How Can I Determine the Best Fit Line for My Driving Data?

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In summary, the conversation discusses a driving log from a recent trip to Moncton and the process of finding a linear approximation to represent the data. The conversation also mentions using a mathematical test and entering the data into Excel to find a "treadline." The speakers also bring up the idea of using the approximation to estimate travel time for a different distance.
  • #1
Physics197
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Homework Statement



On a recent trip to Moncton my driving log reads as:
1 hr, 0km
20min, 10km
1hr, 80km
20min, 0km
1hr, 110km
40min, 70km
15min, 10km
a) Plot the distance as a function of time and determine a good linear approximation. (d=at+b)

b) Since there are a number of straight lines that might fit this data, what mathematical test could you think of to determine what might be the "best fit" to the data.

c. Enter into excel and fit a 'treadline' to data.

d. How does the treadline match with my answer.

e) Could you use the approximation to estimate the time required to travel to st John (412km). Explain.

Homework Equations





The Attempt at a Solution


Already have it graphed and given a line of best fit.

Really need help with B

Entered into excel already

Should I compare the slope and y-intercept?

are there toomany variables to include that would make this approximation useless? or could you use it.

Thanks, Just need a steer in the right direction.
 
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  • #2
Please, need help
 

1. What is an approximation?

An approximation is an estimate or a close representation of a value or quantity that is not exact but is close enough for practical purposes. It is often used when the exact value is unknown or difficult to calculate.

2. How are approximations different from exact values?

Approximations are not exact values and may have a certain degree of error or uncertainty. They are used when the exact value is not available or difficult to obtain. Exact values, on the other hand, are precise and do not have any margin of error.

3. What are some examples of approximations in science?

One example of an approximation in science is the use of the ideal gas law in chemistry to estimate the behavior of real gases. Another example is the use of the Hubble constant to estimate the expansion rate of the universe.

4. How are approximations useful in scientific calculations?

Approximations are useful in scientific calculations as they provide a quick and practical way to estimate values that are otherwise difficult to obtain. They also allow scientists to simplify complex problems and make predictions with reasonable accuracy.

5. What are some limitations of using approximations in science?

One limitation of using approximations in science is that they may introduce errors or inaccuracies in calculations. They may also not be applicable in certain scenarios where exact values are required. Additionally, the level of accuracy of an approximation may vary depending on the context and assumptions made.

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