9AB_Activity
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Mathematics
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Apr 3, 2024
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Activity: Linear Models
The spreadsheet 9AB_Activity contains three sets of data, each on a different tab. In this activity, you will plot and analyze the data using linear models.
1.
100-meter dash
This tab has the data on world records in the 100-meter dash, dating back to 1968, for both males and females. Each data point gives the world record time and the year the record was set or matched.
a)
Make a scatter plot with both sets of data on one graph.
b)
Add the trendlines for both sets of data and display the equations on the graph.
c)
Why do you think the female trendline is steeper than the male trendline?
Because they are improving at a faster rate than the males.
d)
According to the trendlines, when will the male and female records be broken? I.e., when will the trendlines be below the current record times?
According to the trendline, the male record of 9.58 will be broken in 2033, assuming the new record would be 9.57 and the female record of 10.49 will be broken in 1993, assuming the new record would be 10.48
e)
According to the trendlines, when will the female record be better than the male record?
According to the trendlines, the female record will be better than the male record in 2029
f)
To answer the previous question, you need to extrapolate from the trendlines. Why could this extrapolation be problematic? I.e., why might your answer to the previous question be wrong? The extrapolation could be problematic because our data do not have a consistent rate of change. The trendline we have is a line of “best fit”, which would give us a rough estimate of the
rate of change.
2.
Global Temperature
This tab has the data for the “temperature anomaly” from 1880 to the present. The “temperature anomaly” is the difference between the current temperature and the average temperature from 1901 to
2000. Positive values of the anomaly mean the temperature is above average, while negative values of the anomaly mean the temperature is below average. The units of temperature are given in degrees Celsius. a)
Make a scatter plot of the data.
b)
Add the trendline. Does the trend appear to be consistent over time? Do you observe shifts in the trend?
The trend appears to be moderately consistent at first but from around the year 2000, the anomalies begin to increase exponentially in relation to past records. The trend shifts here, and the gradient is steeper
c)
Make a new scatter plot, but using only the data from 1964-2020. Add a trendline to this section
of data and display the equation on the graph.
d)
What does the slope mean in this context?
The slope means that the rate of change of anomalies per year is increasing.
e)
In what year do we expect the anomaly to reach 2 degrees? (See this article
for why small changes in temperature matter. In mid-latitudes like New Hampshire, a 2
◦
C global temperature increase would correspond to a regional climate that is about 7
◦
F degrees warmer on average, and with regular extreme heat waves and droughts. There are many more effects discussed in the linked article.)
Using data from 1801 to 2020, an anomaly of 2 is expected to be observed in 2209. Using data from 1964 to 2020, an anomaly of 2 is expected to be observed in 2079.
3.
Political Affiliation
This tab has data on the percentage of voters who identify as Republicans, independents, or democrats from 2004 to 2020. The data comes from surveys done by the Gallup organization in early November of each year.
a)
Plot all three series of data on one graph and add trendlines.
b)
Describe the correlations that you see on the graph.
For Republicans, there is a very weak positive correlation. A very weak positive correlation is also observed in the democrats, almost as weak as the republicans. the independents however have a negative correlation which is slightly stronger in magnitude than both democrats and republicans but is still a weak negative correlation.
c)
Would you feel comfortable using the equations of the lines to predict party affiliation in the upcoming years? Explain why or why not?
I would not feel comfortable using the equations to predict party affiliation in the upcoming years. The equation’s validity relies on a constant rate of change throughout the years, which should be applied to political views, which are liable to change on a whim. Many factors exist that affect this data that simply cannot be represented in this equation. For example, one democratic president might serve a term and not yield satisfactory results, which could possibly result in radical changes in affiliation. Something like this cannot be represented fully by an equation.
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