Fitting a graph to data points.

In summary, the problem involves finding a function T(d,h) that represents the time taken for a person to walk a certain distance and maximum height difference. The data points provided are used to determine the constants in a function of the form T = ad + bh + c.
  • #1
bon
559
0

Homework Statement



I'm told that someone goes for a walk on some cliffs and given data for the total time of the trip and the distance traveled and the maximum height difference during the walk.

I'm asked to find a function for T(d,h) i.e. time taken as a function of distance and max height.

Data points:

Distance points (feet): 52800, 58080, 73920
Height points (corresponding to the above three - also in feet): 1500, 1300, 1000
Time points: (hours - again, corresponding): 5.4, 7.9, 6.7

Homework Equations


The Attempt at a Solution



I first assumed a simple proportionality like T = k dh and tried to find k but that didnt work..

what kind of proportionality should i be expecting?

Thanks
 
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  • #2
You notation isn't clear. Guessing at what it means, maybe your are suppose to use
dT = k dh.

If that fails, you can always try T(h) = kh + c, where k and c are constants.
or h(T) = kT + c
 
  • #3
Steven Tashi, bon specifically said that "d" is the distance walked, not a differential.

bon, since you are given three data points try something like T= ad+ bh+ c with three constants, a, b, and c. Putting in the data given gives you three equations to solve for a, b, and c.
 

1. What is the purpose of fitting a graph to data points?

Fitting a graph to data points allows us to visualize the relationship between variables and make predictions based on the data. It also helps us identify any patterns or trends that may exist within the data.

2. What methods can be used to fit a graph to data points?

Some common methods for fitting a graph to data points include linear regression, polynomial regression, and exponential regression. Other methods such as moving averages and smoothing techniques can also be used.

3. How do you determine which type of regression to use for fitting a graph?

The type of regression to use depends on the type of relationship between the variables. For example, if the relationship is linear, then linear regression would be appropriate. If the relationship is curved, then polynomial or exponential regression may be more suitable.

4. Can you fit a graph to data points if the data is not perfectly linear or curved?

Yes, it is possible to fit a graph to data points even if the data is not perfectly linear or curved. In some cases, a combination of regression methods or other techniques such as data transformation may be used to better fit the data.

5. How can you determine if the fitted graph accurately represents the data?

To determine the accuracy of a fitted graph, we can use statistical measures such as the coefficient of determination (R2) or the root mean square error (RMSE). These measures provide a quantifiable way to assess the fit between the data and the fitted graph.

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