Intelligence vs. Brain size
Collection project was designed to teach students how to collect, and organize, describe and document data using Excel lists and graphs. I chose this particular subject to research to further my understanding of the evolution of human species. “Can intelligence and brain size be directly related, and as intelligence increases, what happens to the size of our brains? I conducted my research through the internet by searching for previous, creditable research by someone trained in the field of Anthropology. My hypothesis is that as humans evolve, and intelligence increases, so do the size of the brain. The tools used in this project were the website from which I obtained the information and Microsoft excel which I used to document and chart the data. Using that data I was able to formulate a graph and a mathematical model that could test and support my hypothesis.
The mathematical model formulated from the graphed data will allow future testing to see if the trend still continues, or if the size of a human brain reaches a maximum or minimum. The goal was to chart previous data collected by experts to support my hypothesis as well as predict and test the size of human brains in the future if the trend continued and develop a linear equation to represent the findings. I began by collecting 12 points of data on the average size of human brains at a specific time (years) in history. I recorded the average size of the brain in the year that correlated it. After collecting the data, I plotted the data in Excel and used the best line fit to give me a linear equation/linear regression model to represent my data. See table below: We entered the data is as follows: The independent variable was the number of rubber bands that represented the x-axis. The dependent variable was how far the egg fell, which represented the y-axis. We chose a domain of 0 to 25 because the number of rubber bands we used ranged from 0 bands to 15 bands.
By choosing a domain or an x-axis of this amount, it gives you a graph that allows you to see the line past 15 rubber bands. We went with a range for 0 to 90 inches because according to our data, the maximum number of inches that the egg dropped was 67 inches so in order to get a better picture of the data we extended the y-axis to 90 inches. The linear regression model that fitted our data was D(r) = 3. 948r + 5. 758, with the y-intercept being (0, 5. 758) and m= 3. 948 inches. Interpretation for the data in the context of the study based on our linear regression model, is at zero rubber bands, the egg would fall 5. 758 inches, and with each added rubber band the egg would fall an additional 3. 948 inches. To test this linear regression equation we were given a length of 67 inches.
To mathematically solve for 67 inches to predict the number of rubber bands needed, we solved for (r) as follows: D(r) = 3. 948r + 5. 758 67(r) = 3. 948r + 5. 758 r = 15. 5. What we concluded from our mathematical prediction was that it would take 15. rubber bands to have a successful fall of 67 inches. Because it was not realistic to use 15. 5 rubber bands, we went with 15 instead. This was a realistic prediction because the length that the egg fell was 66 inches, without imposing any damage to the egg and leaving us 1 inch from the original test value of 67 inches. Had we used 16 rubber bands instead, based on our linear regression model which states that for every rubber band added the egg would fall an additional 3. 948 inches it would have left our fall around 69. 48 inches and as a result leaving us more than 2 inches from the original test value of 67 inches.
The reasons for error in the project could be based on several components. The elasticity of the rubber bands varies from band to band which would cause a difference in the length of the fall and a change not resulting in a slope of 3. 948 inches. During the earlier part of the project, for an unknown reason, but not as a result of the test, the egg cracked, resulting in a possible change in the distribution of the weight of the egg and affecting the resulting length of the fall. And furthermore, if our linear regression equation was tested in the future, the results may not be the same if another egg was used due to the mass of every egg varying. In summary, after testing several jumps involving a different number of rubber bands each time and recording the corresponding length of how far the egg fell we had enough data to plot a scatter graph and formulate a linear regression equation that we could test any hypothesis without having to repeat the project itself. Discoveries made during the project was the close comparison in the tested data and the mathematical equation formulated by using excel or a scientific calculator. For example, when we tested 1 rubber band, the egg fell 10. 5 inches.
Using the equation to solve for the answer: D(r) = 3. 948(r) + 5. 758 D(r) = 3. 948(1) + 5. 758 D(r) = 9. 706 inches The experiment itself and the equation formulated from it, although not precise, it is an accurate representation of real outcomes of the amount of stretch in the rubber bands as shown in the comparison model above.
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