was chosen to demonstrate the primary drawback of linear models: they are accurate only within specific error margins. As a result, if a linear model of the dataset is found to fall short of the line of best fit, other models are available, such as exponential, polynomial, logarithmic, and regression, among others (Halilaj et al., 2018). These models are both linear and non-linear (Perrin, 2017). Furthermore, there are techniques available to linearize the non-linear models if needed.
In conclusion, the objective of this report was to establish a relationship between the total fat content and calorie count per serving of 10 of the most popular breakfast cereal brands in America. Even though a linear model was created, it was concluded that it did not fit the dataset. Therefore, any interpolations and predictions made using the model would be subject to scrutiny as the margin of error for the model is large.
References
Ali, Z., & Abizari, A. R. (2018). Ramadan fasting alters food patterns, dietary diversity and body weight among Ghanaian adolescents. Nutrition journal , 17 (1), 75.
Halilaj, E., Rajagopal, A., Fiterau, M., Hicks, J. L., Hastie, T. J., & Delp, S. L. (2018). Machine learning in human movement biomechanics: best practices, common pitfalls, and new opportunities. Journal of biomechanics , 81 , 1-11.
Perrin, C. L. (2017). Linear or nonlinear least-squares analysis of kinetic data?. Journal of Chemical Education , 94 (6), 669-672.
Saeedi, P., Skeaff, S. A., Wong, J. E., & Skidmore, P. M. (2016). Reproducibility and relative validity of a short food frequency questionnaire in 9–10 year-old children. Nutrients , 8 (5), 271.
