Curve Fitting

Practice

practice problem 1

simple-pendulum.txt
In this experiment, simple pendulums of different lengths were constructed and their periods measured. This data set looks linear, but is it really? What effect does length have on the period of a simple pendulum?

solution

practice problem 2

vostok.txt
Snow rarely gets a chance to melt in Antarctica, even in the summer when the sun never sets. In the interior of the continent, the temperature of the air hasn't been above the freezing point of water in any significant way for the last 900,000 years. The snow that falls there accumulates and accumulates and accumulates until it compresses into rock solid ice — up to 4.5 km thick in some regions. Since the snow that falls is originally fluffy with air, the ice that eventually forms still holds remnants of this air — very, very old air. By examining the isotopic composition of the gases in carefully extracted cores of this ice we can learn things about the past climatic conditions on earth. By extension we might also predict some things about the climate of the future. The columns in this data set are as follows:
  1. Age of air (years before present)
  2. Temperature anomaly with respect to the mean recent time value (℃)
  3. Carbon dioxide concentration (ppm)
  4. Dust concentration (ppm)
Source: Adapted from Petit, et al. 1999.

Questions …

  1. CO2
    1. Construct a set of overlapping time series graphs for CO2 concentration and temperature anomaly.
    2. Construct a scatterplot of temperature anomaly vs. CO2 concentration.
    3. How does atmospheric carbon dioxide affect global climate?
    4. What global average temperature deviation might one expect given current atmospheric CO2 levels?
  2. Dust
    1. Construct a set of overlapping time series graphs for dust and temperature anomaly.
    2. Construct a scatterplot of temperature anomaly vs. dust concentration.
    3. How does atmospheric dust affect global climate?
    4. What global average temperature deviation might one expect from exceptionally high levels of atmospheric dust?

solution

  1. Linear
    1. look at it it.


      [magnify]

    2. Substitute
  2. Exponential Approach
    1. Behold


      [magnify]

    2. Extrapolate

practice problem 3

Write something else.

solution

practice problem 4

pizza.txt
An Internet search engine was queried for pizzerias in the area centered on Brooklyn College. The name, phone number, and address were recorded for the first six hits. How is the building number of a pizzeria in Brooklyn affected by the last four digits of its phone number?

solution

 

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